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    [{"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" : 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: "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" : 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["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" : 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"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" : 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["IsSearchTable"]},{"name" : "IsVectorSearchTable","type" : "GAP_Category","implied" : ["IsSearchTable","IsVectorSearchTable"]},{"name" : "IsIntegers","type" : "GAP_Category","implied" : 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["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" 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["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" : 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"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" : 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"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" : 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"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" : 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["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" : 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"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" : 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"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" : 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["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" : 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["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" : 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["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" : 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"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" : 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: "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" : 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: "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" : 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"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" : 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[["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 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[["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" : 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[["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 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[["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" : 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[[["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" : 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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" : 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[["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: 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[["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" : 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"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" : 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[["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 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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" : 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[["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" : 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[["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" : 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[],"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" : 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[],"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" : 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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" : 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: 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" : 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