diff --git a/gap/gaptypes.json b/gap/gaptypes.json
index 506cfe545a5397aeeab6a4f9439b8c08508dce20..b3433d0aae143708ff43e9097180d5a71fba4711 100644
--- a/gap/gaptypes.json
+++ b/gap/gaptypes.json
@@ -1,433702 +1 @@
-[
- {
- "implied": [],
- "name": "IsObject",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_MUTABLE_OBJ",
- "IsMutable"
- ],
- "implied": [
- "IsMutable",
- "IsCopyable"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/object.gd",
- "line": 217
- },
- "name": "IsMutable",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_COPYABLE_OBJ",
- "IsCopyable"
- ],
- "implied": [
- "IsCopyable"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/object.gd",
- "line": 183
- },
- "name": "IsCopyable",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_FUNCTION",
- "IsFunction"
- ],
- "implied": [
- "IsFunction"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/function.g",
- "line": 42
- },
- "name": "IsFunction",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_OPERATION",
- "IsOperation"
- ],
- "implied": [
- "IsFunction",
- "IsOperation"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/function.g",
- "line": 75
- },
- "name": "IsOperation",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_INT",
- "IsInt"
- ],
- "implied": [
- "IsInt",
- "IsRat",
- "IsCyc",
- "IsExtAElement",
- "IsNearAdditiveElement",
- "IsNearAdditiveElementWithZero",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsMultiplicativeElement",
- "IsMultiplicativeElementWithOne",
- "IsMultiplicativeElementWithInverse",
- "IsZDFRE",
- "IsAssociativeElement",
- "IsAdditivelyCommutativeElement",
- "IsCommutativeElement",
- "IsCyclotomic"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/cyclotom.g",
- "line": 124
- },
- "name": "IsInt",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_RAT",
- "IsRat"
- ],
- "implied": [
- "IsRat",
- "IsCyc",
- "IsExtAElement",
- "IsNearAdditiveElement",
- "IsNearAdditiveElementWithZero",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsMultiplicativeElement",
- "IsMultiplicativeElementWithOne",
- "IsMultiplicativeElementWithInverse",
- "IsZDFRE",
- "IsAssociativeElement",
- "IsAdditivelyCommutativeElement",
- "IsCommutativeElement",
- "IsCyclotomic"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/cyclotom.g",
- "line": 106
- },
- "name": "IsRat",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_CYC",
- "IsCyc"
- ],
- "implied": [
- "IsCyc",
- "IsExtAElement",
- "IsNearAdditiveElement",
- "IsNearAdditiveElementWithZero",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsMultiplicativeElement",
- "IsMultiplicativeElementWithOne",
- "IsMultiplicativeElementWithInverse",
- "IsZDFRE",
- "IsAssociativeElement",
- "IsAdditivelyCommutativeElement",
- "IsCommutativeElement",
- "IsCyclotomic"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/cyclotom.g",
- "line": 56
- },
- "name": "IsCyc",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_FFE",
- "IsFFE"
- ],
- "implied": [
- "IsFFE",
- "IsExtAElement",
- "IsNearAdditiveElement",
- "IsNearAdditiveElementWithZero",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsMultiplicativeElement",
- "IsMultiplicativeElementWithOne",
- "IsMultiplicativeElementWithInverse",
- "IsZDFRE",
- "IsAssociativeElement",
- "IsAdditivelyCommutativeElement",
- "IsCommutativeElement"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/ffe.gd",
- "line": 223
- },
- "name": "IsFFE",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_PERM",
- "IsPerm"
- ],
- "implied": [
- "IsPerm",
- "IsExtLElement",
- "IsExtRElement",
- "IsMultiplicativeElement",
- "IsMultiplicativeElementWithOne",
- "IsMultiplicativeElementWithInverse",
- "IsAssociativeElement",
- "IsFiniteOrderElement"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/permutat.g",
- "line": 92
- },
- "name": "IsPerm",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_TRANS",
- "IsTransformation"
- ],
- "implied": [
- "IsTransformation",
- "IsExtLElement",
- "IsExtRElement",
- "IsMultiplicativeElement",
- "IsMultiplicativeElementWithOne",
- "IsMultiplicativeElementWithInverse",
- "IsAssociativeElement"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/trans.g",
- "line": 4
- },
- "name": "IsTransformation",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_PPERM",
- "IsPartialPerm"
- ],
- "implied": [
- "IsPartialPerm",
- "IsExtLElement",
- "IsExtRElement",
- "IsMultiplicativeElement",
- "IsMultiplicativeElementWithOne",
- "IsMultiplicativeElementWithInverse",
- "IsAssociativeElement"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/pperm.g",
- "line": 3
- },
- "name": "IsPartialPerm",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_BOOL",
- "IsBool"
- ],
- "implied": [
- "IsBool"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/boolean.g",
- "line": 35
- },
- "name": "IsBool",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_ATOMIC_RECORD",
- "IS_REC",
- "IsRecord"
- ],
- "implied": [
- "IsRecord"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/record.g",
- "line": 50
- },
- "name": "IsRecord",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_LIST",
- "IsList"
- ],
- "implied": [
- "IsList",
- "IsListOrCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 35
- },
- "name": "IsList",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_DENSE_LIST",
- "IsDenseList"
- ],
- "implied": [
- "IsList",
- "IsDenseList",
- "IsListOrCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 376
- },
- "name": "IsDenseList",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_HOMOG_LIST",
- "IsHomogeneousList"
- ],
- "implied": [
- "IsList",
- "IsDenseList",
- "IsHomogeneousList",
- "IsListOrCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 410
- },
- "name": "IsHomogeneousList",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_TABLE_LIST",
- "IsTable"
- ],
- "implied": [
- "IsList",
- "IsDenseList",
- "IsHomogeneousList",
- "IsTable",
- "IsListOrCollection",
- "IsCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 598
- },
- "name": "IsTable",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "HasIsSSortedList"
- ],
- "implied": [
- "Tester(IS_SSORT_LIST)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 503
- },
- "name": "Tester(IS_SSORT_LIST)",
- "type": "GAP_TrueProperty"
- },
- {
- "aka": [
- "HasIsNSortedList"
- ],
- "implied": [
- "Tester(IS_NSORT_LIST)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 516
- },
- "name": "Tester(IS_NSORT_LIST)",
- "type": "GAP_TrueProperty"
- },
- {
- "aka": [
- "HasIsPositionsList"
- ],
- "implied": [
- "Tester(IS_POSS_LIST)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 569
- },
- "name": "Tester(IS_POSS_LIST)",
- "type": "GAP_TrueProperty"
- },
- {
- "aka": [
- "IS_PLIST_REP",
- "IsPlistRep"
- ],
- "implied": [
- "Tester(LENGTH)",
- "IsPlistRep",
- "IsInternalRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.gd",
- "line": 64
- },
- "name": "IsPlistRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IS_BLIST",
- "IsBlist"
- ],
- "implied": [
- "IsList",
- "IsDenseList",
- "IsHomogeneousList",
- "IsBlist",
- "IsListOrCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.g",
- "line": 744
- },
- "name": "IsBlist",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_BLIST_REP",
- "IsBlistRep"
- ],
- "implied": [
- "IsBlistRep",
- "IsInternalRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.g",
- "line": 784
- },
- "name": "IsBlistRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IS_RANGE",
- "IsRange"
- ],
- "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)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.g",
- "line": 528
- },
- "name": "IsRange",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_RANGE_REP",
- "IsRangeRep"
- ],
- "implied": [
- "IsRangeRep",
- "IsInternalRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/list.g",
- "line": 545
- },
- "name": "IsRangeRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IS_STRING",
- "IsString"
- ],
- "implied": [
- "IsList",
- "IsDenseList",
- "IsHomogeneousList",
- "IsString",
- "IsListOrCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/string.g",
- "line": 102
- },
- "name": "IsString",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IS_STRING_REP",
- "IsStringRep"
- ],
- "implied": [
- "IsStringRep",
- "IsInternalRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/string.g",
- "line": 127
- },
- "name": "IsStringRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsWPObj",
- "IsWeakPointerObject"
- ],
- "implied": [
- "IsList",
- "IsWeakPointerObject",
- "IsListOrCollection",
- "IsFinite",
- "Tester(IsFinite)",
- "IsSmallList",
- "Tester(IsSmallList)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/wpobj.gd",
- "line": 59
- },
- "name": "IsWeakPointerObject",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsNoImmediateMethodsObject"
- ],
- "implied": [
- "IsNoImmediateMethodsObject"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/oper.g",
- "line": 193
- },
- "name": "IsNoImmediateMethodsObject",
- "type": "GAP_Filter"
- },
- {
- "aka": [
- "IsInternalRep"
- ],
- "implied": [
- "IsInternalRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 320
- },
- "name": "IsInternalRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsPositionalObjectRep"
- ],
- "implied": [
- "IsPositionalObjectRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 321
- },
- "name": "IsPositionalObjectRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsComponentObjectRep"
- ],
- "implied": [
- "IsComponentObjectRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 322
- },
- "name": "IsComponentObjectRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsDataObjectRep"
- ],
- "implied": [
- "IsDataObjectRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 323
- },
- "name": "IsDataObjectRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsNonAtomicComponentObjectRep"
- ],
- "implied": [
- "IsComponentObjectRep",
- "IsNonAtomicComponentObjectRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 326
- },
- "name": "IsNonAtomicComponentObjectRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsReadOnlyPositionalObjectRep"
- ],
- "implied": [
- "IsPositionalObjectRep",
- "IsReadOnlyPositionalObjectRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 328
- },
- "name": "IsReadOnlyPositionalObjectRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsAtomicPositionalObjectRep"
- ],
- "implied": [
- "IsPositionalObjectRep",
- "IsAtomicPositionalObjectRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 330
- },
- "name": "IsAtomicPositionalObjectRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsAttributeStoringRep"
- ],
- "implied": [
- "IsComponentObjectRep",
- "IsAttributeStoringRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 354
- },
- "name": "IsAttributeStoringRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsFamily"
- ],
- "implied": [
- "IsFamily"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 363
- },
- "name": "IsFamily",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsType"
- ],
- "implied": [
- "IsType"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 364
- },
- "name": "IsType",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsFamilyOfFamilies"
- ],
- "implied": [
- "IsFamily",
- "IsFamilyOfFamilies"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 365
- },
- "name": "IsFamilyOfFamilies",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsFamilyOfTypes"
- ],
- "implied": [
- "IsFamily",
- "IsFamilyOfTypes"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 366
- },
- "name": "IsFamilyOfTypes",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsFamilyDefaultRep"
- ],
- "implied": [
- "IsComponentObjectRep",
- "IsFamilyDefaultRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 373
- },
- "name": "IsFamilyDefaultRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsTypeDefaultRep"
- ],
- "implied": [
- "IsPositionalObjectRep",
- "IsTypeDefaultRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/type.g",
- "line": 377
- },
- "name": "IsTypeDefaultRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsPackedElementDefaultRep"
- ],
- "implied": [
- "IsPositionalObjectRep",
- "IsPackedElementDefaultRep"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/object.gd",
- "line": 824
- },
- "name": "IsPackedElementDefaultRep",
- "type": "GAP_Representation"
- },
- {
- "aka": [
- "IsToBeDefinedObj"
- ],
- "implied": [
- "IsToBeDefinedObj"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/variable.g",
- "line": 24
- },
- "name": "IsToBeDefinedObj",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsLVarsBag"
- ],
- "implied": [
- "IsLVarsBag"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/variable.g",
- "line": 258
- },
- "name": "IsLVarsBag",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsListOrCollection"
- ],
- "implied": [
- "IsListOrCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 66
- },
- "name": "IsListOrCollection",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsCollection"
- ],
- "implied": [
- "IsListOrCollection",
- "IsCollection"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 90
- },
- "name": "IsCollection",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsCollectionFamily"
- ],
- "implied": [
- "IsFamily",
- "CategoryFamily(IsCollection)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 143
- },
- "name": "CategoryFamily(IsCollection)",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "IsStandardIterator"
- ],
- "implied": [
- "IsStandardIterator"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1132
- },
- "name": "IsStandardIterator",
- "type": "GAP_Filter"
- },
- {
- "aka": [
- "IsIterator"
- ],
- "implied": [
- "IsIterator"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1175
- },
- "name": "IsIterator",
- "type": "GAP_Category"
- },
- {
- "aka": [
- "HasIsEmpty"
- ],
- "implied": [
- "Tester(IsEmpty)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1344
- },
- "name": "Tester(IsEmpty)",
- "type": "GAP_TrueProperty"
- },
- {
- "aka": [
- "HasIsTrivial"
- ],
- "implied": [
- "Tester(IsTrivial)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1363
- },
- "name": "Tester(IsTrivial)",
- "type": "GAP_TrueProperty"
- },
- {
- "aka": [
- "HasIsNonTrivial"
- ],
- "implied": [
- "Tester(IsNonTrivial)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1404
- },
- "name": "Tester(IsNonTrivial)",
- "type": "GAP_TrueProperty"
- },
- {
- "aka": [
- "HasIsFinite"
- ],
- "implied": [
- "Tester(IsFinite)"
- ],
- "location": {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1430
- },
- "name": "Tester(IsFinite)",
- "type": "GAP_TrueProperty"
- },
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- "Tester(IsAdditivelyCommutative)",
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- "Tester(Dimension)"
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- "rank": 41
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- "Tester(GeneratorsOfLeftOperatorRingWithOne)"
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- "rank": 40
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- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
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- "rank": 39
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- {
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- [
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- "IsDistributiveLOpDSum",
- "IsMagma",
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- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
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- "IsFreeLeftModule",
- "Tester(Dimension)"
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- "rank": 39
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- {
- "comment": "ViewObj: for an algebra with known dimension",
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- [
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- "IsAssociativeLOpEProd",
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- "rank": 38
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- "rank": 38
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- "comment": "ViewObj: for an algebra with known generators",
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- "rank": 37
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- "IsLDistributive",
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- "rank": 37
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- {
- "comment": "ViewObj: for an algebra",
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- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
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- "rank": 36
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- {
- "comment": "ViewObj: for a FLMLOR with known dimension",
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- [
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- "IsDistributiveLOpDSum",
- "IsMagma",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
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- "rank": 36
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- {
- "comment": "ViewObj: for a character",
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- [
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- "IsCharacter",
- "Tester(IsCharacter)"
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- "rank": 35
- },
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- [
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- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
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- "Tester(GeneratorsOfLeftOperatorRing)"
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- "rank": 35
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- "comment": "ViewObj: for a group",
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- [
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- "rank": 35
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- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
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- "IsMagma",
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- "IsAdditivelyCommutative",
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- "IsLDistributive",
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- "IsBlockMatrixRep"
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- "rank": 34
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- "Tester(IsZ_pi)"
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- [
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- "IsFinite",
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- "rank": 32
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- [
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- [
- "IsNullMapMatrix"
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- [
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- "Tester(GeneratorsOfRingWithOne)"
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- "rank": 30
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- [
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- [
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- "rank": 29
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- {
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- [
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- "Tester(IsRightSemigroupCongruence)"
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- "rank": 29
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- {
- "comment": "ViewObj: for a LeftSemigroupCongruence with known generating pairs",
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- [
- "Tester(GeneratingPairsOfMagmaCongruence)",
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- "Tester(IsLeftSemigroupCongruence)"
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- "rank": 29
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- {
- "comment": "ViewObj: For a compressed MatFFE",
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- [
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- "Tester(IsSmallList)",
- "Is8BitMatrixRep"
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- "rank": 28
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- {
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- [
- "IsHomogeneousList",
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- "rank": 28
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- {
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- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
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- "Tester(IsLeftActedOnByDivisionRing)",
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- "rank": 27
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- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
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- "IsDistributiveLOpESum",
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- "IsLeftActedOnByDivisionRing",
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- "IsNearAdditiveMagma",
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- "Tester(Dimension)"
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- "rank": 27
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- {
- "comment": "ViewObj: for a ring with known generators",
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- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRing)"
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- "rank": 27
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- {
- "comment": "ViewObj: for a magma congruence with generating pairs",
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- [
- "IsMagmaCongruence",
- "Tester(GeneratingPairsOfMagmaCongruence)"
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- ],
- "rank": 27
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- {
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- [
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- ],
- "rank": 27
- },
- {
- "comment": "ViewObj: for a LeftMagmaCongruence with known generating pairs",
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- [
- "IsLeftMagmaCongruence",
- "Tester(GeneratingPairsOfMagmaCongruence)"
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- ],
- "rank": 27
- },
- {
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- [
- "IsList",
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- "IsDuplicateFree",
- "Tester(IsDuplicateFree)",
- "IsEnumeratorByFunctionsRep"
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- "rank": 27
- },
- {
- "comment": "ViewObj: for vector space with known generators",
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- [
- "IsExtLSet",
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- "IsDistributiveLOpDSum",
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- "Tester(IsLeftActedOnByDivisionRing)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
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- "rank": 26
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- {
- "comment": "ViewObj: for a ring",
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- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
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- "rank": 26
- },
- {
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- [
- "IsMagmaCongruence"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "ViewObj: for a fp monoid with generators",
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- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsMagmaWithOne",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsElementOfFpMonoid)"
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- ],
- "rank": 25
- },
- {
- "comment": "ViewObj: for a free monoid containing the whole family",
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- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections((IsWord and IsAssociativeElement))"
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- ],
- "rank": 25
- },
- {
- "comment": "ViewObj: for an algebra g.m.b.i",
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- [
- "IsGeneralMapping",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "ViewObj: for vector space",
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- [
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- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
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- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
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- ],
- "rank": 25
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- {
- "comment": "ViewObj: pcgs",
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- [
- "IsPcgs",
- "IsPcgsDefaultRep"
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- ],
- "rank": 24
- },
- {
- "comment": "ViewObj: For a compressed VecFFE",
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- [
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- "Tester(IsSmallList)",
- "Is8BitVectorRep"
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- ],
- "rank": 24
- },
- {
- "comment": "ViewObj: for free left module with known generators",
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- [
- "IsFreeLeftModule",
- "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ViewObj: for free left module with known dimension",
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- [
- "IsFreeLeftModule",
- "Tester(Dimension)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ViewObj: for a RightSemigrouCongruence",
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- [
- "IsRightSemigroupCongruence",
- "Tester(IsRightSemigroupCongruence)"
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- ],
- "rank": 24
- },
- {
- "comment": "ViewObj: for a LeftSemigroupCongruence",
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- [
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- "Tester(IsLeftSemigroupCongruence)"
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- ],
- "rank": 24
- },
- {
- "comment": "ViewObj: for saturated Fitting formation",
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- [
- "IsGroupClass",
- "Tester(IsGroupClass)",
- "ContainsTrivialGroup",
- "Tester(ContainsTrivialGroup)",
- "IsNormalSubgroupClosed",
- "Tester(IsNormalSubgroupClosed)",
- "IsQuotientClosed",
- "Tester(IsQuotientClosed)",
- "IsResiduallyClosed",
- "Tester(IsResiduallyClosed)",
- "IsNormalProductClosed",
- "Tester(IsNormalProductClosed)",
- "IsSaturated",
- "Tester(IsSaturated)",
- "IsClassByPropertyRep"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for GreensHRelation",
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- [
- "IsGreensHRelation"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for GreensDRelation",
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- [
- "IsGreensDRelation"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for GreensJRelation",
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- [
- "IsGreensJRelation"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for embedding into wreath product",
- "filters": [
- [
- "IsEmbeddingWreathProductPermGroup"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for projection from subdirect product",
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- [
- "IsProjectionSubdirectProductPermGroup"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for projection from a direct product",
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- [
- "IsProjectionDirectProductPermGroup"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for embedding into direct product",
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- [
- "IsEmbeddingDirectProductPermGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for nat. hom. of pc group",
- "filters": [
- [
- "IsNaturalHomomorphismPcGroupRep"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for conjugator isomorphism",
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- [
- "IsConjugatorIsomorphism",
- "Tester(IsConjugatorIsomorphism)"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for an ring g.m.b.i",
- "filters": [
- [
- "IsGeneralMapping",
- "IsRingGeneralMappingByImagesDefaultRep"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for a left module m.b.m.",
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- [
- "IsGeneralMapping",
- "IsLinearMappingByMatrixDefaultRep"
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- "rank": 23
- },
- {
- "comment": "ViewObj: for a left module g.m.b.i",
- "filters": [
- [
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- "IsLinearGeneralMappingByImagesDefaultRep"
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- "rank": 23
- },
- {
- "comment": "ViewObj: for free left module",
- "filters": [
- [
- "IsFreeLeftModule"
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- ],
- "rank": 23
- },
- {
- "comment": "ViewObj: for a zero group",
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- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsMagmaWithZeroAdjoined"
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- "rank": 23
- },
- {
- "comment": "ViewObj: for an iterator that perhaps has its own `ViewObj' function",
- "filters": [
- [
- "IsIterator",
- "IsIteratorByFunctionsRep"
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- "rank": 23
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- {
- "comment": "ViewObj: for a Brauer table",
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- [
- "IsBrauerTable"
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- "rank": 22
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- [
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- [
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- {
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- [
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- {
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- [
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- [
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- [
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- [
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- "Tester(IsGroupClass)",
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- {
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- [
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- "rank": 19
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- {
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- [
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- [
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- [
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- {
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- [
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- {
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- [
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- "Tester(IsFinite)",
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- "rank": 19
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- {
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- [
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- "Tester(IsFinite)",
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- [
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- [
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- [
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- {
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- [
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- [
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- "rank": 14
- },
- {
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- [
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- {
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- "rank": 14
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- "rank": 13
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- {
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- "rank": 12
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- {
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- "rank": 12
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- "rank": 11
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- "rank": 11
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- "rank": 10
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- {
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- "rank": 10
- },
- {
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- [
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- "rank": 10
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- "rank": 10
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- {
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- [
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- ],
- "rank": 9
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- {
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- [
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- ],
- "rank": 9
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- {
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- "rank": 9
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- {
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- [
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- ],
- "rank": 9
- },
- {
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- ],
- "rank": 9
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- {
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- "rank": 9
- },
- {
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- "Tester(IsFinite)"
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- "rank": 8
- },
- {
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- "Tester(BasisVectors)"
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- "rank": 8
- },
- {
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- [
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- "Tester(IsFinite)"
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- "rank": 8
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- {
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- [
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- "rank": 8
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- {
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- [
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- "rank": 7
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- {
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- "rank": 7
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- {
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- [
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- "rank": 7
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- {
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- "rank": 7
- },
- {
- "comment": "ViewObj: for a basis",
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- [
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- "rank": 7
- },
- {
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- [
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- "rank": 7
- },
- {
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- [
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- "rank": 6
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- {
- "comment": "ViewObj: for residue class unions (ResClasses)",
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- "rank": 6
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- {
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- "rank": 6
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- {
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- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ]
- ],
- "rank": 43
- },
- {
- "comment": "=: for Frobenius automorphism and identity mapping",
- "filters": [
- [
- "IsFrobeniusAutomorphism"
- ],
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ]
- ],
- "rank": 43
- },
- {
- "comment": "=: for identity mapping and Frobenius automorphism",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ],
- [
- "IsFrobeniusAutomorphism"
- ]
- ],
- "rank": 43
- },
- {
- "comment": "=: for eqivalence relations",
- "filters": [
- [
- "IsEquivalenceRelation",
- "Tester(IsEquivalenceRelation)"
- ],
- [
- "IsEquivalenceRelation",
- "Tester(IsEquivalenceRelation)"
- ]
- ],
- "rank": 42
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,one,scal. mult.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ]
- ],
- "rank": 42
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsUnicodeCharacter"
- ],
- [
- "IsUnicodeCharacter"
- ]
- ],
- "rank": 40
- },
- {
- "comment": "=: for two underlying relations of general mappings",
- "filters": [
- [
- "IsCollection",
- "IsGeneralizedDomain",
- "CategoryCollections(IsDirectProductElement)",
- "Tester(UnderlyingGeneralMapping)"
- ],
- [
- "IsCollection",
- "IsGeneralizedDomain",
- "CategoryCollections(IsDirectProductElement)",
- "Tester(UnderlyingGeneralMapping)"
- ]
- ],
- "rank": 40
- },
- {
- "comment": "=: homomorphism by images with homomorphism: compare generator images",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)",
- "IsGroupGeneralMappingByImages"
- ],
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ]
- ],
- "rank": 39
- },
- {
- "comment": "=: homomorphism with general mapping: test b=a",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)",
- "IsGroupGeneralMappingByImages"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "=: for ring ring general mapping and ring g.m.b.i.",
- "filters": [
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "IsRingGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "=: for ring g.m.b.i. and ring general mapping",
- "filters": [
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "IsRingGeneralMappingByImagesDefaultRep"
- ],
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,scal. mult.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect mult.,one,add.,add.inv.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "=: for two unknowns in default representation",
- "filters": [
- [
- "IsUnknown",
- "IsUnknownDefaultRep"
- ],
- [
- "IsUnknown",
- "IsUnknownDefaultRep"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "=: for internal FFE and element in Z/pZ (ModulusRep)",
- "filters": [
- [
- "IsFFE",
- "IsInternalRep"
- ],
- [
- "IsFFE",
- "IsZmodnZObj",
- "IsModulusRep"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "=: for element in Z/pZ (ModulusRep) and internal FFE",
- "filters": [
- [
- "IsFFE",
- "IsZmodnZObj",
- "IsModulusRep"
- ],
- [
- "IsFFE",
- "IsInternalRep"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "=: for semigroup homomorphism by images",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "IsSemigroupHomomorphismByImagesRep"
- ],
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "IsSemigroupHomomorphismByImagesRep"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsFFE",
- "IsCoeffsModConwayPolRep"
- ],
- [
- "IsFFE",
- "IsCoeffsModConwayPolRep"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: BFElm=BFElm",
- "filters": [
- [
- "IsAlgBFRep"
- ],
- [
- "IsAlgBFRep"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: BFElm<AlgElm",
- "filters": [
- [
- "IsAlgBFRep"
- ],
- [
- "IsKroneckerConstRep"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: AlgElm=BFElm",
- "filters": [
- [
- "IsKroneckerConstRep"
- ],
- [
- "IsAlgBFRep"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: AlgElm=AlgElm",
- "filters": [
- [
- "IsKroneckerConstRep"
- ],
- [
- "IsKroneckerConstRep"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: laurent",
- "filters": [
- [
- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ],
- [
- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,scal. mult.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect mult.,add.,add.inv.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "=: for a list and a class function",
- "filters": [
- [
- "IsList"
- ],
- [
- "IsClassFunction"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "=: for a class function and a list",
- "filters": [
- [
- "IsClassFunction"
- ],
- [
- "IsList"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "=: IsTransformationRepOfEndo, IsTransformationRepOfEndo",
- "filters": [
- [
- "IsGeneralMapping",
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsTransformationRepOfEndo"
- ],
- [
- "IsGeneralMapping",
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsTransformationRepOfEndo"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "=: RightCosets",
- "filters": [
- [
- "IsRightCoset"
- ],
- [
- "IsRightCoset"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsFFE",
- "IsCoeffsModConwayPolRep"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsFFE",
- "IsCoeffsModConwayPolRep"
- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "=: for two elements in Z/nZ (ModulusRep)",
- "filters": [
- [
- "IsZmodnZObj",
- "IsModulusRep"
- ],
- [
- "IsZmodnZObj",
- "IsModulusRep"
- ]
- ],
- "rank": 32
- },
- {
- "aka": [
- "IsProtected",
- "IsReadOnly",
- "RETURN_FALSE",
- "ReturnFalse"
- ],
- "comment": "=: for cyclotomic and unknown",
- "filters": [
- [
- "IsCyc"
- ],
- [
- "IsUnknown"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "=: for unknown and cyclotomic",
- "filters": [
- [
- "IsUnknown"
- ],
- [
- "IsCyc"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "=: for semigroup with generators and semigroup with generators",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ],
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "=: for `-infinity' and cyclotomic",
- "filters": [
- [
- "IsNegInfinity"
- ],
- [
- "IsCyclotomic"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "=: for cyclotomic and `-infinity'",
- "filters": [
- [
- "IsCyclotomic"
- ],
- [
- "IsNegInfinity"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "=: for `infinity' and cyclotomic",
- "filters": [
- [
- "IsInfinity"
- ],
- [
- "IsCyclotomic"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "=: for cyclotomic and `infinity'",
- "filters": [
- [
- "IsCyclotomic"
- ],
- [
- "IsInfinity"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "=: for two plist matrices",
- "filters": [
- [
- "IsPlistMatrixRep"
- ],
- [
- "IsPlistMatrixRep"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "=: univariate = univariate",
- "filters": [
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ],
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect add. and add. inv.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect mult. and inv.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "=: for two direct product elements",
- "filters": [
- [
- "IsDirectProductElement"
- ],
- [
- "IsDirectProductElement"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "=: for a collection, and an empty row vector in the same family",
- "filters": [
- [
- "IsCollection"
- ],
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "=: for an empty row vector, and a collection in the same family",
- "filters": [
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 30
- },
- {
- "aka": [
- "COMPARE_FLOAT_ANY"
- ],
- "comment": "=: for float and rational",
- "filters": [
- [
- "IsFloat"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "=: for rational and float",
- "filters": [
- [
- "IsRat"
- ],
- [
- "IsFloat"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "=: IsEndoMapping, IsTransformationRepOfEndo",
- "filters": [
- [
- "IsGeneralMapping",
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ],
- [
- "IsGeneralMapping",
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsTransformationRepOfEndo"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "=: IsTransformationRepOfEndo, IsEndoMapping",
- "filters": [
- [
- "IsGeneralMapping",
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsTransformationRepOfEndo"
- ],
- [
- "IsGeneralMapping",
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsPadicExtensionNumber"
- ],
- [
- "IsPadicExtensionNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsPurePadicNumber"
- ],
- [
- "IsPurePadicNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "=: polynomial",
- "filters": [
- [
- "IsPolynomial",
- "Tester(IsPolynomial)"
- ],
- [
- "IsPolynomial",
- "Tester(IsPolynomial)"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "=: for additive group and additive coset",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ],
- [
- "IsAdditiveCoset"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "=: for additive coset and additive group",
- "filters": [
- [
- "IsAdditiveCoset"
- ],
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "=: classes for perm group",
- "filters": [
- [
- "IsConjugacyClassPermGroupRep"
- ],
- [
- "IsConjugacyClassPermGroupRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: compare source generator images",
- "filters": [
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
- "filters": [
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ],
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: rational functions",
- "filters": [
- [
- "IsRationalFunction"
- ],
- [
- "IsRationalFunction"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: for s. c. ring elements in dense vector rep.",
- "filters": [
- [
- "IsSCRingObj",
- "IsDenseCoeffVectorRep"
- ],
- [
- "IsSCRingObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: for two Lie objects in default representation",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: for s. c. algebra elements in dense vector rep.",
- "filters": [
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ],
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect add. and zero",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsZero",
- "Tester(RespectsZero)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsZero",
- "Tester(RespectsZero)"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect mult. and one",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "=: for floats",
- "filters": [
- [
- "IsFloat"
- ],
- [
- "IsFloat"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "=: FElm=BFElm",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsAlgBFRep"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "=: BFElm=FElm",
- "filters": [
- [
- "IsAlgBFRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "=: FElm=AlgElm",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsKroneckerConstRep"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "=: AlgElm=FElm",
- "filters": [
- [
- "IsKroneckerConstRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsRationalClassPermGroupRep"
- ],
- [
- "IsRationalClassPermGroupRep"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "=: xorbs which know their size",
- "filters": [
- [
- "Tester(Size)",
- "IsExternalOrbit"
- ],
- [
- "Tester(Size)",
- "IsExternalOrbit"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "=: for two UEALattice elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsUEALatticeElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsUEALatticeElement"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "=: for two additive cosets",
- "filters": [
- [
- "IsAdditiveCoset"
- ],
- [
- "IsAdditiveCoset"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "=: for binary relss over [1..n] with images list",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsConjugacyClassSubgroupsRep"
- ],
- [
- "IsConjugacyClassSubgroupsRep"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsRationalClassGroupRep"
- ],
- [
- "IsRationalClassGroupRep"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: xorbs with canonicalRepresentativeDeterminator",
- "filters": [
- [
- "IsExternalOrbit",
- "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
- ],
- [
- "IsExternalOrbit",
- "Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: for two plist vectors",
- "filters": [
- [
- "IsPlistVectorRep"
- ],
- [
- "IsPlistVectorRep"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: for s. c. algebra elements",
- "filters": [
- [
- "IsSCAlgebraObj"
- ],
- [
- "IsSCAlgebraObj"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: for two normalized f.p. algebra elements",
- "filters": [
- [
- "IsElementOfFpAlgebra",
- "IsNormalForm",
- "Tester(IsNormalForm)"
- ],
- [
- "IsElementOfFpAlgebra",
- "IsNormalForm",
- "Tester(IsNormalForm)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: for two free magma ring elements",
- "filters": [
- [
- "IsElementOfMagmaRingModuloRelations"
- ],
- [
- "IsElementOfMagmaRingModuloRelations"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect add.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsAddition",
- "Tester(RespectsAddition)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: method for two s.v. gen. mappings that respect mult.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "=: xorbs",
- "filters": [
- [
- "IsExternalOrbit"
- ],
- [
- "IsExternalOrbit"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "=: for two weight rep elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsWeightRepElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsWeightRepElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "=: for two cochains",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsCochain"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsCochain"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "=: for direct sum elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsDirectSumElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsDirectSumElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "=: for sparse rowspace elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsSparseRowSpaceElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsSparseRowSpaceElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "=: for monomial elements",
- "filters": [
- [
- "IsMonomialElement",
- "IsMonomialElementRep"
- ],
- [
- "IsMonomialElement",
- "IsMonomialElementRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "=: for two algebra module elements in packed representation",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsAlgebraModuleElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsAlgebraModuleElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "=: for two residue class unions in different rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "=: for two residue class unions in different rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "=: for two residue class unions in sparse rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "=: for two residue class unions in standard rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "=: for two f.p. algebra elements (try nice monomorphism)",
- "filters": [
- [
- "IsElementOfFpAlgebra"
- ],
- [
- "IsElementOfFpAlgebra"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "=: method for two s.v. gen. mappings",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ]
- ],
- "rank": 18
- },
- {
- "aka": [
- "EQ_LIST_LIST_DEFAULT"
- ],
- "comment": "=: for two small lists",
- "filters": [
- [
- "IsList",
- "IsSmallList",
- "Tester(IsSmallList)"
- ],
- [
- "IsList",
- "IsSmallList",
- "Tester(IsSmallList)"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "=: for fp monoid elts produced by the Froidure-Pin algorithm",
- "filters": [
- [
- "IsFpMonoidReducedElt",
- "Tester(IsFpMonoidReducedElt)"
- ],
- [
- "IsFpMonoidReducedElt",
- "Tester(IsFpMonoidReducedElt)"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "=: DoubleCosets",
- "filters": [
- [
- "IsDoubleCoset"
- ],
- [
- "IsDoubleCoset"
- ]
- ],
- "rank": 16
- },
- {
- "aka": [
- "InfBits_Equal"
- ],
- "comment": "=: for two inf. bits assoc. words",
- "filters": [
- [
- "IsInfBitsAssocWord"
- ],
- [
- "IsInfBitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "=: for two 32 bits assoc. words",
- "filters": [
- [
- "Is32BitsAssocWord"
- ],
- [
- "Is32BitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "=: for two 16 bits assoc. words",
- "filters": [
- [
- "Is16BitsAssocWord"
- ],
- [
- "Is16BitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "=: for two 8 bits assoc. words",
- "filters": [
- [
- "Is8BitsAssocWord"
- ],
- [
- "Is8BitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsUnicodeString"
- ],
- [
- "IsUnicodeString"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for fp semigp elts produced by the Froidure-Pin algorithm",
- "filters": [
- [
- "IsFpSemigpReducedElt",
- "Tester(IsFpSemigpReducedElt)"
- ],
- [
- "IsFpSemigpReducedElt",
- "Tester(IsFpSemigpReducedElt)"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for Green's classes",
- "filters": [
- [
- "IsGreensClass"
- ],
- [
- "IsGreensClass"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for two f.p. group elements",
- "filters": [
- [
- "IsElementOfFpGroup"
- ],
- [
- "IsElementOfFpGroup"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: wreath elements",
- "filters": [
- [
- "IsWreathProductElement"
- ],
- [
- "IsWreathProductElement"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for two elements of magma by mult. table",
- "filters": [
- [
- "IsMagmaByMultiplicationTableObj"
- ],
- [
- "IsMagmaByMultiplicationTableObj"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for two elements of a magma with zero adjoined",
- "filters": [
- [
- "IsMagmaWithZeroAdjoinedElementRep"
- ],
- [
- "IsMagmaWithZeroAdjoinedElementRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for two general mappings",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- [
- "IsGeneralMapping"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for two finite lists (not necessarily small)",
- "filters": [
- [
- "IsList",
- "IsFinite",
- "Tester(IsFinite)"
- ],
- [
- "IsList",
- "IsFinite",
- "Tester(IsFinite)"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "=: for two unions of residue classes with fixed rep's (ResClasses)",
- "filters": [
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ],
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=: for a list of elements and an infinite domain (ResClasses)",
- "filters": [
- [
- "IsList",
- "IsFinite",
- "Tester(IsFinite)"
- ],
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=: for an infinite domain and a list of elements (ResClasses)",
- "filters": [
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ],
- [
- "IsList",
- "IsFinite",
- "Tester(IsFinite)"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=: for pcp elements",
- "filters": [
- [
- "IsPcpElement"
- ],
- [
- "IsPcpElement"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsMonoidByAdjoiningIdentityElt"
- ],
- [
- "IsMonoidByAdjoiningIdentityElt"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=: for two elements of a f.p. monoid",
- "filters": [
- [
- "IsElementOfFpMonoid"
- ],
- [
- "IsElementOfFpMonoid"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsMultiplicativeElementWithInverseByRws"
- ],
- [
- "IsMultiplicativeElementWithInverseByRws"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=: assoc words in letter rep",
- "filters": [
- [
- "IsAssociativeElement",
- "IsWord",
- "IsLetterAssocWordRep"
- ],
- [
- "IsAssociativeElement",
- "IsWord",
- "IsLetterAssocWordRep"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=: for two equivalence classes",
- "filters": [
- [
- "IsEquivalenceClass"
- ],
- [
- "IsEquivalenceClass"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "=: for elements of a Rees 0-matrix semigroup",
- "filters": [
- [
- "IsReesZeroMatrixSemigroupElement"
- ],
- [
- "IsReesZeroMatrixSemigroupElement"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: for elements of a Rees matrix semigroup",
- "filters": [
- [
- "IsReesMatrixSemigroupElement"
- ],
- [
- "IsReesMatrixSemigroupElement"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: for two Knuth-Bendix rewriting systems",
- "filters": [
- [
- "IsKnuthBendixRewritingSystem",
- "IsKnuthBendixRewritingSystemRep"
- ],
- [
- "IsKnuthBendixRewritingSystem",
- "IsKnuthBendixRewritingSystemRep"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: for two elements of a f.p. semigroup",
- "filters": [
- [
- "IsElementOfFpSemigroup"
- ],
- [
- "IsElementOfFpSemigroup"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: for two domains",
- "filters": [
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ],
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: for a domain and a list",
- "filters": [
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ],
- [
- "IsList",
- "IsCollection"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: for a list and a domain",
- "filters": [
- [
- "IsList",
- "IsCollection"
- ],
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: wrapped additive elements",
- "filters": [
- [
- "IsAdditiveElementAsMultiplicativeElementRep"
- ],
- [
- "IsAdditiveElementAsMultiplicativeElementRep"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "=: for two words",
- "filters": [
- [
- "IsWord"
- ],
- [
- "IsWord"
- ]
- ],
- "rank": 8
- },
- {
- "comment": "=",
- "filters": [
- [
- "IsWyckoffPosition"
- ],
- [
- "IsWyckoffPosition"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "=: for two lists with length - last resort",
- "filters": [
- [
- "IsList",
- "Tester(LENGTH)"
- ],
- [
- "IsList",
- "Tester(LENGTH)"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "=: for classes",
- "filters": [
- [
- "IsClass"
- ],
- [
- "IsClass"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "=: for two IO_Results",
- "filters": [
- [
- "IO_Result"
- ],
- [
- "IO_Result"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "=: for two lists - last resort",
- "filters": [
- [
- "IsList"
- ],
- [
- "IsList"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "=: for two info classes",
- "filters": [
- [
- "IsInfoClassListRep"
- ],
- [
- "IsInfoClassListRep"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "=: for two IsFile objects",
- "filters": [
- [
- "IsFile"
- ],
- [
- "IsFile"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "=: for another object and an IO_Result",
- "filters": [
- [],
- [
- "IO_Result"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "=: for an IO_Result and another object",
- "filters": [
- [
- "IO_Result"
- ],
- []
- ],
- "rank": 2
- },
- {
- "comment": "=: for two directories",
- "filters": [
- [
- "IsDirectory"
- ],
- [
- "IsDirectory"
- ]
- ],
- "rank": 2
- },
- {
- "aka": [
- "IS_IDENTICAL_OBJ",
- "IsIdenticalObj"
- ],
- "comment": "=: for two families: delegate to `IsIdenticalObj'",
- "filters": [
- [
- "IsFamily"
- ],
- [
- "IsFamily"
- ]
- ],
- "rank": 2
- },
- {
- "aka": [
- "EQ_PREC"
- ],
- "comment": "=: record = record",
- "filters": [
- [
- "IsRecord"
- ],
- [
- "IsRecord"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "=: fallback method to test conditions",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
- "IsMagmaWithInverses",
- "IsAssociative",
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- },
- {
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- },
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- },
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- },
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- },
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- "rank": 34
- },
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- "rank": 34
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- "rank": 32
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- ],
- "rank": 32
- },
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- [
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- ],
- "rank": 32
- },
- {
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- [
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- ]
- ],
- "rank": 32
- },
- {
- "comment": "<: for `-infinity' and cyclotomic",
- "filters": [
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- ],
- [
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- ]
- ],
- "rank": 31
- },
- {
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- ],
- [
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- ],
- "rank": 31
- },
- {
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- ],
- [
- "IsCyclotomic"
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- ],
- "rank": 31
- },
- {
- "comment": "<: for cyclotomic and `infinity'",
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- ],
- [
- "IsInfinity"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "<: for two plist matrices",
- "filters": [
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- "IsPlistMatrixRep"
- ],
- [
- "IsPlistMatrixRep"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "<: for two direct product elements",
- "filters": [
- [
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- ],
- [
- "IsDirectProductElement"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "<: for two finite field elements in different characteristic",
- "filters": [
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- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "<: for a finite field element, and a cyclotomic",
- "filters": [
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- ],
- [
- "IsCyclotomic"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "<: for a cyclotomic, and a finite field element",
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- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "<: for a module and a list of elements (ResClasses)",
- "filters": [
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- "Tester(IsRowModule)"
- ],
- [
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- ]
- ],
- "rank": 29
- },
- {
- "comment": "<: for a list of elements and a module (ResClasses)",
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- ],
- [
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- ],
- "rank": 29
- },
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- "comment": "<: for float and rational",
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- ],
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- ]
- ],
- "rank": 29
- },
- {
- "comment": "<: for rational and float",
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- ],
- [
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- ]
- ],
- "rank": 29
- },
- {
- "comment": "<: IsTransformationRepOfEndo, IsEndoMapping",
- "filters": [
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- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
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- "Tester(IsTotal)",
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- "Tester(IsSingleValued)",
- "IsTransformationRepOfEndo"
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- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
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- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ]
- ],
- "rank": 29
- },
- {
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- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
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- "Tester(IsTotal)",
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- "Tester(IsSingleValued)"
- ],
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- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
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- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsTransformationRepOfEndo"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "<: for a ring and a list of elements (ResClasses)",
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- [
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
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- ]
- ],
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- },
- {
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- ],
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- "IsNearAdditiveGroup",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "<",
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- [
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- ],
- [
- "IsPadicExtensionNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "<",
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- ],
- [
- "IsPurePadicNumber"
- ]
- ],
- "rank": 28
- },
- {
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- "IsZmodnZepsRep"
- ],
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- "IsZmodnZepsRep"
- ]
- ],
- "rank": 26
- },
- {
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- "IsDenseCoeffVectorRep"
- ],
- [
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- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "<: for two Lie objects in default representation",
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- "IsLieObject"
- ],
- [
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- "IsLieObject"
- ]
- ],
- "rank": 26
- },
- {
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- ],
- [
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- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "<: for floats",
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- ],
- [
- "IsFloat"
- ]
- ],
- "rank": 25
- },
- {
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- ],
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- ]
- ],
- "rank": 25
- },
- {
- "comment": "<: BFElm<FElm",
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- ],
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- "IsAdditiveElement",
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- ]
- ],
- "rank": 25
- },
- {
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- ]
- ],
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- },
- {
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- ],
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- "IsMultiplicativeElement"
- ]
- ],
- "rank": 25
- },
- {
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- ],
- "comment": "<: rational functions",
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- [
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- ],
- [
- "IsPolynomialFunction"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "<: for two UEALattice elements",
- "filters": [
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- "IsUEALatticeElement"
- ],
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- "IsUEALatticeElement"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "<: for binary rels over [1..n] with images list",
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- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
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- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "<: for a permutation, and a finite field element",
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- [
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- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "<: for a permutation, and a cyclotomic",
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- ],
- [
- "IsCyclotomic"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "<: for a finite field element, and a permutation",
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- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "<: for a cyclotomic, and a permutation",
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- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 23
- },
- {
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- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "<: for a finite field element and transformation",
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- ],
- [
- "IsTransformation"
- ]
- ],
- "rank": 22
- },
- {
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- ],
- [
- "IsTransformation"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "<: for a transformation and cyclotomic",
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- [
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- ],
- [
- "IsCyclotomic"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "<: for two plist vectors",
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- [
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- ],
- [
- "IsPlistVectorRep"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "<: for s. c. algebra elements",
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- ],
- [
- "IsSCAlgebraObj"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "<: for two normalized f.p. algebra elements",
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- [
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- "IsNormalForm",
- "Tester(IsNormalForm)"
- ],
- [
- "IsElementOfFpAlgebra",
- "IsNormalForm",
- "Tester(IsNormalForm)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "<: for two free magma ring elements",
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- [
- "IsElementOfMagmaRingModuloRelations"
- ],
- [
- "IsElementOfMagmaRingModuloRelations"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "<: xorbs, via AsSSortedList",
- "filters": [
- [
- "IsExternalOrbit"
- ],
- [
- "IsExternalOrbit"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "<: for two weight rep elements",
- "filters": [
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- "IsWeightRepElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsWeightRepElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "<: for two cochains",
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- "IsCochain"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsCochain"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "<: for direct sum elements",
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- "IsDirectSumElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsDirectSumElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "<: for sparse rowspace elements",
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- "IsSparseRowSpaceElement"
- ],
- [
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- "IsSparseRowSpaceElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "<: for monomial elements",
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- "IsMonomialElementRep"
- ],
- [
- "IsMonomialElement",
- "IsMonomialElementRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "<: for two algebra module elements in packed representation",
- "filters": [
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- "IsAlgebraModuleElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsAlgebraModuleElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "<",
- "filters": [
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- "IsModulusRep"
- ],
- [
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- ]
- ],
- "rank": 19
- },
- {
- "comment": "<",
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- ],
- [
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- ]
- ],
- "rank": 19
- },
- {
- "comment": "<",
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- ],
- [
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- ]
- ],
- "rank": 19
- },
- {
- "comment": "<",
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- ],
- [
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- ]
- ],
- "rank": 19
- },
- {
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- ],
- [
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- ]
- ],
- "rank": 18
- },
- {
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- ],
- "rank": 18
- },
- {
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- ],
- "rank": 18
- },
- {
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- ],
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- ]
- ],
- "rank": 18
- },
- {
- "comment": "<: for two f.p. algebra elements (try nice monomorphism)",
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- ],
- [
- "IsElementOfFpAlgebra"
- ]
- ],
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- },
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- ],
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- ],
- "rank": 18
- },
- {
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- ],
- "rank": 18
- },
- {
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- ],
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- ]
- ],
- "rank": 17
- },
- {
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- ],
- [
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- ]
- ],
- "rank": 17
- },
- {
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- ],
- [
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- ]
- ],
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- },
- {
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- ],
- [
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- ]
- ],
- "rank": 17
- },
- {
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- "Tester(IsFpMonoidReducedElt)"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "<: for two 32 bits assoc. words",
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- [
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- ],
- [
- "Is32BitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
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- ],
- [
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- ],
- "rank": 16
- },
- {
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- ],
- [
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- ]
- ],
- "rank": 16
- },
- {
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- ],
- [
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- ]
- ],
- "rank": 16
- },
- {
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- ],
- [
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- ]
- ],
- "rank": 16
- },
- {
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- ],
- [
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- ]
- ],
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- },
- {
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- ],
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- ]
- ],
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- },
- {
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- ]
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- },
- {
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- ]
- ],
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- {
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- ]
- ],
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- },
- {
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- [
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- ]
- ],
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- },
- {
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- ],
- "rank": 14
- },
- {
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- ],
- [
- "IsElementOfFpGroup"
- ]
- ],
- "rank": 14
- },
- {
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- ],
- [
- "IsWreathProductElement"
- ]
- ],
- "rank": 14
- },
- {
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- ],
- [
- "IsMagmaByMultiplicationTableObj"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "<: for two elements of magmas with zero adjoined",
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- ],
- [
- "IsMagmaWithZeroAdjoinedElementRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "<: for two general mappings",
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- ],
- [
- "IsGeneralMapping"
- ]
- ],
- "rank": 14
- },
- {
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- ],
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- "IsFinite",
- "Tester(IsFinite)"
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- "IsHomogeneousList",
- "IsFinite",
- "Tester(IsFinite)"
- ]
- ],
- "rank": 14
- },
- {
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- ],
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "<: for pcp elements",
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- "IsPcpElement"
- ],
- [
- "IsPcpElement"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "<",
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- ],
- [
- "IsMonoidByAdjoiningIdentityElt"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "<: for two elements of a f.p. monoid",
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- ],
- [
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- ]
- ],
- "rank": 12
- },
- {
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- ],
- [
- "IsMultiplicativeElementWithInverseByRws"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "<: assoc words in letter rep",
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- "IsWord",
- "IsLetterAssocWordRep"
- ],
- [
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- "IsLetterAssocWordRep"
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- ],
- "rank": 12
- },
- {
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- ],
- [
- "IsEquivalenceClass"
- ]
- ],
- "rank": 12
- },
- {
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- [
- "IsReesZeroMatrixSemigroupElement"
- ]
- ],
- "rank": 10
- },
- {
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- ],
- [
- "IsReesMatrixSemigroupElement"
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- ],
- "rank": 10
- },
- {
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- "IsElementOfFpSemigroup"
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- ],
- "rank": 10
- },
- {
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- ],
- "rank": 10
- },
- {
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- "IsGeneralizedDomain"
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- },
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- },
- {
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- },
- {
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- [
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- ]
- ],
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- },
- {
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- ],
- [
- "IsAdditiveElementAsMultiplicativeElementRep"
- ]
- ],
- "rank": 10
- },
- {
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- [
- "IsPerm"
- ]
- ],
- "rank": 9
- },
- {
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- "IsBool"
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- },
- {
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- ],
- "rank": 10000
- },
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- "Tester(IsNonTrivial)",
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- "IsExtLSet",
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- "IsDistributiveLOpESum",
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- "IsRDistributive",
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- ],
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- },
- {
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- "Tester(IsCyclotomicField)"
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- ],
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- "Tester(IsAbelianNumberField)"
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- {
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- ],
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- },
- {
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- "Tester(IsNaturalSymmetricGroup)"
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- "rank": 62
- },
- {
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- ]
- ],
- "rank": 61
- },
- {
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- "Tester(IsFullRowModule)"
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- },
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- {
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- },
- {
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- "Tester(IsZ_pi)"
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- "rank": 33
- },
- {
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- ]
- ],
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- },
- {
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- "Tester(IsInverseSemigroup)",
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- ],
- "rank": 27
- },
- {
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- "Tester(IsAssociative)",
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- "Tester(IsInverseSemigroup)"
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- "rank": 26
- },
- {
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- "Tester(IsConjugatorIsomorphism)"
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- ],
- "rank": 23
- },
- {
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- ],
- "rank": 22
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- {
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- "Tester(IsInverseSemigroup)"
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- "rank": 21
- },
- {
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- "rank": 21
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- {
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- "rank": 20
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- {
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- "IsZmodnZObj",
- "IsModulusRep"
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- ],
- "rank": 18
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- {
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- "IsUnknownDefaultRep"
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- "rank": 18
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- {
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- "rank": 18
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- {
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- "rank": 17
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- {
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- {
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- "rank": 17
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- {
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- ],
- "rank": 17
- },
- {
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- "rank": 17
- },
- {
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- "rank": 17
- },
- {
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- "rank": 17
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- {
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- "rank": 16
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- {
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- "Tester(IsAssociative)"
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- "rank": 16
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- {
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- ]
- ],
- "rank": 16
- },
- {
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- "rank": 16
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- {
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- ],
- "rank": 16
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- {
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- ]
- ],
- "rank": 15
- },
- {
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- ]
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- "rank": 15
- },
- {
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- "Tester(IsUnivariateRationalFunction)"
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- ],
- "rank": 15
- },
- {
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- "IsAssociative",
- "Tester(IsAssociative)"
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- "rank": 15
- },
- {
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- [
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- "Tester(IsPolynomial)"
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- "rank": 14
- },
- {
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- "rank": 13
- },
- {
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- ]
- ],
- "rank": 13
- },
- {
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- "rank": 11
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- {
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- ]
- ],
- "rank": 11
- },
- {
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- "rank": 11
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- {
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- [
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- "rank": 11
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- {
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- "IsNBitsPcWordRep"
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- "rank": 9
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- "rank": 8
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- {
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- "rank": 7
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- {
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- "rank": 7
- },
- {
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- "rank": 6
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- {
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- ]
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- "rank": 6
- },
- {
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- "rank": 6
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- {
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- "rank": 5
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- ],
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- "rank": 5
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- {
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- "rank": 5
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- "rank": 5
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- {
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- "rank": 2
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- {
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- {
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- "rank": 1
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- "rank": 1
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- "rank": 0
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- "rank": 10022
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- "rank": 10009
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- "IsLeftActedOnByRing",
- "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": 54
- },
- {
- "comment": "PrintObj: for a pcp group",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsPcpElement)"
- ]
- ],
- "rank": 48
- },
- {
- "comment": "PrintObj: for full matrix module",
- "filters": [
- [
- "IsFreeLeftModule",
- "IsFullMatrixModule",
- "Tester(IsFullMatrixModule)"
- ]
- ],
- "rank": 48
- },
- {
- "comment": "PrintObj: for full row module",
- "filters": [
- [
- "IsFreeLeftModule",
- "IsFullRowModule",
- "Tester(IsFullRowModule)"
- ]
- ],
- "rank": 48
- },
- {
- "comment": "PrintObj: for a matrix group",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 45
- },
- {
- "comment": "PrintObj: for a semigroup with known generators",
- "filters": [
- [
- "CategoryCollections(IsPartialPerm)",
- "IsMagma",
- "IsMagmaWithInverses",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 40
- },
- {
- "comment": "PrintObj: for an algebra-with-one with known generators",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfLeftOperatorRing)"
- ]
- ],
- "rank": 40
- },
- {
- "comment": "PrintObj: for an algebra-with-one",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 39
- },
- {
- "comment": "PrintObj: for a semigroup with known generators",
- "filters": [
- [
- "CategoryCollections(IsTransformation)",
- "IsMagma",
- "IsMagmaWithInverses",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "PrintObj: for a FLMLOR-with-one with known generators",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "Tester(GeneratorsOfLeftOperatorRing)"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "PrintObj: for an algebra with known generators",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfLeftOperatorRing)"
- ]
- ],
- "rank": 37
- },
- {
- "comment": "PrintObj: for a FLMLOR-with-one",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 37
- },
- {
- "comment": "PrintObj: for an algebra",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "PrintObj: for a free magma ring",
- "filters": [
- [
- "IsFreeMagmaRing"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "PrintObj: for a group with generators",
- "filters": [
- [
- "IsMagmaWithInverses",
- "Tester(GeneratorsOfMagmaWithInverses)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "PrintObj: for a character",
- "filters": [
- [
- "IsClassFunction",
- "IsCharacter",
- "Tester(IsCharacter)"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "PrintObj: for a FLMLOR with known generators",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "Tester(GeneratorsOfLeftOperatorRing)"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "PrintObj: for a group",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "PrintObj: for a FLMLOR",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "PrintObj: for an ordinary block matrix",
- "filters": [
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "PrintObj: for Z_(pi) (ResClasses)",
- "filters": [
- [
- "IsZ_pi",
- "Tester(IsZ_pi)"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "PrintObj: for a virtual character",
- "filters": [
- [
- "IsClassFunction",
- "IsVirtualCharacter",
- "Tester(IsVirtualCharacter)"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "PrintObj: for a semigroup Congruence with known generating pairs",
- "filters": [
- [
- "Tester(GeneratingPairsOfMagmaCongruence)",
- "IsSemigroupCongruence",
- "Tester(IsSemigroupCongruence)"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "PrintObj: for a semigroup congruence",
- "filters": [
- [
- "IsSemigroupCongruence",
- "Tester(IsSemigroupCongruence)"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "PrintObj: for a class function",
- "filters": [
- [
- "IsClassFunction"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PrintObj: for an algebra-with-one hom. b.i",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsOne",
- "Tester(RespectsOne)",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PrintObj: for null map matrix",
- "filters": [
- [
- "IsNullMapMatrix"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PrintObj: for a ring-with-one with generators",
- "filters": [
- [
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRingWithOne)"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "PrintObj: for an alg. hom. from f. p. algebra",
- "filters": [
- [
- "IsAlgebraHomomorphismFromFpRep"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PrintObj: for an operation algebra homomorphism",
- "filters": [
- [
- "IsOperationAlgebraHomomorphismDefaultRep"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PrintObj: for an algebra hom. b.i.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PrintObj: for a two-sided ideal with known generators",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfTwoSidedIdeal)",
- "Tester(LeftActingRingOfIdeal)",
- "Tester(RightActingRingOfIdeal)"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PrintObj: for a ring-with-one",
- "filters": [
- [
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PrintObj: for a right semigroup congruence with known generating pairs",
- "filters": [
- [
- "Tester(GeneratingPairsOfMagmaCongruence)",
- "IsRightSemigroupCongruence",
- "Tester(IsRightSemigroupCongruence)"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PrintObj: for a left semigroup congruence with known generating pairs",
- "filters": [
- [
- "Tester(GeneratingPairsOfMagmaCongruence)",
- "IsLeftSemigroupCongruence",
- "Tester(IsLeftSemigroupCongruence)"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PrintObj: For a compressed MatFFE",
- "filters": [
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "Is8BitMatrixRep"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PrintObj: for a right ideal with known generators",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRightIdeal)",
- "Tester(RightActingRingOfIdeal)"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PrintObj: for a left ideal with known generators",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfLeftIdeal)",
- "Tester(LeftActingRingOfIdeal)"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PrintObj: for inner automorphism",
- "filters": [
- [
- "IsInnerAutomorphism",
- "Tester(IsInnerAutomorphism)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for an ring hom. b.i.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsRingGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for algebra module",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsAlgebraModule",
- "Tester(IsAlgebraModule)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for an algebra-with-one g.m.b.i",
- "filters": [
- [
- "IsGeneralMapping",
- "RespectsOne",
- "Tester(RespectsOne)",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for a left module hom. b.i",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsLinearGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for a ring with generators",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRing)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for a inverse monoid with known generators",
- "filters": [
- [
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsInverseSemigroup",
- "Tester(IsInverseSemigroup)",
- "Tester(GeneratorsOfInverseMonoid)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for a magma Congruence with known generating pairs",
- "filters": [
- [
- "IsMagmaCongruence",
- "Tester(GeneratingPairsOfMagmaCongruence)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for a right magma congruence with known generating pairs",
- "filters": [
- [
- "IsRightMagmaCongruence",
- "Tester(GeneratingPairsOfMagmaCongruence)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for a left magma congruence with known generating pairs",
- "filters": [
- [
- "IsLeftMagmaCongruence",
- "Tester(GeneratingPairsOfMagmaCongruence)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintObj: for ANF automorphism",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "PrintObj: for a Frobenius automorphism",
- "filters": [
- [
- "IsFrobeniusAutomorphism"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "PrintObj: method for vector space with left module generators",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "PrintObj: for a ring",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "PrintObj: for a magma congruence",
- "filters": [
- [
- "IsMagmaCongruence"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "PrintObj: for an algebra g.m.b.i",
- "filters": [
- [
- "IsGeneralMapping",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "PrintObj: method for vector space",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "PrintObj: pcgs",
- "filters": [
- [
- "IsPcgs",
- "IsPcgsDefaultRep"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "PrintObj: For a compressed VecFFE",
- "filters": [
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "Is8BitVectorRep"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "PrintObj: for free left module with known generators",
- "filters": [
- [
- "IsFreeLeftModule",
- "Tester(GeneratorsOfLeftOperatorAdditiveGroup)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "PrintObj: for a right semigroup congruence",
- "filters": [
- [
- "IsRightSemigroupCongruence",
- "Tester(IsRightSemigroupCongruence)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "PrintObj: for a left semigroup congruence",
- "filters": [
- [
- "IsLeftSemigroupCongruence",
- "Tester(IsLeftSemigroupCongruence)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "PrintObj: for saturated Fitting formation",
- "filters": [
- [
- "IsGroupClass",
- "Tester(IsGroupClass)",
- "ContainsTrivialGroup",
- "Tester(ContainsTrivialGroup)",
- "IsNormalSubgroupClosed",
- "Tester(IsNormalSubgroupClosed)",
- "IsQuotientClosed",
- "Tester(IsQuotientClosed)",
- "IsResiduallyClosed",
- "Tester(IsResiduallyClosed)",
- "IsNormalProductClosed",
- "Tester(IsNormalProductClosed)",
- "IsSaturated",
- "Tester(IsSaturated)",
- "IsClassByPropertyRep"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for embedding into wreath product",
- "filters": [
- [
- "IsEmbeddingImprimitiveWreathProductMatrixGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for projection from a direct product",
- "filters": [
- [
- "IsProjectionDirectProductMatrixGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for embedding into direct product",
- "filters": [
- [
- "IsEmbeddingDirectProductMatrixGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for embedding into wreath product",
- "filters": [
- [
- "IsEmbeddingWreathProductPermGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for projection from subdirect product",
- "filters": [
- [
- "IsProjectionSubdirectProductPermGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for projection from a direct product",
- "filters": [
- [
- "IsProjectionDirectProductPermGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for embedding into direct product",
- "filters": [
- [
- "IsEmbeddingDirectProductPermGroup"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: method for a PcGroupHomomorphisms",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsPcGroupGeneralMappingByImages"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for nat. hom. of pc group",
- "filters": [
- [
- "IsNaturalHomomorphismPcGroupRep"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for conjugator isomorphism",
- "filters": [
- [
- "IsConjugatorIsomorphism",
- "Tester(IsConjugatorIsomorphism)"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for an ring g.m.b.i",
- "filters": [
- [
- "IsGeneralMapping",
- "IsRingGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for a left module m.b.m.",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLinearMappingByMatrixDefaultRep"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for a left module g.m.b.i",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLinearGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for free left module",
- "filters": [
- [
- "IsFreeLeftModule"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for a magma with zero adjoined",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsMagmaWithZeroAdjoined"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PrintObj: for a Brauer table",
- "filters": [
- [
- "IsBrauerTable"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PrintObj: for an ordinary table",
- "filters": [
- [
- "IsOrdinaryTable"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PrintObj: for action homomorphism",
- "filters": [
- [
- "IsActionHomomorphism"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PrintObj: for a inverse semigroup with known generators",
- "filters": [
- [
- "IsInverseSemigroup",
- "Tester(IsInverseSemigroup)",
- "Tester(GeneratorsOfInverseSemigroup)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PrintObj: for a right magma congruence",
- "filters": [
- [
- "IsRightMagmaCongruence"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PrintObj: for a left magma congruence",
- "filters": [
- [
- "IsLeftMagmaCongruence"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PrintObj: for a Rees 0-matrix semigroup",
- "filters": [
- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsReesZeroMatrixSemigroup",
- "Tester(IsReesZeroMatrixSemigroup)"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "PrintObj: for a Rees matrix semigroup",
- "filters": [
- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsReesMatrixSemigroup",
- "Tester(IsReesMatrixSemigroup)"
- ]
- ],
- "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 monoid with known generators",
- "filters": [
- [
- "IsMagmaWithOne",
- "Tester(GeneratorsOfMagmaWithOne)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "PrintObj: for an equivalence relation",
- "filters": [
- [
- "IsEquivalenceRelation",
- "Tester(IsEquivalenceRelation)"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "PrintObj: for product of Fitting formations",
- "filters": [
- [
- "IsFittingProductRep",
- "IsFormationProductRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsUnicodeCharacter"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj: modulo pcgs",
- "filters": [
- [
- "IsModuloPcgs"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj: combinatorial collector rep (32 Bits)",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "Is32BitsSingleCollectorRep",
- "IsCombinatorialCollectorRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj: combinatorial collector rep (16 Bits)",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "Is16BitsSingleCollectorRep",
- "IsCombinatorialCollectorRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj: combinatorial collector rep (8 Bits)",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "Is8BitsSingleCollectorRep",
- "IsCombinatorialCollectorRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj: combinatorial collector (up to date)",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "IsUpToDatePolycyclicCollector",
- "IsCombinatorialCollectorRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "IsUpToDatePolycyclicCollector",
- "Is32BitsSingleCollectorRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "IsUpToDatePolycyclicCollector",
- "Is16BitsSingleCollectorRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "IsUpToDatePolycyclicCollector",
- "Is8BitsSingleCollectorRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PrintObj: for 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: 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 mapping by function with inverse",
- "filters": [
- [
- "IsMappingByFunctionWithInverseRep"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "PrintObj: for a subsemigroup of a Rees 0-matrix semigroup",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "PrintObj: for a subsemigroup of a Rees matrix semigroup",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsReesMatrixSemigroupElement)"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsPowerConjugateCollector",
- "IsSingleCollectorRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "PrintObj: zmodnze : for full collection Z/nZ(m)",
- "filters": [
- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "CategoryCollections(IsZmodnZepsObj)"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "PrintObj: for element in Z/pZ (ModulusRep)",
- "filters": [
- [
- "IsFFE",
- "IsZmodnZObj",
- "IsModulusRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "PrintObj: for unknown in default representation",
- "filters": [
- [
- "IsUnknown",
- "IsUnknownDefaultRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "PrintObj: for a semigroup ideal with known generators",
- "filters": [
- [
- "IsLeftActedOnBySuperset",
- "IsRightActedOnBySuperset",
- "IsMagma",
- "Tester(GeneratorsOfMagmaIdeal)",
- "IsSemigroupIdeal",
- "Tester(IsSemigroupIdeal)"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "PrintObj: for a Schunck class",
- "filters": [
- [
- "IsSchunckClass",
- "Tester(IsSchunckClass)",
- "IsClassByPropertyRep"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: for semigroup homomorphism by images",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "IsSemigroupHomomorphismByImagesRep"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: for group general mapping b.i.",
- "filters": [
- [
- "IsGroupGeneralMappingByImages"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: for large finite field elements (use String)",
- "filters": [
- [
- "IsFFE",
- "IsCoeffsModConwayPolRep"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: AlgElm",
- "filters": [
- [
- "IsKroneckerConstRep"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: BFElm",
- "filters": [
- [
- "IsAlgBFRep"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: laurent polynomial",
- "filters": [
- [
- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: for an add. magma-with-inverses with generators",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "Tester(GeneratorsOfNearAdditiveGroup)"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: for a semigroup ideal",
- "filters": [
- [
- "IsLeftActedOnBySuperset",
- "IsRightActedOnBySuperset",
- "IsMagma",
- "IsSemigroupIdeal",
- "Tester(IsSemigroupIdeal)"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintObj: for a Molien series",
- "filters": [
- [
- "IsRationalFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)",
- "Tester(MolienSeriesInfo)"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintObj: RightCoset",
- "filters": [
- [
- "IsRightCoset"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintObj: for element in Z/nZ (ModulusRep)",
- "filters": [
- [
- "IsZmodnZObj",
- "IsModulusRep"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintObj: for a semigroup with known generators",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintObj: for a magma ideal with known generators",
- "filters": [
- [
- "IsLeftActedOnBySuperset",
- "IsRightActedOnBySuperset",
- "IsMagma",
- "Tester(GeneratorsOfMagmaIdeal)"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintObj: for -infinity",
- "filters": [
- [
- "IsNegInfinity"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintObj: for infinity",
- "filters": [
- [
- "IsInfinity"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintObj: for formation product",
- "filters": [
- [
- "IsFormationProductRep"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for formation",
- "filters": [
- [
- "IsGroupClass",
- "Tester(IsGroupClass)",
- "ContainsTrivialGroup",
- "Tester(ContainsTrivialGroup)",
- "IsQuotientClosed",
- "Tester(IsQuotientClosed)",
- "IsResiduallyClosed",
- "Tester(IsResiduallyClosed)",
- "IsClassByPropertyRep"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for Fitting product",
- "filters": [
- [
- "IsFittingProductRep"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for Fitting class",
- "filters": [
- [
- "IsGroupClass",
- "Tester(IsGroupClass)",
- "ContainsTrivialGroup",
- "Tester(ContainsTrivialGroup)",
- "IsNormalSubgroupClosed",
- "Tester(IsNormalSubgroupClosed)",
- "IsNormalProductClosed",
- "Tester(IsNormalProductClosed)",
- "IsClassByPropertyRep"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for a plist matrix",
- "filters": [
- [
- "IsPlistMatrixRep"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for GF2 matrix",
- "filters": [
- [
- "IsGF2MatrixRep"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: univar",
- "filters": [
- [
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for an add. magma-with-zero with generators",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveMagmaWithZero",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "Tester(GeneratorsOfNearAdditiveMagmaWithZero)"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for a magma ideal",
- "filters": [
- [
- "IsLeftActedOnBySuperset",
- "IsRightActedOnBySuperset",
- "IsMagma"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for a direct product element",
- "filters": [
- [
- "IsDirectProductElement"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "PrintObj: for Fitting set",
- "filters": [
- [
- "IsClassByPropertyRep",
- "IsFittingSetRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsPowerConjugateCollector",
- "IsDeepThoughtCollectorRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsPadicExtensionNumber"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsPurePadicNumber"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj: polynomial",
- "filters": [
- [
- "IsPolynomial",
- "Tester(IsPolynomial)"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj: for a right magma ideal with known generators",
- "filters": [
- [
- "IsRightActedOnBySuperset",
- "Tester(GeneratorsOfExtRSet)",
- "IsMagma"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj: for a left magma ideal with known generators",
- "filters": [
- [
- "IsLeftActedOnBySuperset",
- "Tester(GeneratorsOfExtLSet)",
- "IsMagma"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj: for mapping by function",
- "filters": [
- [
- "IsMappingByFunctionRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintObj: for from-the-left collector",
- "filters": [
- [
- "IsFromTheLeftCollectorRep"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "PrintObj: for floats",
- "filters": [
- [
- "IsFloat"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "PrintObj: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep)",
- "filters": [
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "PrintObj: rational function",
- "filters": [
- [
- "IsRationalFunction"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "PrintObj: for an add. magma with generators",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "Tester(GeneratorsOfNearAdditiveMagma)"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "PrintObj: for a right magma ideal",
- "filters": [
- [
- "IsRightActedOnBySuperset",
- "IsMagma"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "PrintObj: for a left magma ideal",
- "filters": [
- [
- "IsLeftActedOnBySuperset",
- "IsMagma"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsPowerCommutatorCollector"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsPowerConjugateCollector"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PrintObj: for UEALattice element",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsUEALatticeElement"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PrintObj: for an additive coset",
- "filters": [
- [
- "IsAdditiveCoset"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PrintObj: for an add. magma",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PrintObj: for a binary relation on n points",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsConjugacyClassSubgroupsRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsRationalClassGroupRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsConjugacyClassGroupRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsPolycyclicCollector"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for a plist vector",
- "filters": [
- [
- "IsPlistVectorRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for GF2 vector",
- "filters": [
- [
- "IsGF2VectorRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for s. c. ring element",
- "filters": [
- [
- "IsSCRingObj"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for symmetric elements",
- "filters": [
- [
- "IsSymmetricPowerElement",
- "IsMonomialElementRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for wedge elements",
- "filters": [
- [
- "IsWedgeElement",
- "IsMonomialElementRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for tensor elements",
- "filters": [
- [
- "IsTensorElement",
- "IsMonomialElementRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for s. c. algebra element",
- "filters": [
- [
- "IsSCAlgebraObj"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: fp algebra elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsElementOfFpAlgebra"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for magma ring element",
- "filters": [
- [
- "IsElementOfMagmaRingModuloRelations"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for a mapping",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintObj: for external orbit",
- "filters": [
- [
- "IsExternalOrbit"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: pcword",
- "filters": [
- [
- "IsMultiplicativeElementWithInverseByPolycyclicCollector",
- "IsNBitsPcWordRep"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsRewritingSystem",
- "IsBuiltFromGroup",
- "Tester(IsBuiltFromGroup)"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: for weight rep element",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsWeightRepElement"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: for direct sum elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsDirectSumElement"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: for algebra module element in packed representation",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsAlgebraModuleElement"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: method for a subspaces domain",
- "filters": [
- [
- "IsSubspacesVectorSpace",
- "IsSubspacesVectorSpaceDefaultRep"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: for a semi-echelonized basis with basis vectors",
- "filters": [
- [
- "IsBasis",
- "IsSemiEchelonized",
- "Tester(IsSemiEchelonized)",
- "Tester(BasisVectors)"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: method for a weak pointer object",
- "filters": [
- [
- "IsWeakPointerObject"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "PrintObj: for residue class unions in sparse rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj: for residue class unions in standard rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj: for an element of an f.p. group (default repres.)",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsElementOfFpGroup"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj: sliced perm",
- "filters": [
- [
- "IsSlicedPermInv"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj: sliced perm",
- "filters": [
- [
- "IsSlicedPerm"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj: for external subset",
- "filters": [
- [
- "IsExternalSubset"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj: for a semi-echelonized basis",
- "filters": [
- [
- "IsBasis",
- "IsSemiEchelonized",
- "Tester(IsSemiEchelonized)"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj: for right transversal",
- "filters": [
- [
- "IsList",
- "IsRightTransversalRep"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsMultiplicativeElementWithInverseByRws"
- ]
- ],
- "rank": 8
- },
- {
- "comment": "PrintObj: for a cochain",
- "filters": [
- [
- "IsCochain"
- ]
- ],
- "rank": 8
- },
- {
- "comment": "PrintObj: for a sparse rowspace element",
- "filters": [
- [
- "IsSparseRowSpaceElement"
- ]
- ],
- "rank": 8
- },
- {
- "comment": "PrintObj: for a basis with basis vectors",
- "filters": [
- [
- "IsBasis",
- "Tester(BasisVectors)"
- ]
- ],
- "rank": 8
- },
- {
- "comment": "PrintObj: for IsGroupClass and IsClassByPropertyRep",
- "filters": [
- [
- "IsGroupClass",
- "Tester(IsGroupClass)",
- "IsClassByPropertyRep"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsUnicodeString"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for a Green's class",
- "filters": [
- [
- "IsGreensClass"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for a partial perm",
- "filters": [
- [
- "IsPartialPerm"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: wreath elements",
- "filters": [
- [
- "IsWreathProductElement"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for element of magma by mult. table",
- "filters": [
- [
- "IsMagmaByMultiplicationTableObj"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for sparse hash tables",
- "filters": [
- [
- "IsSparseHashRep"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for dense hash tables",
- "filters": [
- [
- "IsDenseHashRep"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for a basis",
- "filters": [
- [
- "IsBasis"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for an element of a magma with zero adjoined",
- "filters": [
- [
- "IsMagmaWithZeroAdjoinedElementRep"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for a general mapping",
- "filters": [
- [
- "IsGeneralMapping"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for an enumerator that perhaps has its own `PrintObj' function",
- "filters": [
- [
- "IsList",
- "IsDenseList",
- "IsDuplicateFree",
- "Tester(IsDuplicateFree)",
- "IsEnumeratorByFunctionsRep"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintObj: for unions of residue classes with fixed rep's (ResClasses)",
- "filters": [
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsSimpleInvAutomatonRep"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj: for pcp elements",
- "filters": [
- [
- "IsPcpElement"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsMonoidByAdjoiningIdentityElt"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj: for an fp monoid element",
- "filters": [
- [
- "IsElementOfFpMonoid"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj: External Set",
- "filters": [
- [
- "IsExternalSet"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj: assoc word in letter rep",
- "filters": [
- [
- "IsAssociativeElement",
- "IsWord",
- "IsLetterAssocWordRep"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj: for an eq. class",
- "filters": [
- [
- "IsEquivalenceClass"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj: iostream",
- "filters": [
- [
- "IsInputOutputStream",
- "IsInputOutputStreamByPtyRep"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "PrintObj: for IsGroupClassByListRep",
- "filters": [
- [
- "IsGroupClassByListRep"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for IsClassByUnionRep",
- "filters": [
- [
- "IsClassByUnionRep"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for IsClassByIntersectionRep",
- "filters": [
- [
- "IsClassByIntersectionRep"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for IsClassByComplementRep",
- "filters": [
- [
- "IsClassByComplementRep"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for IsClassByPropertyRep",
- "filters": [
- [
- "IsClassByPropertyRep"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for a Rees 0-matrix semigroup element",
- "filters": [
- [
- "IsReesZeroMatrixSemigroupElement"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for a Rees matrix semigroup element",
- "filters": [
- [
- "IsReesMatrixSemigroupElement"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for an f.p. semigroup element",
- "filters": [
- [
- "IsElementOfFpSemigroup"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for a presentation in default representation",
- "filters": [
- [
- "IsPresentation",
- "IsPresentationDefaultRep"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for an associative word",
- "filters": [
- [
- "IsAssociativeElement",
- "IsWord"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for a nonassociative word",
- "filters": [
- [
- "IsNonassocWord"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: wrapped additive elements",
- "filters": [
- [
- "IsAdditiveElementAsMultiplicativeElementRep"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "PrintObj: for an infinite list of generators",
- "filters": [
- [
- "IsList",
- "IsInfiniteListOfGeneratorsRep"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "PrintObj: for an infinite list of names",
- "filters": [
- [
- "IsList",
- "IsInfiniteListOfNamesRep"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "PrintObj: for an enumerator",
- "filters": [
- [
- "IsList",
- "IsAttributeStoringRep"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "PrintObj: Wyckoff position",
- "filters": [
- [
- "IsWyckoffPosition"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj: lattice",
- "filters": [
- [
- "IsLatticeSubgroupsRep"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj: for mutable basis with underlying mutable basis",
- "filters": [
- [
- "IsMutableBasis",
- "IsMutableBasisViaUnderlyingMutableBasisRep"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj: for a mutable basis of a Gaussian matrix space",
- "filters": [
- [
- "IsMutableBasis",
- "IsMutableBasisOfGaussianMatrixSpaceRep"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj: for a mutable basis of a Gaussian row space",
- "filters": [
- [
- "IsMutableBasis",
- "IsMutableBasisOfGaussianRowSpaceRep"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj: for mutable basis represented by a nice mutable basis",
- "filters": [
- [
- "IsMutableBasis",
- "IsMutableBasisViaNiceMutableBasisRep"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj: for mutable basis represented by an immutable basis",
- "filters": [
- [
- "IsMutableBasis",
- "IsMutableBasisByImmutableBasisRep"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj: for an iterator that perhaps has its own `PrintObj' function",
- "filters": [
- [
- "IsIterator",
- "IsIteratorByFunctionsRep"
- ]
- ],
- "rank": 3
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsRewritingSystem"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsRandomSource"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: output text none",
- "filters": [
- [
- "IsOutputTextNoneRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: output text file",
- "filters": [
- [
- "IsOutputTextFileRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: output text string",
- "filters": [
- [
- "IsOutputTextStringRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: input text none",
- "filters": [
- [
- "IsInputTextNoneRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: input text file",
- "filters": [
- [
- "IsInputTextFileRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: input text string",
- "filters": [
- [
- "IsInputTextStringRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: default directory rep",
- "filters": [
- [
- "IsDirectoryRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: for an info class",
- "filters": [
- [
- "IsInfoClassListRep"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: for an operation",
- "filters": [
- [
- "IsOperation"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "PrintObj: for a straight line decision",
- "filters": [
- [
- "IsStraightLineDecision"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: for a black box program",
- "filters": [
- [
- "IsBBoxProgram"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: for pcp",
- "filters": [
- [
- "IsPcp"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsRecord"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: IsObjToBePrinted",
- "filters": [
- [
- "IsObjToBePrinted"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: for a straight line program",
- "filters": [
- [
- "IsStraightLineProgram"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj",
- "filters": [
- [
- "IsTableOfMarks"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: for a root system",
- "filters": [
- [
- "IsRootSystem"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: closed stream",
- "filters": [
- [
- "IsClosedStream"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: for an iterator",
- "filters": [
- [
- "IsIterator"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: record",
- "filters": [
- [
- "IsRecord"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: for 'to be defined' objects",
- "filters": [
- [
- "IsToBeDefinedObj"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PRINT_OBJ: for a type",
- "filters": [
- [
- "IsType"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PRINT_OBJ: for a family",
- "filters": [
- [
- "IsFamily"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "PrintObj: default method delegating to PrintString",
- "filters": [
- []
- ],
- "rank": 0
- }
- ],
- "2args": [],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "PrintObj",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "PrintString"
- ],
- "filters": [
- [
- []
- ],
- [
- [],
- [
- "IsInt"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/object.gd",
- "line": 485
- },
- {
- "file": "/home/makx/ac/gap/lib/object.gd",
- "line": 486
- }
- ],
- "methods": {
- "0args": [],
- "1args": [
- {
- "comment": "PrintString: for a group with generators",
- "filters": [
- [
- "IsMagmaWithInverses",
- "Tester(GeneratorsOfMagmaWithInverses)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "PrintString: for a inverse monoid with known generators",
- "filters": [
- [
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsInverseSemigroup",
- "Tester(IsInverseSemigroup)",
- "Tester(GeneratorsOfInverseMonoid)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PrintString: for a inverse semigroup with known generators",
- "filters": [
- [
- "IsInverseSemigroup",
- "Tester(IsInverseSemigroup)",
- "Tester(GeneratorsOfInverseSemigroup)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PrintString: for monoid with known generators",
- "filters": [
- [
- "IsMagmaWithOne",
- "Tester(GeneratorsOfMagmaWithOne)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "PrintString: for a magma-with-inverses with generators",
- "filters": [
- [
- "IsMagmaWithInverses",
- "Tester(GeneratorsOfMagmaWithInverses)"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "PrintString: RightCoset",
- "filters": [
- [
- "IsRightCoset"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintString: for a semigroup with known generators",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "PrintString: for a magma-with-one with generators",
- "filters": [
- [
- "IsMagmaWithOne",
- "Tester(GeneratorsOfMagmaWithOne)"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "PrintString: for a magma with generators",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PrintString: for a magma",
- "filters": [
- [
- "IsMagma"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PrintString: for right transversal",
- "filters": [
- [
- "IsList",
- "IsRightTransversalRep"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "PrintString: for a Green's class",
- "filters": [
- [
- "IsGreensClass"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintString: for a partial perm",
- "filters": [
- [
- "IsPartialPerm"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintString: for a transformation",
- "filters": [
- [
- "IsTransformation"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "PrintString: default method delegating to String",
- "filters": [
- []
- ],
- "rank": -1
- }
- ],
- "2args": [
- {
- "comment": "PrintString: for an object, and zero",
- "filters": [
- [],
- [
- "IsZeroCyc"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "PrintString: for an object, and a negative integer",
- "filters": [
- [],
- [
- "IsInt",
- "IsNegRat"
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- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1636
- },
- {
- "file": "/home/makx/ac/gap/lib/coll.gd",
- "line": 1637
- },
- {
- "file": "/home/makx/ac/gap/lib/random.gd",
- "line": 72
- },
- {
- "file": "/home/makx/ac/gap/lib/random.gd",
- "line": 73
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- ],
- "methods": {
- "0args": [],
- "1args": [
- {
- "comment": "Random",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsFinite",
- "Tester(IsFinite)",
- "CategoryCollections(IsFFE)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
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- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
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- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "IsMagmaWithOne",
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- "Tester(IsCommutative)",
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- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
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- ],
- "rank": 432
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- {
- "comment": "Random: for natural SL",
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- [
- "IsFinite",
- "Tester(IsFinite)",
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- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
- "IsMagmaWithInverses",
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- "Tester(IsAssociative)",
- "IsNaturalSL",
- "Tester(IsNaturalSL)"
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- ],
- "rank": 399
- },
- {
- "comment": "Random: for natural GL",
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- [
- "IsFinite",
- "Tester(IsFinite)",
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- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNaturalGL",
- "Tester(IsNaturalGL)"
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- "rank": 397
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- {
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- [
- "IsMagmaWithInverses",
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- "rank": 370
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- {
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- [
- "IsList",
- "IsInternalRep"
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- "rank": 119
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- {
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- [
- "IsHash",
- "IsSparseHashRep"
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- "rank": 107
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- {
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- [
- "IsHash",
- "IsDenseHashRep"
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- {
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- [
- "IsNaturalAlternatingGroup",
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- {
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- [
- "IsNaturalSymmetricGroup",
- "Tester(IsNaturalSymmetricGroup)"
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- "rank": 72
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- {
- "comment": "Random: for Rationals",
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- [
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- "IsLeftActedOnByDivisionRing",
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- "Tester(IsAssociative)",
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- "Tester(IsCommutative)",
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- "IsRDistributive",
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- "IsEuclideanRing",
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- "Tester(IsPrimeField)"
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- "rank": 69
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- {
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- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
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- "Tester(IsAssociative)"
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- ],
- "rank": 68
- },
- {
- "comment": "Random: for a finite prime field",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsFinite",
- "Tester(IsFinite)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "IsAssociative",
- "Tester(IsAssociative)",
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- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "IsRDistributive",
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- "IsEuclideanRing",
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- "Tester(IsPrimeField)"
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- ],
- "rank": 60
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- {
- "comment": "Random: for a finite field with known primitive root",
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- [
- "IsNonTrivial",
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- "Tester(IsFinite)",
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- "IsDistributiveLOpESum",
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- "IsLeftActedOnByRing",
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- "Tester(IsAssociative)",
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- "Tester(IsRDistributive)",
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- "rank": 59
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- {
- "comment": "Random: Alg",
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- [
- "IsAlgebraicExtension"
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- "rank": 55
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- {
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- [
- "IsWholeFamily",
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- "rank": 49
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- {
- "comment": "Random: for a pcp group",
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- [
- "IsMagmaWithInverses",
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- "Tester(IsAssociative)",
- "CategoryCollections(IsPcpElement)"
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- "rank": 48
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- {
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- [
- "IsFreeLeftModule",
- "IsFullMatrixModule",
- "Tester(IsFullMatrixModule)"
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- "rank": 48
- },
- {
- "comment": "Random: for full row module",
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- [
- "IsFreeLeftModule",
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- "Tester(IsFullRowModule)"
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- "rank": 48
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- {
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- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsSubgroupFpGroup"
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- "rank": 46
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- {
- "comment": "Random: pcgs computable groups",
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- [
- "IsFinite",
- "Tester(IsFinite)",
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- "Tester(IsAssociative)",
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- ]
- ],
- "rank": 45
- },
- {
- "comment": "Random: for a free group",
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- [
- "IsMagmaWithInverses",
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- "Tester(IsAssociative)",
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- "rank": 44
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- {
- "comment": "Random: LAGUNA: for a Lie algebra coming from an associative algebra",
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- [
- "IsExtLSet",
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- "IsDistributiveLOpESum",
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- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsJacobianRing",
- "Tester(IsJacobianRing)",
- "IsZeroSquaredRing",
- "Tester(IsZeroSquaredRing)",
- "IsLieAlgebraByAssociativeAlgebra"
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- ],
- "rank": 43
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- {
- "comment": "Random: for `Integers'",
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- [
- "IsIntegers"
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- ],
- "rank": 39
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- {
- "comment": "Random: LAGUNA: for full ot normalized unit group of group ring",
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- [
- "IsGroupOfUnitsOfMagmaRing",
- "Tester(IsGroupOfUnitsOfMagmaRing)"
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- ],
- "rank": 37
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- {
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- [
- "CategoryCollections(IsGeneralMapping)",
- "IsFreeLeftModule",
- "IsFullHomModule",
- "Tester(IsFullHomModule)"
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- ],
- "rank": 36
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- {
- "comment": "Random: for a free monoid",
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- [
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
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- ],
- "rank": 24
- },
- {
- "comment": "Random: for a free left module",
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- [
- "IsFreeLeftModule"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "Random: for a free semigroup",
- "filters": [
- [
- "IsMagma",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections((IsWord and IsAssociativeElement))"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "Random: zmodnze : for full collection Z/nZ(m)",
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- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "CategoryCollections(IsZmodnZepsObj)"
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- ],
- "rank": 18
- },
- {
- "comment": "Random: RightCoset",
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- [
- "IsRightCoset"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "Random: for a free magma",
- "filters": [
- [
- "IsMagma",
- "CategoryCollections(IsNonassocWord)"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "Random: for an additive coset",
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- [
- "IsAdditiveCoset"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "Random: for external orbit: via acting domain",
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- [
- "IsExternalOrbit"
- ]
- ],
- "rank": 10
- },
- {
- "aka": [
- "RandomList"
- ],
- "comment": "Random: for a dense small list",
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- [
- "IsList",
- "IsDenseList",
- "IsSmallList",
- "Tester(IsSmallList)"
- ]
- ],
- "rank": 9
- },
- {
- "comment": "Random: double coset",
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- [
- "IsDoubleCoset"
- ]
- ],
- "rank": 8
- },
- {
- "comment": "Random",
- "filters": [
- [
- "CategoryFamily(IsPadicExtensionNumber)"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "Random",
- "filters": [
- [
- "CategoryFamily(IsPurePadicNumber)"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "Random: for an infinite list of generators",
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- [
- "IsList",
- "IsInfiniteListOfGeneratorsRep"
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- ],
- "rank": 4
- },
- {
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- [
- "IsCollection",
- "IsFinite",
- "Tester(IsFinite)"
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- "rank": 4
- },
- {
- "comment": "Random: for a dense (small) list",
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- [
- "IsList",
- "IsDenseList"
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- ],
- "rank": 3
- },
- {
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- [
- "IsCollection"
- ]
- ],
- "rank": 0
- }
- ],
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- "comment": "Random: for two integers",
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- [
- "IsInt"
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- [
- "IsInt"
- ]
- ],
- "rank": 36
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- {
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- [
- "IsRealRandomSource"
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- [
- "IsList"
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- "rank": 5
- },
- {
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- "filters": [
- [
- "IsMersenneTwister"
- ],
- [
- "IsList"
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- "rank": 5
- },
- {
- "comment": "Random",
- "filters": [
- [
- "IsGAPRandomSource"
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- [
- "IsList"
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- "rank": 5
- },
- {
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- "filters": [
- [
- "IsGlobalRandomSource"
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- [
- "IsList"
- ]
- ],
- "rank": 5
- },
- {
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- [
- "IsRandomSource"
- ],
- [
- "IsList"
- ]
- ],
- "rank": 4
- }
- ],
- "3args": [
- {
- "comment": "Random: for a real random source and two integers",
- "filters": [
- [
- "IsRealRandomSource"
- ],
- [
- "IsInt"
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- [
- "IsInt"
- ]
- ],
- "rank": 39
- },
- {
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- "filters": [
- [
- "IsMersenneTwister"
- ],
- [
- "IsInt"
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- [
- "IsInt"
- ]
- ],
- "rank": 39
- },
- {
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- "filters": [
- [
- "IsRandomSource"
- ],
- [
- "IsInt"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 38
- }
- ],
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- "5args": [],
- "6args": []
- },
- "name": "Random",
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- },
- {
- "aka": [
- "PseudoRandom"
- ],
- "filters": [
- [
- [
- "IsListOrCollection"
- ]
- ]
- ],
- "locations": [
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- }
- ],
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- {
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- [
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- {
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- [
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- "rank": 36
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- {
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- [
- "IsPolynomialRing"
- ]
- ],
- "rank": 27
- },
- {
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- [
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- ],
- "rank": 16
- },
- {
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- [
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- ],
- "rank": 8
- },
- {
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- [
- "IsListOrCollection"
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- ],
- "rank": 1
- }
- ],
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- },
- "name": "PseudoRandom",
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- {
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- [
- [
- "IsListOrCollection"
- ]
- ]
- ],
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- }
- ],
- "methods": {
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- "1args": [
- {
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- [
- "IsAttributeStoringRep",
- "Tester(PseudoRandomSeed)"
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- ],
- "rank": 20004
- }
- ],
- "2args": [],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "PseudoRandomSeed",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "SetPseudoRandomSeed"
- ],
- "filters": [
- [
- [
- "IsListOrCollection"
- ],
- []
- ]
- ],
- "locations": [
- {
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- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
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- [
- "IsAttributeStoringRep"
- ],
- []
- ],
- "rank": 2
- },
- {
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- [],
- []
- ],
- "rank": 0
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "Setter(PseudoRandomSeed)",
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- },
- {
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- ],
- "filters": [
- [
- [
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- ]
- ],
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- {
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- "methods": {
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- },
- "name": "Tester(PseudoRandomSeed)",
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- {
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- [
- [
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- "methods": {
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- {
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- [
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- "Tester(Enumerator)"
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- ],
- "rank": 20004
- },
- {
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- ],
- "comment": "Enumerator: for full ring Z/nZ",
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- [
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- "Tester(IsWholeFamily)",
- "CategoryCollections(IsZmodnZObjNonprime)"
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- ],
- "rank": 10023
- },
- {
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- [
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- "rank": 10003
- },
- {
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- },
- {
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- [
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- },
- {
- "comment": "Enumerator: use nice monomorphism",
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- [
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- "Tester(IsFinite)",
- "IsMagmaWithInverses",
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- "Tester(IsAssociative)",
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- ],
- "rank": 379
- },
- {
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- "EnumeratorOfTrivialMagmaWithOne"
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- "comment": "Enumerator: for trivial magma-with-one",
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- [
- "IsTrivial",
- "Tester(IsTrivial)",
- "IsMagmaWithOne"
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- ],
- "rank": 71
- },
- {
- "comment": "Enumerator: for `Rationals'",
- "filters": [
- [
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- "Tester(IsNonTrivial)",
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- "IsAssociativeLOpDProd",
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- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
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- "Tester(IsLeftActedOnByDivisionRing)",
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- "Tester(IsPrimeField)"
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- ],
- "rank": 69
- },
- {
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- "comment": "Enumerator: for a finite prime field",
- "filters": [
- [
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- "Tester(IsNonTrivial)",
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- "Tester(IsFinite)",
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- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
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- "Tester(IsRDistributive)",
- "IsEuclideanRing",
- "IsPrimeField",
- "Tester(IsPrimeField)"
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- ],
- "rank": 60
- },
- {
- "comment": "Enumerator: for a permutation group",
- "filters": [
- [
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- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
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- ],
- "rank": 58
- },
- {
- "comment": "Enumerator: for AffineCrystGroup",
- "filters": [
- [
- "IsAffineCrystGroupOnLeftOrRight",
- "Tester(IsAffineCrystGroupOnLeftOrRight)"
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- ],
- "rank": 50
- },
- {
- "comment": "Enumerator: for enumerator of a free group",
- "filters": [
- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
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- ],
- "rank": 47
- },
- {
- "comment": "Enumerator: fp gp.",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsSubgroupFpGroup"
- ]
- ],
- "rank": 46
- },
- {
- "comment": "Enumerator: finite pc computable groups",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CanEasilyComputePcgs"
- ]
- ],
- "rank": 45
- },
- {
- "comment": "Enumerator: for integers",
- "filters": [
- [
- "IsIntegers"
- ]
- ],
- "rank": 39
- },
- {
- "aka": [
- "GroupEnumeratorByClosure"
- ],
- "comment": "Enumerator: generic method for a group",
- "filters": [
- [
- "IsAttributeStoringRep",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
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- ],
- "rank": 37
- },
- {
- "aka": [
- "EnumeratorOfRing"
- ],
- "comment": "Enumerator: generic method for a ring-with-one with known generators",
- "filters": [
- [
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRingWithOne)"
- ]
- ],
- "rank": 30
- },
- {
- "aka": [
- "EnumeratorOfIdeal"
- ],
- "comment": "Enumerator: generic method for a two-sided ideal with known generators",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfTwoSidedIdeal)"
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- ],
- "rank": 27
- },
- {
- "comment": "Enumerator: generic method for a right ideal with known generators",
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- [
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "IsRDistributive",
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- "Tester(GeneratorsOfRightIdeal)"
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- ],
- "rank": 27
- },
- {
- "comment": "Enumerator: generic method for a left ideal with known generators",
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- [
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
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- "Tester(GeneratorsOfLeftIdeal)"
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- ],
- "rank": 27
- },
- {
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- [
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- "IsNearAdditiveMagma",
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- ],
- "rank": 27
- },
- {
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- [
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- "IsNearAdditiveMagma",
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- "IsRDistributive",
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- "Tester(GeneratorsOfRightIdeal)"
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- ],
- "rank": 27
- },
- {
- "comment": "Enumerator: generic method for a left ideal with known generators",
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- [
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
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- "Tester(GeneratorsOfLeftIdeal)"
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- ],
- "rank": 27
- },
- {
- "comment": "Enumerator: generic method for a ring with known generators",
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- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRing)"
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- ],
- "rank": 27
- },
- {
- "comment": "Enumerator: for a free monoid",
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- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
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- ],
- "rank": 26
- },
- {
- "comment": "Enumerator: for free left module (delegate to 'EnumeratorByBasis')",
- "filters": [
- [
- "IsFreeLeftModule"
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- ],
- "rank": 23
- },
- {
- "comment": "Enumerator: for a full transformation semigroup",
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- [
- "IsFullTransformationSemigroup",
- "Tester(IsFullTransformationSemigroup)"
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- ],
- "rank": 22
- },
- {
- "comment": "Enumerator: for a Rees 0-matrix semigroup",
- "filters": [
- [
- "IsReesZeroMatrixSemigroup",
- "Tester(IsReesZeroMatrixSemigroup)",
- "Tester(UnderlyingSemigroup)"
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- ],
- "rank": 20
- },
- {
- "comment": "Enumerator: for a free semigroup",
- "filters": [
- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsMagma",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections((IsWord and IsAssociativeElement))"
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- ],
- "rank": 20
- },
- {
- "comment": "Enumerator: for an underlying relation of a general mapping",
- "filters": [
- [
- "IsCollection",
- "IsGeneralizedDomain",
- "CategoryCollections(IsDirectProductElement)",
- "Tester(UnderlyingGeneralMapping)"
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- ],
- "rank": 20
- },
- {
- "aka": [
- "EnumeratorOfTrivialAdditiveMagmaWithZero"
- ],
- "comment": "Enumerator: for trivial add. magma-with-zero",
- "filters": [
- [
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- "Tester(IsTrivial)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveMagmaWithZero",
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- "Tester(IsAdditivelyCommutative)"
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- ],
- "rank": 19
- },
- {
- "comment": "Enumerator: zmodnze : for full collection Z/nZ(m)",
- "filters": [
- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "CategoryCollections(IsZmodnZepsObj)"
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- ],
- "rank": 18
- },
- {
- "comment": "Enumerator: for a semigroup ideal",
- "filters": [
- [
- "Tester(GeneratorsOfMagmaIdeal)",
- "IsSemigroupIdeal",
- "Tester(IsSemigroupIdeal)"
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- ],
- "rank": 18
- },
- {
- "comment": "Enumerator: for a Rees matrix semigroup",
- "filters": [
- [
- "IsReesMatrixSemigroup",
- "Tester(IsReesMatrixSemigroup)"
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- ],
- "rank": 17
- },
- {
- "aka": [
- "EnumeratorOfMagmaIdeal"
- ],
- "comment": "Enumerator: generic method for a magma ideal",
- "filters": [
- [
- "IsAttributeStoringRep",
- "IsLeftActedOnBySuperset",
- "IsRightActedOnBySuperset",
- "IsMagma"
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- ],
- "rank": 17
- },
- {
- "comment": "Enumerator: for a right coset",
- "filters": [
- [
- "IsRightCoset"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "Enumerator: for a left semigroup ideal",
- "filters": [
- [
- "Tester(GeneratorsOfExtLSet)",
- "IsLeftSemigroupIdeal",
- "Tester(IsLeftSemigroupIdeal)"
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- ],
- "rank": 16
- },
- {
- "comment": "Enumerator: for a right semigroup ideal",
- "filters": [
- [
- "Tester(GeneratorsOfExtRSet)",
- "IsRightSemigroupIdeal",
- "Tester(IsRightSemigroupIdeal)"
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- ],
- "rank": 16
- },
- {
- "comment": "Enumerator: for a generic semigroup",
- "filters": [
- [
- "IsMagma",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
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- ],
- "rank": 16
- },
- {
- "comment": "Enumerator: for a free magma",
- "filters": [
- [
- "IsWholeFamily",
- "Tester(IsWholeFamily)",
- "IsMagma",
- "CategoryCollections(IsWord)"
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- ],
- "rank": 14
- },
- {
- "aka": [
- "EnumeratorOfAdditiveMagma"
- ],
- "comment": "Enumerator: generic method for an add. magma",
- "filters": [
- [
- "IsAttributeStoringRep",
- "IsNearAdditiveMagma",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
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- ],
- "rank": 14
- },
- {
- "comment": "Enumerator",
- "filters": [
- [
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- ],
- "rank": 13
- },
- {
- "aka": [
- "EnumeratorOfMagma"
- ],
- "comment": "Enumerator: generic method for a magma",
- "filters": [
- [
- "IsAttributeStoringRep",
- "IsMagma"
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- ],
- "rank": 13
- },
- {
- "comment": "Enumerator",
- "filters": [
- [
- "IsRationalClassPermGroupRep"
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- ],
- "rank": 12
- },
- {
- "comment": "Enumerator: for an additive coset",
- "filters": [
- [
- "IsAdditiveCoset"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "Enumerator",
- "filters": [
- [
- "IsRationalClassGroupRep"
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- ],
- "rank": 11
- },
- {
- "comment": "Enumerator: xorb by stabilizer",
- "filters": [
- [
- "IsExternalOrbitByStabilizerRep"
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- ],
- "rank": 11
- },
- {
- "comment": "Enumerator: <xorb by pcgs>",
- "filters": [
- [
- "IsExternalOrbit",
- "IsExternalSetByPcgs"
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- ],
- "rank": 11
- },
- {
- "comment": "Enumerator: for external orbit: compute orbit",
- "filters": [
- [
- "IsExternalOrbit"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "Enumerator: for external subset with home enumerator",
- "filters": [
- [
- "IsExternalSubset",
- "Tester(HomeEnumerator)"
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- ],
- "rank": 10
- },
- {
- "comment": "Enumerator: method for a subspaces domain",
- "filters": [
- [
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- "IsSubspacesVectorSpaceDefaultRep"
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- ],
- "rank": 10
- },
- {
- "comment": "Enumerator: for a magma congruence class",
- "filters": [
- [
- "IsCongruenceClass"
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- ],
- "rank": 10
- },
- {
- "aka": [
- "IncludedElements"
- ],
- "comment": "Enumerator: for degenerated residue class unions of Z^2 (ResClasses)",
- "filters": [
- [
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- "Tester(IsFinite)",
- "IsResidueClassUnionOfZxZ"
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- ],
- "rank": 9
- },
- {
- "comment": "Enumerator: for a double coset",
- "filters": [
- [
- "IsDoubleCoset"
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- ],
- "rank": 8
- },
- {
- "comment": "Enumerator",
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- [
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- "IsCollection",
- "Tester(EnumeratorSorted)",
- "IsGeneralizedDomain"
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- ],
- "rank": 8
- },
- {
- "comment": "Enumerator: for sparse hash tables",
- "filters": [
- [
- "IsHash",
- "IsSparseHashRep"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "Enumerator: for dense hash tables",
- "filters": [
- [
- "IsDenseHashRep"
- ]
- ],
- "rank": 7
- },
- {
- "comment": "Enumerator: external set -> HomeEnumerator",
- "filters": [
- [
- "IsExternalSet"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "Enumerator: for list dictionaries",
- "filters": [
- [
- "IsListDictionary"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "Enumerator: for equivalence classes",
- "filters": [
- [
- "IsEquivalenceClass"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "Enumerator: for a domain with stored domain generators",
- "filters": [
- [
- "IsCollection",
- "IsGeneralizedDomain",
- "Tester(GeneratorsOfDomain)"
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- ],
- "rank": 6
- },
- {
- "aka": [
- "IMMUTABLE_COPY_OBJ",
- "Immutable"
- ],
- "comment": "Enumerator: for a collection that is a list",
- "filters": [
- [
- "IsList",
- "IsCollection"
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- ],
- "rank": 5
- },
- {
- "comment": "Enumerator",
- "filters": [
- [
- "IsAttributeStoringRep",
- "IsCollection",
- "Tester(AsList)"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "Enumerator: for a list",
- "filters": [
- [
- "IsList"
- ]
- ],
- "rank": 2
- }
- ],
- "2args": [],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "Enumerator",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "SetEnumerator"
- ],
- "filters": [
- [
- [
- "IsListOrCollection"
- ],
- []
- ]
- ],
- "locations": [
- {
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- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "Setter(Enumerator): system setter",
- "filters": [
- [
- "IsAttributeStoringRep"
- ],
- []
- ],
- "rank": 2
- },
- {
- "comment": "Setter(Enumerator): default method, does nothing",
- "filters": [
- [],
- []
- ],
- "rank": 0
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "Setter(Enumerator)",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "HasEnumerator"
- ],
- "filters": [
- [
- [
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- ]
- ],
- "locations": [
- {
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- ],
- "methods": {
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- "1args": [],
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- "4args": [],
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- "6args": []
- },
- "name": "Tester(Enumerator)",
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- },
- {
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- [
- [
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- ]
- ],
- "locations": [
- {
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- ],
- "methods": {
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- "rank": 20004
- },
- {
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- "rank": 10003
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- {
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- "rank": 60
- },
- {
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- "rank": 50
- },
- {
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- "IsPlistRep"
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- "rank": 21
- },
- {
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- "rank": 5
- },
- {
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- "rank": 5
- },
- {
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- "rank": 2
- }
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- },
- "name": "EnumeratorSorted",
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- {
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- "filters": [
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- },
- {
- "comment": "IsSubset: field, 8bit-vector",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsFinite",
- "Tester(IsFinite)",
- "CategoryCollections(IsFFE)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "CategoryCollections(IsFFE)",
- "IsGF2VectorRep"
- ]
- ],
- "rank": 472
- },
- {
- "comment": "IsSubset: polynomial rings",
- "filters": [
- [
- "IsPolynomialRing"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 129
- },
- {
- "comment": "IsSubset: for two finite fields in the same family",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsFinite",
- "Tester(IsFinite)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsFinite",
- "Tester(IsFinite)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ]
- ],
- "rank": 116
- },
- {
- "comment": "IsSubset: for Integers and Rationals (ResClasses)",
- "filters": [
- [
- "IsIntegers"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "CategoryCollections(IsCyclotomic)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing",
- "IsPrimeField",
- "Tester(IsPrimeField)"
- ]
- ],
- "rank": 109
- },
- {
- "comment": "IsSubset",
- "filters": [
- [
- "IsAffineCrystGroupOnLeft",
- "Tester(IsAffineCrystGroupOnLeft)"
- ],
- [
- "IsAffineCrystGroupOnRight",
- "Tester(IsAffineCrystGroupOnRight)"
- ]
- ],
- "rank": 104
- },
- {
- "comment": "IsSubset",
- "filters": [
- [
- "IsAffineCrystGroupOnRight",
- "Tester(IsAffineCrystGroupOnRight)"
- ],
- [
- "IsAffineCrystGroupOnLeft",
- "Tester(IsAffineCrystGroupOnLeft)"
- ]
- ],
- "rank": 104
- },
- {
- "aka": [
- "DivisionRing_IsSubset"
- ],
- "comment": "IsSubset: for two division rings",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ]
- ],
- "rank": 104
- },
- {
- "comment": "IsSubset: for Z_pi and Rationals (ResClasses)",
- "filters": [
- [
- "IsZ_pi",
- "Tester(IsZ_pi)"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "CategoryCollections(IsCyclotomic)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing",
- "IsPrimeField",
- "Tester(IsPrimeField)"
- ]
- ],
- "rank": 102
- },
- {
- "comment": "IsSubset: for Rationals and Z_(pi) (ResClasses)",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "CategoryCollections(IsCyclotomic)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing",
- "IsPrimeField",
- "Tester(IsPrimeField)"
- ],
- [
- "IsZ_pi",
- "Tester(IsZ_pi)"
- ]
- ],
- "rank": 102
- },
- {
- "comment": "IsSubset: for subgroups of free groups",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsFinitelyGeneratedGroup",
- "Tester(IsFinitelyGeneratedGroup)",
- "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsFinitelyGeneratedGroup",
- "Tester(IsFinitelyGeneratedGroup)",
- "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
- ]
- ],
- "rank": 100
- },
- {
- "comment": "IsSubset: for certain cyclotomic semirings",
- "filters": [
- [
- "CategoryCollections(IsCyclotomic)",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "CategoryCollections(IsCyclotomic)",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 82
- },
- {
- "comment": "IsSubset: 2-sided ideal in ring, naive",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(LeftActingRingOfIdeal)",
- "Tester(RightActingRingOfIdeal)"
- ]
- ],
- "rank": 80
- },
- {
- "comment": "IsSubset: subgroups of fp group by quot. rep",
- "filters": [
- [
- "IsSubgroupFpGroup",
- "IsSubgroupOfWholeGroupByQuotientRep"
- ],
- [
- "IsSubgroupFpGroup",
- "IsSubgroupOfWholeGroupByQuotientRep"
- ]
- ],
- "rank": 76
- },
- {
- "comment": "IsSubset: subgroups of fp group: test generators",
- "filters": [
- [
- "IsSubgroupFpGroup"
- ],
- [
- "Tester(GeneratorsOfMagmaWithInverses)",
- "IsSubgroupFpGroup"
- ]
- ],
- "rank": 75
- },
- {
- "comment": "IsSubset: subgp fp group: via quotient rep",
- "filters": [
- [
- "IsSubgroupFpGroup"
- ],
- [
- "IsSubgroupFpGroup"
- ]
- ],
- "rank": 74
- },
- {
- "comment": "IsSubset: for two FLMLORs-with-one",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 74
- },
- {
- "comment": "IsSubset: for Z_(pi) and Integers (ResClasses)",
- "filters": [
- [
- "IsZ_pi",
- "Tester(IsZ_pi)"
- ],
- [
- "IsIntegers"
- ]
- ],
- "rank": 73
- },
- {
- "comment": "IsSubset: pcgs computable groups",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "Tester(FamilyPcgs)",
- "CanEasilyComputePcgs"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 72
- },
- {
- "comment": "IsSubset: generic method for two groups",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 70
- },
- {
- "comment": "IsSubset: for two FLMLORs",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 68
- },
- {
- "comment": "IsSubset: for Z_(pi)'s (ResClasses)",
- "filters": [
- [
- "IsZ_pi",
- "Tester(IsZ_pi)"
- ],
- [
- "IsZ_pi",
- "Tester(IsZ_pi)"
- ]
- ],
- "rank": 66
- },
- {
- "comment": "IsSubset: for two rings-with-one",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRingWithOne)"
- ]
- ],
- "rank": 56
- },
- {
- "comment": "IsSubset: for two rings",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(GeneratorsOfRing)"
- ]
- ],
- "rank": 53
- },
- {
- "comment": "IsSubset: for two free left modules",
- "filters": [
- [
- "IsFreeLeftModule"
- ],
- [
- "IsFreeLeftModule"
- ]
- ],
- "rank": 46
- },
- {
- "comment": "IsSubset: for two magmas with inverses",
- "filters": [
- [
- "IsMagmaWithInverses"
- ],
- [
- "IsMagmaWithInverses"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "IsSubset: for two additive magmas with inverses",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ],
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "IsSubset: for two additive magmas with zero",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveMagmaWithZero",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ],
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveMagmaWithZero",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "IsSubset: for two magmas with one",
- "filters": [
- [
- "IsMagmaWithOne"
- ],
- [
- "IsMagmaWithOne"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "IsSubset: for two additive magmas",
- "filters": [
- [
- "IsNearAdditiveMagma",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ],
- [
- "IsNearAdditiveMagma",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "IsSubset: for two magmas",
- "filters": [
- [
- "IsMagma"
- ],
- [
- "IsMagma"
- ]
- ],
- "rank": 22
- },
- {
- "aka": [
- "IsSubsetSet"
- ],
- "comment": "IsSubset: for two collections that are internal lists",
- "filters": [
- [
- "IsList",
- "IsInternalRep",
- "IsCollection"
- ],
- [
- "IsList",
- "IsInternalRep",
- "IsCollection"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "IsSubset: for two internal lists",
- "filters": [
- [
- "IsList",
- "IsInternalRep"
- ],
- [
- "IsList",
- "IsInternalRep"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "IsSubset: for collection and empty list",
- "filters": [
- [
- "IsCollection"
- ],
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "IsSubset: for empty list and collection",
- "filters": [
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "IsSubset: for two residue class unions in different rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "IsSubset: for two residue class unions in different rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "IsSubset: for two residue class unions in sparse rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "IsSubset: for two residue class unions in standard rep. (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ],
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "IsSubset: for two unions of residue classes with fixed rep's (ResClasses)",
- "filters": [
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ],
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "IsSubset: for a residue class union and the base ring (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion"
- ],
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "IsSubset: for the base ring and a residue class union (ResClasses)",
- "filters": [
- [
- "IsCollection",
- "IsGeneralizedDomain"
- ],
- [
- "IsResidueClassUnion"
- ]
- ],
- "rank": 11
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- "rank": 44
- },
- {
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- ],
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- "IsBlockMatrixRep"
- ]
- ],
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- },
- {
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- ],
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- "IsGeneralizedRowVector"
- ]
- ],
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- },
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- "Tester(RespectsMultiplication)",
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- "RespectsMultiplication",
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- ],
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- },
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- ],
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- },
- {
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- "Tester(IsSingleValued)",
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- ]
- ],
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- },
- {
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- "Tester(IsSingleValued)"
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- ],
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- },
- {
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- "Tester(IsSingleValued)"
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- "IsSingleValued",
- "Tester(IsSingleValued)",
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- ]
- ],
- "rank": 38
- },
- {
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- "Tester(IsSingleValued)"
- ]
- ],
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- },
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- ],
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- ]
- ],
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- },
- {
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- "IsLogOrderedFFE",
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- ],
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- "IsInternalRep"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "+",
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- "IsCoeffsModConwayPolRep"
- ]
- ],
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- },
- {
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- [
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- "IsModulusRep"
- ]
- ],
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- },
- {
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- "IsModulusRep"
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- [
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- ]
- ],
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- },
- {
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- ],
- [
- "IsAlgBFRep"
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- },
- {
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- ],
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- },
- {
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- },
- {
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- ],
- [
- "IsKroneckerConstRep"
- ]
- ],
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- },
- {
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- ],
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- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
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- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "+",
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- "Tester(IsSmallList)",
- "IsListDefault"
- ],
- [
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- "Tester(IsSmallList)",
- "IsListDefault"
- ]
- ],
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- },
- {
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- [
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- "IsModulusRep"
- ]
- ],
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- },
- {
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- "IsModulusRep"
- ],
- [
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- ]
- ],
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- },
- {
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- "IsCheckingMatrix"
- ],
- [
- "IsPlistMatrixRep",
- "IsCheckingMatrix"
- ]
- ],
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- },
- {
- "comment": "+",
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- ],
- [
- "IsFFE",
- "IsCoeffsModConwayPolRep"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "+",
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- [
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- ]
- ],
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- },
- {
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- [
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- ]
- ],
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- },
- {
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- ]
- ],
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- },
- {
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- ],
- [
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- "IsModulusRep"
- ]
- ],
- "rank": 32
- },
- {
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- ],
- [
- "IsUnknown"
- ]
- ],
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- },
- {
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- ],
- [
- "IsUnknown"
- ]
- ],
- "rank": 32
- },
- {
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- ],
- [
- "IsCyc"
- ]
- ],
- "rank": 32
- },
- {
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- ],
- [
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- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "+: for an algebra g.m.b.i. and general mapping",
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- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ],
- [
- "IsGeneralMapping"
- ]
- ],
- "rank": 32
- },
- {
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- ],
- [
- "IsNegInfinity"
- ]
- ],
- "rank": 32
- },
- {
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- ],
- [
- "IsNegInfinity"
- ]
- ],
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- },
- {
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- [
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- ]
- ],
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- },
- {
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- [
- "IsInfinity"
- ]
- ],
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- },
- {
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- [
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- ]
- ],
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- },
- {
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- ],
- [
- "IsCyc"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "+: for object, and class function",
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- [
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- ]
- ],
- "rank": 31
- },
- {
- "comment": "+: for class function, and object",
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- ],
- []
- ],
- "rank": 31
- },
- {
- "comment": "+: for two plist matrices",
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- ],
- [
- "IsPlistMatrixRep"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "+",
- "filters": [
- [
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- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 30
- },
- {
- "aka": [
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- ],
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- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
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- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
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- ],
- "rank": 30
- },
- {
- "comment": "+: for general mapping and linear g.m.b.i.",
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- ],
- [
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- "IsLinearGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 30
- },
- {
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- "IsLinearGeneralMappingByImagesDefaultRep"
- ],
- [
- "IsGeneralMapping"
- ]
- ],
- "rank": 30
- },
- {
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- ],
- [
- "IsDirectProductElement"
- ]
- ],
- "rank": 30
- },
- {
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- ],
- [
- "IsRat"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "+: for rational and float",
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- ],
- [
- "IsFloat"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "+",
- "filters": [
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- "IsPadicExtensionNumber"
- ],
- [
- "IsPadicExtensionNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "+",
- "filters": [
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- ],
- [
- "IsPurePadicNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "+: zmodnze : for cyclotomic and element in Z/nZ(m) (ZmodnZepsRep)",
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- "IsZmodnZepsRep"
- ]
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- },
- {
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- "IsZmodnZepsRep"
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- ]
- ],
- "rank": 28
- },
- {
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- "Tester(IsPolynomial)"
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- [
- "IsPolynomial",
- "Tester(IsPolynomial)"
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- ],
- "rank": 28
- },
- {
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- "IsZmodnZepsRep"
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- "IsZmodnZepsRep"
- ]
- ],
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- },
- {
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- ],
- [
- "IsRationalFunction"
- ]
- ],
- "rank": 26
- },
- {
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- "IsDenseCoeffVectorRep"
- ],
- [
- "IsSCRingObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
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- "IsLieObject"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ]
- ],
- "rank": 26
- },
- {
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- "IsDenseCoeffVectorRep"
- ],
- [
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- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
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- ],
- [
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- ]
- ],
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- },
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- "IsMultiplicativeElement"
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- ]
- ],
- "rank": 25
- },
- {
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- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 25
- },
- {
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- "IsAdditiveElement",
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- [
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- ]
- ],
- "rank": 25
- },
- {
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- "IsMultiplicativeElement"
- ]
- ],
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- },
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- ]
- ],
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- "Tester(IsLaurentPolynomial)"
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- ],
- "rank": 25
- },
- {
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- [
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- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 25
- },
- {
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- "IsAdditiveElement",
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- "Tester(IsUnivariateRationalFunction)",
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- "Tester(IsLaurentPolynomial)"
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- ],
- "rank": 25
- },
- {
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- ],
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- [
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- ]
- ],
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- },
- {
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- ],
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- [
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- ],
- "rank": 25
- },
- {
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- ],
- [
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- "IsCheckingVector"
- ]
- ],
- "rank": 24
- },
- {
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- "IsUEALatticeElement"
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- ],
- "rank": 24
- },
- {
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- [
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- "IsBinaryRelationOnPointsRep"
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- ],
- "rank": 24
- },
- {
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- ]
- ],
- "rank": 24
- },
- {
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- ]
- ],
- "rank": 24
- },
- {
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- [
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- "rank": 24
- },
- {
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- "rank": 23
- },
- {
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- ]
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- },
- {
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- ]
- ],
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- },
- {
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- "DIFF_DEFAULT"
- ],
- "comment": "-: for external add. element, and additive-element-with-zero",
- "filters": [
- [
- "IsExtAElement"
- ],
- [
- "IsNearAdditiveElementWithInverse"
- ]
- ],
- "rank": 5
- },
- {
- "comment": "-: for ring element and residue class union (ResClasses)",
- "filters": [
- [],
- [
- "IsListOrCollection"
- ]
- ],
- "rank": 1
- },
- {
- "comment": "-: for residue class union and ring element (ResClasses)",
- "filters": [
- [
- "IsListOrCollection"
- ],
- []
- ],
- "rank": 1
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "-",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "*",
- "PROD"
- ],
- "filters": [
- [
- [
- "IsExtRElement"
- ],
- [
- "IsExtLElement"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/arith.gd",
- "line": 1522
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "*: additive element with zero * zero integer",
- "filters": [
- [
- "IsNearAdditiveElementWithZero"
- ],
- [
- "IsInt",
- "IsZeroCyc"
- ]
- ],
- "rank": 10024
- },
- {
- "aka": [
- "PROD_INT_OBJ"
- ],
- "comment": "*: zero integer * additive element with zero",
- "filters": [
- [
- "IsInt",
- "IsZeroCyc"
- ],
- [
- "IsNearAdditiveElementWithZero"
- ]
- ],
- "rank": 10024
- },
- {
- "comment": "*: objects with memory",
- "filters": [
- [
- "IsObjWithMemory"
- ],
- [
- "IsObjWithMemory"
- ]
- ],
- "rank": 214
- },
- {
- "comment": "*: straight line program elements",
- "filters": [
- [
- "IsStraightLineProgElm"
- ],
- [
- "IsStraightLineProgElm"
- ]
- ],
- "rank": 214
- },
- {
- "comment": "*: for a row vector and a matrix with memory",
- "filters": [
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "IsListDefault"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsObjWithMemory"
- ]
- ],
- "rank": 151
- },
- {
- "comment": "*: for a matrix with memory and a scalar",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsObjWithMemory"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 144
- },
- {
- "comment": "*: for a scalar and a matrix with memory",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsObjWithMemory"
- ]
- ],
- "rank": 144
- },
- {
- "comment": "*: x with straight line program element",
- "filters": [
- [
- "IsMultiplicativeElement"
- ],
- [
- "IsStraightLineProgElm"
- ]
- ],
- "rank": 110
- },
- {
- "comment": "*: straight line program element with x",
- "filters": [
- [
- "IsStraightLineProgElm"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 110
- },
- {
- "comment": "*: More efficient non-recursive kernel method for vector*matrix of cyclotomics",
- "filters": [
- [
- "IsPlistRep",
- "IsSmallList",
- "Tester(IsSmallList)",
- "CategoryCollections(IsCyclotomic)",
- "IsListDefault"
- ],
- [
- "IsPlistRep",
- "IsSmallList",
- "Tester(IsSmallList)",
- "CategoryCollections(CategoryCollections(IsCyclotomic))",
- "IsListDefault",
- "IsRectangularTable",
- "Tester(IsRectangularTable)"
- ]
- ],
- "rank": 96
- },
- {
- "comment": "*: More efficient non-recursive method for matrix*matrix of cyclotomics",
- "filters": [
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "CategoryCollections(CategoryCollections(IsCyclotomic))",
- "IsListDefault"
- ],
- [
- "IsPlistRep",
- "IsSmallList",
- "Tester(IsSmallList)",
- "CategoryCollections(CategoryCollections(IsCyclotomic))",
- "IsListDefault",
- "IsRectangularTable",
- "Tester(IsRectangularTable)"
- ]
- ],
- "rank": 95
- },
- {
- "aka": [
- "PROD_GF2MAT_GF2MAT"
- ],
- "comment": "*: for GF2 matrix and GF2 matrix",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsListDefault",
- "IsGF2MatrixRep"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsListDefault",
- "IsGF2MatrixRep"
- ]
- ],
- "rank": 90
- },
- {
- "aka": [
- "PROD_MAT8BIT_MAT8BIT"
- ],
- "comment": "*: 8 bit matrix * 8 bit matrix",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "Is8BitMatrixRep"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "Is8BitMatrixRep"
- ]
- ],
- "rank": 88
- },
- {
- "comment": "*: for two empty matrices",
- "filters": [
- [
- "IsTable",
- "IsEmpty",
- "Tester(IsEmpty)",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ],
- [
- "IsTable",
- "IsEmpty",
- "Tester(IsEmpty)",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 84
- },
- {
- "aka": [
- "PROD_GF2VEC_GF2MAT"
- ],
- "comment": "*: for GF2 vector and GF2 matrix",
- "filters": [
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsListDefault",
- "IsGF2VectorRep"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsListDefault",
- "IsGF2MatrixRep"
- ]
- ],
- "rank": 78
- },
- {
- "aka": [
- "PROD_MAT8BIT_VEC8BIT"
- ],
- "comment": "*: 8 bit matrix * 8 bit vector",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "Is8BitMatrixRep"
- ],
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "Is8BitVectorRep"
- ]
- ],
- "rank": 77
- },
- {
- "aka": [
- "PROD_VEC8BIT_MAT8BIT"
- ],
- "comment": "*: 8 bit vector * 8 bit matrix",
- "filters": [
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "Is8BitVectorRep"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "Is8BitMatrixRep"
- ]
- ],
- "rank": 77
- },
- {
- "aka": [
- "PROD_VEC8BIT_MATRIX"
- ],
- "comment": "*: For an 8 bit vector and a compatible matrix",
- "filters": [
- [
- "IsList",
- "IsHomogeneousList",
- "IsSmallList",
- "Tester(IsSmallList)",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "Is8BitVectorRep"
- ],
- [
- "IsTable",
- "IsPlistRep",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 74
- },
- {
- "comment": "*: for two ordinary block matrices",
- "filters": [
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ],
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ]
- ],
- "rank": 74
- },
- {
- "aka": [
- "PROD_GF2VEC_ANYMAT"
- ],
- "comment": "*: For a GF2 vector and a compatible matrix",
- "filters": [
- [
- "IsList",
- "IsHomogeneousList",
- "IsSmallList",
- "Tester(IsSmallList)",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsGF2VectorRep"
- ],
- [
- "IsTable",
- "IsPlistRep",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 71
- },
- {
- "comment": "*: for two characters",
- "filters": [
- [
- "IsCharacter",
- "Tester(IsCharacter)"
- ],
- [
- "IsCharacter",
- "Tester(IsCharacter)"
- ]
- ],
- "rank": 70
- },
- {
- "aka": [
- "PROD_GF2MAT_GF2VEC"
- ],
- "comment": "*: for GF2 matrix and GF2 vector",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsListDefault",
- "IsGF2MatrixRep"
- ],
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsListDefault",
- "IsGF2VectorRep"
- ]
- ],
- "rank": 70
- },
- {
- "comment": "*: for two virtual characters",
- "filters": [
- [
- "IsVirtualCharacter",
- "Tester(IsVirtualCharacter)"
- ],
- [
- "IsVirtualCharacter",
- "Tester(IsVirtualCharacter)"
- ]
- ],
- "rank": 66
- },
- {
- "aka": [
- "PROD_GF2VEC_GF2VEC"
- ],
- "comment": "*: for GF2 vectors",
- "filters": [
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsListDefault",
- "IsGF2VectorRep"
- ],
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsListDefault",
- "IsGF2VectorRep"
- ]
- ],
- "rank": 66
- },
- {
- "aka": [
- "PROD_VEC8BIT_VEC8BIT"
- ],
- "comment": "*: For 2 8 bit vectors",
- "filters": [
- [
- "IsList",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "CategoryCollections(IsAdditiveElement)",
- "CategoryCollections(IsMultiplicativeElement)",
- "Is8BitVectorRep"
- ],
- [
- "IsList",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "CategoryCollections(IsAdditiveElement)",
- "CategoryCollections(IsMultiplicativeElement)",
- "Is8BitVectorRep"
- ]
- ],
- "rank": 64
- },
- {
- "comment": "*: for two class functions",
- "filters": [
- [
- "IsClassFunction"
- ],
- [
- "IsClassFunction"
- ]
- ],
- "rank": 62
- },
- {
- "comment": "*: for ffe and ordinary block matrix of integers",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsOrdinaryMatrix",
- "CategoryCollections(CategoryCollections(IsCyclotomic))",
- "IsBlockMatrixRep"
- ]
- ],
- "rank": 62
- },
- {
- "comment": "*: for ordinary block matrix of integers and ffe",
- "filters": [
- [
- "IsOrdinaryMatrix",
- "CategoryCollections(CategoryCollections(IsCyclotomic))",
- "IsBlockMatrixRep"
- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 62
- },
- {
- "comment": "*: for two null map matrices",
- "filters": [
- [
- "IsNullMapMatrix"
- ],
- [
- "IsNullMapMatrix"
- ]
- ],
- "rank": 62
- },
- {
- "comment": "*: for matrix and null map matrix",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ],
- [
- "IsNullMapMatrix"
- ]
- ],
- "rank": 61
- },
- {
- "comment": "*: for GF2 matrix and GF2 element",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsListDefault",
- "IsGF2MatrixRep"
- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 60
- },
- {
- "comment": "*: for GF2 element and GF2 matrix",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsListDefault",
- "IsGF2MatrixRep"
- ]
- ],
- "rank": 60
- },
- {
- "comment": "*: scalar * 8 bit matrix",
- "filters": [
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "Is8BitMatrixRep"
- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "*: scalar * 8 bit matrix",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "Is8BitMatrixRep"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "*: for empty list, and empty matrix",
- "filters": [
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ],
- [
- "IsTable",
- "IsEmpty",
- "Tester(IsEmpty)",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "*: for empty matrix, and empty list",
- "filters": [
- [
- "IsTable",
- "IsEmpty",
- "Tester(IsEmpty)",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ],
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsRowModule",
- "Tester(IsRowModule)"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "*: for two empty row vectors in the same family",
- "filters": [
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ],
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ]
- ],
- "rank": 56
- },
- {
- "comment": "*: for GF2 vector and FFE",
- "filters": [
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsGF2VectorRep"
- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 55
- },
- {
- "comment": "*: for FFE and GF2 vector",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsGF2VectorRep"
- ]
- ],
- "rank": 55
- },
- {
- "comment": "*: for character, and positive integer",
- "filters": [
- [
- "IsCharacter",
- "Tester(IsCharacter)"
- ],
- [
- "IsInt",
- "IsPosRat"
- ]
- ],
- "rank": 54
- },
- {
- "comment": "*: for positive integer, and character",
- "filters": [
- [
- "IsInt",
- "IsPosRat"
- ],
- [
- "IsCharacter",
- "Tester(IsCharacter)"
- ]
- ],
- "rank": 54
- },
- {
- "comment": "*: for ring and right ideal (construct a two-sided ideal)",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(RightActingRingOfIdeal)"
- ]
- ],
- "rank": 53
- },
- {
- "comment": "*: for left ideal and ring (construct a two-sided ideal)",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(LeftActingRingOfIdeal)"
- ],
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 53
- },
- {
- "comment": "*: for integer and ordinary block matrix",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ]
- ],
- "rank": 52
- },
- {
- "comment": "*: for ordinary block matrix and integer",
- "filters": [
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 52
- },
- {
- "comment": "*: for virtual character, and integer",
- "filters": [
- [
- "IsVirtualCharacter",
- "Tester(IsVirtualCharacter)"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 51
- },
- {
- "comment": "*: for integer, and virtual character",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsVirtualCharacter",
- "Tester(IsVirtualCharacter)"
- ]
- ],
- "rank": 51
- },
- {
- "comment": "*: for ring element, and empty matrix",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsTable",
- "IsEmpty",
- "Tester(IsEmpty)",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 50
- },
- {
- "comment": "*: for empty matrix, and ring element",
- "filters": [
- [
- "IsTable",
- "IsEmpty",
- "Tester(IsEmpty)",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 50
- },
- {
- "comment": "*: for empty list and null map matrix",
- "filters": [
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ],
- [
- "IsNullMapMatrix"
- ]
- ],
- "rank": 48
- },
- {
- "comment": "*: for empty list and matrix (ResClasses)",
- "filters": [
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 47
- },
- {
- "comment": "*: for class function, and cyclotomic",
- "filters": [
- [
- "IsClassFunction"
- ],
- [
- "IsCyc"
- ]
- ],
- "rank": 47
- },
- {
- "comment": "*: for cyclotomic, and class function",
- "filters": [
- [
- "IsCyc"
- ],
- [
- "IsClassFunction"
- ]
- ],
- "rank": 47
- },
- {
- "comment": "*: For an 8 bit vector of char 2 and a GF2 vector",
- "filters": [
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "Is8BitVectorRep"
- ],
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsGF2VectorRep"
- ]
- ],
- "rank": 47
- },
- {
- "comment": "*: For a GF2 vector and an 8 bit vector of char 2",
- "filters": [
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsGF2VectorRep"
- ],
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "Is8BitVectorRep"
- ]
- ],
- "rank": 47
- },
- {
- "comment": "*: for vector and ordinary block matrix",
- "filters": [
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject"
- ],
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ]
- ],
- "rank": 46
- },
- {
- "comment": "*: for ordinary block matrix and vector",
- "filters": [
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ],
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject"
- ]
- ],
- "rank": 46
- },
- {
- "comment": "*: for empty row vector, and integer",
- "filters": [
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 46
- },
- {
- "comment": "*: for integer, and empty row vector",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ]
- ],
- "rank": 46
- },
- {
- "comment": "*: for a scalar and Z^2 (ResClasses)",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsRowModule",
- "Tester(IsRowModule)"
- ]
- ],
- "rank": 45
- },
- {
- "comment": "*: for FFE and GF2 vector",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsGF2VectorRep"
- ]
- ],
- "rank": 45
- },
- {
- "comment": "*: for FFE and GF2 vector",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsList",
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "CategoryCollections(IsNearAdditiveElementWithInverse)",
- "IsAdditiveElement",
- "CategoryCollections(IsAdditiveElement)",
- "IsExtLElement",
- "IsExtRElement",
- "CategoryCollections(IsMultiplicativeElement)",
- "IsOddAdditiveNestingDepthObject",
- "IsGF2VectorRep"
- ]
- ],
- "rank": 45
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsRat"
- ],
- [
- "IsList",
- "CategoryCollections(IsPadicNumber)"
- ]
- ],
- "rank": 44
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsList",
- "CategoryCollections(IsPadicNumber)"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 44
- },
- {
- "comment": "*: for a mgrv, and an ordinary block matrix",
- "filters": [
- [
- "IsMultiplicativeGeneralizedRowVector"
- ],
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ]
- ],
- "rank": 43
- },
- {
- "comment": "*: for an ordinary block matrix, and a mgrv",
- "filters": [
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ],
- [
- "IsMultiplicativeGeneralizedRowVector"
- ]
- ],
- "rank": 43
- },
- {
- "aka": [
- "PROD_FFE_VEC8BIT"
- ],
- "comment": "*: For an FFE and an 8 bit vector ",
- "filters": [
- [
- "IsFFE",
- "IsInternalRep"
- ],
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "Is8BitVectorRep"
- ]
- ],
- "rank": 42
- },
- {
- "aka": [
- "PROD_VEC8BIT_FFE"
- ],
- "comment": "*: For an 8 bit vector and an FFE",
- "filters": [
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "Is8BitVectorRep"
- ],
- [
- "IsFFE",
- "IsInternalRep"
- ]
- ],
- "rank": 42
- },
- {
- "comment": "*: for ring element and ordinary block matrix",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ]
- ],
- "rank": 42
- },
- {
- "comment": "*: for ordinary block matrix and ring element",
- "filters": [
- [
- "IsOrdinaryMatrix",
- "IsBlockMatrixRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 42
- },
- {
- "comment": "*: for list in `IsListDefault', and class function",
- "filters": [
- [
- "IsListDefault"
- ],
- [
- "IsClassFunction"
- ]
- ],
- "rank": 41
- },
- {
- "comment": "*: for class function, and list in `IsListDefault'",
- "filters": [
- [
- "IsClassFunction"
- ],
- [
- "IsListDefault"
- ]
- ],
- "rank": 41
- },
- {
- "comment": "*: for a null map matrix and a scalar",
- "filters": [
- [
- "IsNullMapMatrix"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 41
- },
- {
- "comment": "*: for a scalar and a null map matrix",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsNullMapMatrix"
- ]
- ],
- "rank": 41
- },
- {
- "aka": [
- "CharacterTableDirectProduct"
- ],
- "comment": "*: for two nearly character tables (call `CharacterTableDirectProduct')",
- "filters": [
- [
- "IsNearlyCharacterTable"
- ],
- [
- "IsNearlyCharacterTable"
- ]
- ],
- "rank": 40
- },
- {
- "comment": "*: group times element",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 40
- },
- {
- "comment": "*: for vector and null map matrix",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement"
- ],
- [
- "IsNullMapMatrix"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "*: for residue class union of Z^2 and matrix (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnionOfZxZ"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 37
- },
- {
- "comment": "*: for a ring element and the base ring (ResClasses)",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsMagma",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "*: for internal FFE and element in Z/pZ (ModulusRep)",
- "filters": [
- [
- "IsFFE",
- "IsInternalRep"
- ],
- [
- "IsFFE",
- "IsLogOrderedFFE",
- "IsZmodnZObj",
- "IsModulusRep"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "*: for element in Z/pZ (ModulusRep) and internal FFE",
- "filters": [
- [
- "IsFFE",
- "IsLogOrderedFFE",
- "IsZmodnZObj",
- "IsModulusRep"
- ],
- [
- "IsFFE",
- "IsInternalRep"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "*: for the base module and a scalar / matrix (ResClasses)",
- "filters": [
- [
- "IsRowModule",
- "Tester(IsRowModule)"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "*: internal ffe * (large) integer",
- "filters": [
- [
- "IsFFE",
- "IsInternalRep"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "*: for the base ring and a ring element (ResClasses)",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "*: for infinity and positive rational (RCWA)",
- "filters": [
- [
- "IsInfinity"
- ],
- [
- "IsPosRat"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "*: for positive rational and infinity (RCWA)",
- "filters": [
- [
- "IsPosRat"
- ],
- [
- "IsInfinity"
- ]
- ],
- "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
- },
- {
- "aka": [
- "PRODUCT_LAURPOLS"
- ],
- "comment": "*: laurent * laurent",
- "filters": [
- [
- "IsPolynomialFunction",
- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ],
- [
- "IsPolynomialFunction",
- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "*: for ring and ring element (construct a left ideal)",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "*: for ring element and ring (construct a right ideal)",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "IsListDefault"
- ],
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "IsListDefault"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "*: for rational and element in Z/nZ (ModulusRep)",
- "filters": [
- [
- "IsRat"
- ],
- [
- "IsZmodnZObj",
- "IsModulusRep"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "*: for element in Z/nZ (ModulusRep) and rational",
- "filters": [
- [
- "IsZmodnZObj",
- "IsModulusRep"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "*: for list and null map matrix",
- "filters": [
- [
- "IsList"
- ],
- [
- "IsNullMapMatrix"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "*: for infinity and infinity (RCWA)",
- "filters": [
- [
- "IsInfinity"
- ],
- [
- "IsInfinity"
- ]
- ],
- "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": 32
- },
- {
- "comment": "*: for s. c. ring element in dense vector rep. and integer",
- "filters": [
- [
- "IsSCRingObj",
- "IsDenseCoeffVectorRep"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "*: for integer and s. c. ring element in dense vector rep.",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsSCRingObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "*: for s. c. algebra element in dense vector rep. and integer",
- "filters": [
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "*: for integer and s. c. algebra element in dense vector rep.",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "*: for empty row vector, and multiplicative element",
- "filters": [
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "*: for multiplicative element, and empty row vector",
- "filters": [
- [
- "IsMultiplicativeElement"
- ],
- [
- "IsHomogeneousList",
- "IsEmpty",
- "Tester(IsEmpty)",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject",
- "IsEmptyRowVectorRep"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "*: for two plist matrices",
- "filters": [
- [
- "IsPlistMatrixRep"
- ],
- [
- "IsPlistMatrixRep"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsRat"
- ],
- [
- "IsPadicNumber"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsPadicNumber"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsFFE"
- ],
- [
- "IsFFE"
- ]
- ],
- "rank": 30
- },
- {
- "aka": [
- "PRODUCT_UNIVFUNCS"
- ],
- "comment": "*: univariate * univariate",
- "filters": [
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ],
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "*: for two direct product elements",
- "filters": [
- [
- "IsDirectProductElement"
- ],
- [
- "IsDirectProductElement"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "*: for float and rational",
- "filters": [
- [
- "IsFloat"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "*: for rational and float",
- "filters": [
- [
- "IsRat"
- ],
- [
- "IsFloat"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "*: zmodnze : for element x in Z/nZ and y in Z/nZ(m)",
- "filters": [
- [
- "IsZmodnZObj",
- "IsModulusRep"
- ],
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "*: zmodnze : for element x in Z/nZ(m) and y in Z/nZ",
- "filters": [
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ],
- [
- "IsZmodnZObj",
- "IsModulusRep"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "*: for s. c. algebra element and integer",
- "filters": [
- [
- "IsSCAlgebraObj"
- ],
- [
- "IsInt"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "*: for integer and s. c. algebra element",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsSCAlgebraObj"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsPadicExtensionNumber"
- ],
- [
- "IsPadicExtensionNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsPadicExtensionNumber"
- ],
- [
- "IsPurePadicNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsPurePadicNumber"
- ],
- [
- "IsPadicExtensionNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsPurePadicNumber"
- ],
- [
- "IsPurePadicNumber"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*: zmodnze : for element x in Z/nZ(m) (ZmodnZepsRep) and cyclotomic y",
- "filters": [
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ],
- [
- "IsCyclotomic"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*: zmodnze : for cyclotomic x and element y in Z/nZ(m) (ZmodnZepsRep)",
- "filters": [
- [
- "IsCyclotomic"
- ],
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*: polynomial * polynomial",
- "filters": [
- [
- "IsPolynomial",
- "Tester(IsPolynomial)"
- ],
- [
- "IsPolynomial",
- "Tester(IsPolynomial)"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*: for scalar and algebra g.m.b.i.",
- "filters": [
- [
- "IsMultiplicativeElement"
- ],
- [
- "IsGeneralMapping",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 28
- },
- {
- "aka": [
- "RingElmTimesElm"
- ],
- "comment": "*: for rational, and magma ring element",
- "filters": [
- [
- "IsRat"
- ],
- [
- "IsElementOfMagmaRingModuloRelations"
- ]
- ],
- "rank": 28
- },
- {
- "aka": [
- "ElmTimesRingElm"
- ],
- "comment": "*: for magma ring element, and rational",
- "filters": [
- [
- "IsElementOfMagmaRingModuloRelations"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "*: for a plist vector and a plist matrix",
- "filters": [
- [
- "IsPlistVectorRep"
- ],
- [
- "IsPlistMatrixRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
- "filters": [
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ],
- [
- "IsZmodnZepsObj",
- "IsZmodnZepsRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: univariate * coeff",
- "filters": [
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 26
- },
- {
- "aka": [
- "ProdCoeffUnivfunc"
- ],
- "comment": "*: coeff * univariate",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: rat-fun * rat-fun",
- "filters": [
- [
- "IsRationalFunction"
- ],
- [
- "IsRationalFunction"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: for s. c. ring elements in dense vector rep.",
- "filters": [
- [
- "IsSCRingObj",
- "IsDenseCoeffVectorRep"
- ],
- [
- "IsSCRingObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: for two Lie objects in default representation",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: for s. c. algebra elements in dense vector rep.",
- "filters": [
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ],
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: for scalar and linear m.b.m.",
- "filters": [
- [
- "IsMultiplicativeElement"
- ],
- [
- "IsGeneralMapping",
- "IsLinearMappingByMatrixDefaultRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: for scalar and linear g.m.b.i.",
- "filters": [
- [
- "IsMultiplicativeElement"
- ],
- [
- "IsGeneralMapping",
- "IsLinearGeneralMappingByImagesDefaultRep"
- ]
- ],
- "rank": 26
- },
- {
- "comment": "*: for an integer and a residue class union of Z^2 (ResClasses)",
- "filters": [
- [
- "IsInt"
- ],
- [
- "IsResidueClassUnionOfZxZ"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "*: for floats",
- "filters": [
- [
- "IsFloat"
- ],
- [
- "IsFloat"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "*: laurent * coeff",
- "filters": [
- [
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)",
- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 25
- },
- {
- "aka": [
- "ProdCoeffLaurpol"
- ],
- "comment": "*: coeff * laurent",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)",
- "IsLaurentPolynomial",
- "Tester(IsLaurentPolynomial)"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "*: for row vector and Lie object",
- "filters": [
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "*: for Lie object and row vector",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ],
- [
- "IsHomogeneousList",
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsExtLElement",
- "IsExtRElement",
- "IsOddAdditiveNestingDepthObject"
- ]
- ],
- "rank": 25
- },
- {
- "aka": [
- "PROD_LIST_SCL_DEFAULT"
- ],
- "comment": "*: for a default list, and a direct product element",
- "filters": [
- [
- "IsListDefault"
- ],
- [
- "IsDirectProductElement"
- ]
- ],
- "rank": 25
- },
- {
- "aka": [
- "PROD_SCL_LIST_DEFAULT"
- ],
- "comment": "*: for a direct product element, and a default list",
- "filters": [
- [
- "IsDirectProductElement"
- ],
- [
- "IsListDefault"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "*: for two UEALattice elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsUEALatticeElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsUEALatticeElement"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "*: for binary relations on points",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "*: FElm*Alg",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsAlgebraicElement"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "*: Alg*FElm",
- "filters": [
- [
- "IsAlgebraicElement"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "*: rat-fun * coeff",
- "filters": [
- [
- "IsPolynomialFunction"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "*: coeff * rat-fun",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsPolynomialFunction"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "*: additive element with inverse * negative integer",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse"
- ],
- [
- "IsInt",
- "IsNegRat"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "*: negative integer * additive element with inverse",
- "filters": [
- [
- "IsInt",
- "IsNegRat"
- ],
- [
- "IsNearAdditiveElementWithInverse"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "*: for UEALattice element and scalar",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsUEALatticeElement"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "*: for scalar and UEALattice element",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsUEALatticeElement"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "*: for cochain and scalar",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsCochain"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse",
- "IsZero",
- "Tester(IsZero)"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "*: for scalar and cochain",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse",
- "IsZero",
- "Tester(IsZero)"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsCochain"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "*: for s. c. algebra elements",
- "filters": [
- [
- "IsSCAlgebraObj"
- ],
- [
- "IsSCAlgebraObj"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "*: fp algebra elements",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsElementOfFpAlgebra"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsElementOfFpAlgebra"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "*: for two magma ring elements",
- "filters": [
- [
- "IsElementOfMagmaRingModuloRelations"
- ],
- [
- "IsElementOfMagmaRingModuloRelations"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "*: RightCoset with element",
- "filters": [
- [
- "IsRightCoset"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for a scalar and a checking plist vector",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsPlistVectorRep"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for a scalar and a plist vector",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsPlistVectorRep"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for a checking plist vector and a scalar",
- "filters": [
- [
- "IsPlistVectorRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for a plist vector and a scalar",
- "filters": [
- [
- "IsPlistVectorRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for 0-cochain and scalar",
- "filters": [
- [
- "IsCochain",
- "IsZeroCochainRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for scalar and 0-cochain",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsCochain",
- "IsZeroCochainRep"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for ring element, and Lie object in default representation",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for Lie object in default representation, and ring element",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for s. c. algebra element in dense vector rep. and ring element",
- "filters": [
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: for ring element and s. c. algebra element in dense vector rep.",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsSCAlgebraObj",
- "IsDenseCoeffVectorRep"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: additive element * positive integer",
- "filters": [
- [
- "IsNearAdditiveElement"
- ],
- [
- "IsInt",
- "IsPosRat"
- ]
- ],
- "rank": 21
- },
- {
- "comment": "*: positive integer * additive element",
- "filters": [
- [
- "IsInt",
- "IsPosRat"
- ],
- [
- "IsNearAdditiveElement"
- ]
- ],
- "rank": 21
- },
- {
- "aka": [
- "NBitsPcWord_Product"
- ],
- "comment": "*: generic method for n bits pc word rep",
- "filters": [
- [
- "IsMultiplicativeElementWithInverseByPolycyclicCollector",
- "IsNBitsPcWordRep"
- ],
- [
- "IsMultiplicativeElementWithInverseByPolycyclicCollector",
- "IsNBitsPcWordRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for cochain and scalar",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsCochain"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for scalar and cochain",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsCochain"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for a scalar and an algebra module element in packed representation",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsAlgebraModuleElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for an algebra module element in packed representation and a scalar",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsAlgebraModuleElement"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for two magma congruence classes",
- "filters": [
- [
- "IsCongruenceClass"
- ],
- [
- "IsCongruenceClass"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for permutation and binary relation on points",
- "filters": [
- [
- "IsPerm"
- ],
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for binary relation on points and permutation",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "*: for s. c. algebra element and ring element",
- "filters": [
- [
- "IsSCAlgebraObj"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: for ring element and s. c. algebra element",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsSCAlgebraObj"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: fp algebra el*ring el",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsElementOfFpAlgebra"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: ring el *fp algebra el",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsElementOfFpAlgebra"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: for ring element, and magma ring element",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsElementOfMagmaRingModuloRelations"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: for magma ring element, and ring element",
- "filters": [
- [
- "IsElementOfMagmaRingModuloRelations"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: for binary relation on points and transformation",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
- [
- "IsTransformation"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: for transformation and binary relation on points",
- "filters": [
- [
- "IsTransformation"
- ],
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: for zero and total general mapping",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement",
- "IsZero",
- "Tester(IsZero)"
- ],
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)"
- ]
- ],
- "rank": 19
- },
- {
- "comment": "*: for weight rep element and a scalar",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsWeightRepElement"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for weight rep element and a scalar",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsWeightRepElement"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for a direct sum element and a scalar",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsDirectSumElement"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for a direct sum element and a scalar",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsDirectSumElement"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for a scalar and a sparse rowspace element",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsSparseRowSpaceElement"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for a sparse rowspace element and a scalar",
- "filters": [
- [
- "IsPackedElementDefaultRep",
- "IsSparseRowSpaceElement"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for a scalar and a monomial element",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsMonomialElement",
- "IsMonomialElementRep"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for a monomial element and a scalar",
- "filters": [
- [
- "IsMonomialElement",
- "IsMonomialElementRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 18
- },
- {
- "comment": "*: for residue class union in sparse rep. and ring element (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionClassListRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "*: for residue class union in standard rep. and ring element (ResClasses)",
- "filters": [
- [
- "IsResidueClassUnion",
- "IsResidueClassUnionResidueListRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "*: List*Alg",
- "filters": [
- [
- "IsList"
- ],
- [
- "IsAlgebraicElement"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "*: Alg*List",
- "filters": [
- [
- "IsAlgebraicElement"
- ],
- [
- "IsList"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "*",
- "filters": [
- [],
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "IsListDefault"
- ]
- ],
- "rank": 17
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsSmallList",
- "Tester(IsSmallList)",
- "IsListDefault"
- ],
- []
- ],
- "rank": 17
- },
- {
- "aka": [
- "32Bits_Product"
- ],
- "comment": "*: for two 32 bits assoc. words",
- "filters": [
- [
- "Is32BitsAssocWord"
- ],
- [
- "Is32BitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
- "aka": [
- "16Bits_Product"
- ],
- "comment": "*: for two 16 bits assoc. words",
- "filters": [
- [
- "Is16BitsAssocWord"
- ],
- [
- "Is16BitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
- "aka": [
- "8Bits_Product"
- ],
- "comment": "*: for two 8 bits assoc. words",
- "filters": [
- [
- "Is8BitsAssocWord"
- ],
- [
- "Is8BitsAssocWord"
- ]
- ],
- "rank": 16
- },
- {
- "comment": "*: univariate * rat",
- "filters": [
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "*: rat * univariate",
- "filters": [
- [
- "IsRat"
- ],
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "*: for a non-list, and a direct product element",
- "filters": [
- [],
- [
- "IsDirectProductElement"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "*: for a direct product element, and a non-list",
- "filters": [
- [
- "IsDirectProductElement"
- ],
- []
- ],
- "rank": 15
- },
- {
- "comment": "*: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)",
- "filters": [
- [
- "IsUnionOfResidueClassesWithFixedRepresentatives"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for ring element and residue class union (ResClasses)",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ],
- [
- "IsResidueClassUnion"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for two f.p. group elements",
- "filters": [
- [
- "IsElementOfFpGroup"
- ],
- [
- "IsElementOfFpGroup"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: wreath elements",
- "filters": [
- [
- "IsWreathProductElement"
- ],
- [
- "IsWreathProductElement"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for two elements of magma by mult. table",
- "filters": [
- [
- "IsMagmaByMultiplicationTableObj"
- ],
- [
- "IsMagmaByMultiplicationTableObj"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: assoc words in B letter rep",
- "filters": [
- [
- "IsAssociativeElement",
- "IsWord",
- "IsBLetterAssocWordRep"
- ],
- [
- "IsAssociativeElement",
- "IsWord",
- "IsBLetterAssocWordRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: assoc words in W letter rep",
- "filters": [
- [
- "IsAssociativeElement",
- "IsWord",
- "IsWLetterAssocWordRep"
- ],
- [
- "IsAssociativeElement",
- "IsWord",
- "IsWLetterAssocWordRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for magma ring element and magma element",
- "filters": [
- [
- "IsElementOfMagmaRingModuloRelations"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for magma element and magma ring element",
- "filters": [
- [
- "IsMultiplicativeElement"
- ],
- [
- "IsElementOfMagmaRingModuloRelations"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for two elements of a magma with zero adjoined",
- "filters": [
- [
- "IsMagmaWithZeroAdjoinedElementRep"
- ],
- [
- "IsMagmaWithZeroAdjoinedElementRep"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for two general mappings",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- [
- "IsGeneralMapping"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "*: for list and binary relation on points",
- "filters": [
- [
- "IsListOrCollection"
- ],
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "*: for binary relation on points and list",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
- [
- "IsListOrCollection"
- ]
- ],
- "rank": 13
- },
- {
- "comment": "*",
- "filters": [
- [
- "IsMonoidByAdjoiningIdentityElt"
- ],
- [
- "IsMonoidByAdjoiningIdentityElt"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "*: for two elements of a fp monoid",
- "filters": [
- [
- "IsElementOfFpMonoid"
- ],
- [
- "IsElementOfFpMonoid"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "*: rws-element * rws-element",
- "filters": [
- [
- "IsMultiplicativeElementWithInverseByRws"
- ],
- [
- "IsMultiplicativeElementWithInverseByRws"
- ]
- ],
- "rank": 12
- },
- {
- "aka": [
- "AssocWord_Product"
- ],
- "comment": "*: for two assoc. words in syllable rep",
- "filters": [
- [
- "IsAssociativeElement",
- "IsWord",
- "IsSyllableAssocWordRep"
- ],
- [
- "IsAssociativeElement",
- "IsWord",
- "IsSyllableAssocWordRep"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "*: for elements of a Rees 0-matrix semigroup",
- "filters": [
- [
- "IsReesZeroMatrixSemigroupElement"
- ],
- [
- "IsReesZeroMatrixSemigroupElement"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "*: for elements of a Rees matrix semigroup",
- "filters": [
- [
- "IsReesMatrixSemigroupElement"
- ],
- [
- "IsReesMatrixSemigroupElement"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "*: for two elements of a f.p. semigroup",
- "filters": [
- [
- "IsElementOfFpSemigroup"
- ],
- [
- "IsElementOfFpSemigroup"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "*: for two assoc. words: force syllable rep",
- "filters": [
- [
- "IsAssociativeElement",
- "IsWord"
- ],
- [
- "IsAssociativeElement",
- "IsWord"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "*: for two nonassoc. words",
- "filters": [
- [
- "IsNonassocWord"
- ],
- [
- "IsNonassocWord"
- ]
- ],
- "rank": 10
- },
- {
- "comment": "*: wrapped additive elements",
- "filters": [
- [
- "IsAdditiveElementAsMultiplicativeElementRep"
- ],
- [
- "IsAdditiveElementAsMultiplicativeElementRep"
- ]
- ],
- "rank": 10
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "*",
- "type": "GAP_Operation"
- },
- {
- "filters": [
- [
- [
- "IsMultiplicativeElementWithOne"
- ]
- ],
- [
- [
- "IsFamily"
- ]
- ],
- [
- [
- "IsCollection",
- "CategoryCollections(IsMultiplicativeElementWithOne)",
- "IsGeneralizedDomain"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/arith.gd",
- "line": 1607
- }
- ],
- "methods": {
- "0args": [],
- "1args": [
- {
- "comment": "OneImmutable: system getter",
- "filters": [
- [
- "IsAttributeStoringRep",
- "Tester(OneImmutable)"
- ]
- ],
- "rank": 20007
- },
- {
- "comment": "OneImmutable: for a magma-with-one that has a parent",
- "filters": [
- [
- "Tester(ParentAttr)",
- "IsMagmaWithOne"
- ]
- ],
- "rank": 10015
- },
- {
- "comment": "OneImmutable: partial method for a group (beats to ask family)",
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- [
- "IsMagmaWithOne",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
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- ],
- "rank": 136
- },
- {
- "comment": "OneImmutable: partial method for a magma-with-one (ask family)",
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- [
- "IsMagmaWithOne"
- ]
- ],
- "rank": 114
- },
- {
- "comment": "OneImmutable: objects with memory",
- "filters": [
- [
- "IsObjWithMemory"
- ]
- ],
- "rank": 107
- },
- {
- "comment": "OneImmutable: 8 bit matrix",
- "filters": [
- [
- "IsTable",
- "IsSmallList",
- "Tester(IsSmallList)",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
- "IsMultiplicativeElementWithInverse",
- "IsOrdinaryMatrix",
- "CategoryCollections(CategoryCollections(IsCommutativeElement))",
- "CategoryCollections(CategoryCollections(IsFFE))",
- "Is8BitMatrixRep"
- ]
- ],
- "rank": 56
- },
- {
- "comment": "OneImmutable: for matrix group, call `IdentityMat'",
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- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
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- ],
- "rank": 45
- },
- {
- "comment": "OneImmutable: for GF2 Matrix",
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- [
- "IsMultiplicativeElementWithOne",
- "IsOrdinaryMatrix",
- "IsGF2MatrixRep"
- ]
- ],
- "rank": 44
- },
- {
- "comment": "OneImmutable: for a partial perm monoid with generators",
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- [
- "CategoryCollections(IsPartialPerm)",
- "IsMagmaWithOne",
- "Tester(GeneratorsOfMagma)",
- "IsAssociative",
- "Tester(IsAssociative)"
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- "rank": 26
- },
- {
- "comment": "OneImmutable: for SC Rings -- try generators",
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- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
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- "IsRDistributive",
- "Tester(IsRDistributive)"
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- ],
- "rank": 26
- },
- {
- "comment": "OneImmutable: for finite SC Rings",
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- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
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- ],
- "rank": 26
- },
- {
- "comment": "OneImmutable: for a partial perm semigroup with generators",
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- [
- "CategoryCollections(IsPartialPerm)",
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- "Tester(GeneratorsOfMagma)",
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- "Tester(IsAssociative)"
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- {
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- [
- "IsFFE",
- "IsCoeffsModConwayPolRep"
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- {
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- [
- "IsIEEE754FloatRep"
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- ],
- "rank": 15
- },
- {
- "comment": "OneImmutable: for a partial perm coll",
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- [
- "CategoryCollections(IsPartialPerm)"
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- ],
- "rank": 15
- },
- {
- "comment": "OneImmutable: for a plist matrix",
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- [
- "IsPlistMatrixRep"
- ]
- ],
- "rank": 15
- },
- {
- "aka": [
- "ONE",
- "OneMutable",
- "OneOp"
- ],
- "comment": "OneImmutable: univariate",
- "filters": [
- [
- "IsPolynomialFunction",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
- ]
- ],
- "rank": 15
- },
- {
- "comment": "OneImmutable: for a magma-with-one",
- "filters": [
- [
- "IsMagmaWithOne"
- ]
- ],
- "rank": 14
- },
- {
- "comment": "OneImmutable: for floats",
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- [
- "IsFloat"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "OneImmutable: for binary relation on points and a set of integers",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "OneImmutable: One(<congruence class>)",
- "filters": [
- [
- "IsMultiplicativeElementWithOne",
- "IsCongruenceClass"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "OneImmutable: for a magma",
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- [
- "IsMagma"
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- ],
- "rank": 11
- },
- {
- "comment": "OneImmutable: for a multiplicative element with one collection",
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- [
- "CategoryCollections(IsMultiplicativeElementWithOne)"
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- ],
- "rank": 8
- },
- {
- "comment": "OneImmutable: for an f.p. group element",
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- [
- "IsElementOfFpGroup"
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- ],
- "rank": 7
- },
- {
- "comment": "OneImmutable: for pcp elements",
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- [
- "IsPcpElement"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "OneImmutable",
- "filters": [
- [
- "IsMonoidByAdjoiningIdentityElt"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "OneImmutable: for an fp monoid element",
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- [
- "IsElementOfFpMonoid"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "OneImmutable: for an identity element",
- "filters": [
- [
- "IsMultiplicativeElementWithOne",
- "IsOne",
- "Tester(IsOne)"
- ]
- ],
- "rank": 6
- },
- {
- "comment": "OneImmutable",
- "filters": [
- [
- "CategoryFamily(IsPadicExtensionNumber)"
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- "rank": 5
- },
- {
- "comment": "OneImmutable",
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- [
- "CategoryFamily(IsPurePadicNumber)"
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- "rank": 5
- },
- {
- "comment": "OneImmutable: for a family of FFEs",
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- [
- "CategoryFamily(IsFFE)"
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- ],
- "rank": 5
- },
- {
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- [
- "CategoryFamily(IsSCAlgebraObj)"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "OneImmutable: for a multiplicative-element-with-one (look at the family)",
- "filters": [
- [
- "IsMultiplicativeElementWithOne"
- ]
- ],
- "rank": 4
- },
- {
- "comment": "OneImmutable: for a family of free monoid elements",
- "filters": [
- [
- "CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
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- ],
- "rank": 3
- },
- {
- "comment": "OneImmutable: for a family of fp monoid elements",
- "filters": [
- [
- "CategoryFamily(IsElementOfFpMonoid)"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "OneImmutable: for a family of f.p. group elements",
- "filters": [
- [
- "CategoryFamily(IsElementOfFpGroup)"
- ]
- ],
- "rank": 2
- },
- {
- "comment": "OneImmutable: for any object (call `OneOp' and make immutable)",
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- []
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- "rank": 0
- }
- ],
- "2args": [],
- "3args": [],
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- "name": "OneImmutable",
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- {
- "aka": [
- "SetIdentity",
- "SetOne",
- "SetOneAttr",
- "SetOneImmutable"
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- "filters": [
- [
- [
- "IsMultiplicativeElementWithOne"
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- []
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- [
- [
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- [
- [
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- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "ImagesElm: for ANF automorphism and scalar",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "ImagesElm: for embedding of ring into magma ring, and ring element",
- "filters": [
- [
- "IsEmbeddingRingMagmaRing"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "ImagesElm: for binary relations over [1..n] with images list",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
- [
- "IsInt",
- "IsPosRat"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "ImagesElm: for Frobenius automorphism and source element",
- "filters": [
- [
- "IsFrobeniusAutomorphism"
- ],
- []
- ],
- "rank": 26
- },
- {
- "comment": "ImagesElm: for magma congruence and element",
- "filters": [
- [
- "IsMagmaCongruence"
- ],
- []
- ],
- "rank": 26
- },
- {
- "comment": "ImagesElm: for nilpotent Lie algebra automorphisms",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsNilpotentLieAutomorphismRep"
- ],
- []
- ],
- "rank": 22
- },
- {
- "comment": "ImagesElm: for a Green's equivalence",
- "filters": [
- [
- "IsGreensRelation"
- ],
- []
- ],
- "rank": 22
- },
- {
- "comment": "ImagesElm: for embedding of magma into magma ring, and mult. element",
- "filters": [
- [
- "IsEmbeddingMagmaMagmaRing"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "ImagesElm: for magma congruence and element",
- "filters": [
- [
- "IsRightMagmaCongruence"
- ],
- []
- ],
- "rank": 22
- },
- {
- "comment": "ImagesElm: for magma congruence and element",
- "filters": [
- [
- "IsLeftMagmaCongruence"
- ],
- []
- ],
- "rank": 22
- },
- {
- "comment": "ImagesElm: for equivalence relation with partition and element",
- "filters": [
- [
- "IsEquivalenceRelation",
- "Tester(IsEquivalenceRelation)",
- "Tester(EquivalenceRelationPartition)"
- ],
- []
- ],
- "rank": 22
- },
- {
- "comment": "ImagesElm: for semigroup homomorphism by images",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "IsSemigroupHomomorphismByImagesRep"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "ImagesElm: IsTransformationRepOfEndo",
- "filters": [
- [
- "IsGeneralMapping",
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsTransformationRepOfEndo"
- ],
- []
- ],
- "rank": 16
- },
- {
- "comment": "ImagesElm: method for s.p. gen. mapping respecting add. & add.inv., and element",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "ImagesElm: method for s.p. general mapping respecting mult. & inv., and element",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "ImagesElm: for mapping by function",
- "filters": [
- [
- "IsMappingByFunctionRep"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "ImagesElm: for Lie embedding and object",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLieEmbeddingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "ImagesElm: for a restricted mapping, and an element",
- "filters": [
- [
- "IsGeneralRestrictedMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "ImagesElm: for a composition mapping, and an element",
- "filters": [
- [
- "IsCompositionMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "ImagesElm: for an inverse mapping and an element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsInverseGeneralMappingRep"
- ],
- []
- ],
- "rank": 9
- },
- {
- "comment": "ImagesElm: for constant time access general mapping, and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsConstantTimeAccessGeneralMapping",
- "Tester(IsConstantTimeAccessGeneralMapping)"
- ],
- []
- ],
- "rank": 9
- },
- {
- "comment": "ImagesElm: for non s.p. general mapping, and element",
- "filters": [
- [
- "IsNonSPGeneralMapping"
- ],
- []
- ],
- "rank": 8
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "ImagesElm",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "ImagesRepresentative"
- ],
- "filters": [
- [
- [
- "IsGeneralMapping"
- ],
- []
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 776
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "ImagesRepresentative: for zero mapping and object",
- "filters": [
- [
- "IsZero",
- "Tester(IsZero)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "ImagesRepresentative: for identity mapping and object",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "ImagesRepresentative: for total GGMBPCGS, and mult.-elm.-with-inverse",
- "filters": [
- [
- "IsTotal",
- "Tester(IsTotal)",
- "IsGroupGeneralMappingByPcgs"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 125
- },
- {
- "comment": "ImagesRepresentative: for homomorphisms of free groups",
- "filters": [
- [
- "IsFromFpGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse",
- "IsAssociativeElement",
- "IsWord"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "ImagesRepresentative: for a blow up isomorphism, and a matrix in the source",
- "filters": [
- [
- "IsBlowUpIsomorphism"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 47
- },
- {
- "comment": "ImagesRepresentative: for an alg. hom. from f. p. algebra, and an element",
- "filters": [
- [
- "IsAlgebraHomomorphismFromFpRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 37
- },
- {
- "comment": "ImagesRepresentative: for an operation algebra homomorphism, and an element",
- "filters": [
- [
- "IsOperationAlgebraHomomorphismDefaultRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 37
- },
- {
- "comment": "ImagesRepresentative: for ANF automorphism and scalar",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "ImagesRepresentative: for FromPcpGHBI",
- "filters": [
- [
- "IsFromPcpGHBI"
- ],
- [
- "IsPcpElement"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "ImagesRepresentative: simple tests on equal words to check whether the `generators' are mapped",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsFromFpGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "ImagesRepresentative: map from fp group or free group, use 'MappedWord'",
- "filters": [
- [
- "IsFromFpGroupStdGensGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "ImagesRepresentative: map from (sub)fp group, rewrite",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsFromFpGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "ImagesRepresentative: for embedding of ring into magma ring, and ring element",
- "filters": [
- [
- "IsEmbeddingRingMagmaRing"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 33
- },
- {
- "aka": [
- "FptoSCAMorphismImageElm"
- ],
- "comment": "ImagesRepresentative: for Fp to SCA mapping, and element",
- "filters": [
- [
- "IsFptoSCAMorphism"
- ],
- [
- "IsElementOfFpAlgebra"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "ImagesRepresentative",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsPcgsToPcgsGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "ImagesRepresentative: using `RepresentativeAction'",
- "filters": [
- [
- "Tester(ImagesSource)",
- "IsActionHomomorphismByBase"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "ImagesRepresentative: imprim perm wreath product embedding",
- "filters": [
- [
- "IsEmbeddingImprimitiveWreathProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "ImagesRepresentative: for isom by finite matrix groups (Polenta)",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsIsomorphismByFinitePolycyclicMatrixGroup",
- "Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: for isom by matrix groups (Polenta)",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsIsomorphismByPolycyclicMatrixGroup",
- "Tester(IsIsomorphismByPolycyclicMatrixGroup)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: for group by field elems isom",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsMultGroupByFieldElemsIsomorphism",
- "Tester(IsMultGroupByFieldElemsIsomorphism)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: for unit groups",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsUnitGroupIsomorphism",
- "Tester(IsUnitGroupIsomorphism)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: restricted perm",
- "filters": [
- [
- "IsActionHomomorphismSubset"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: for action hom that is `ByAsGroup'",
- "filters": [
- [
- "IsGroupGeneralMappingByAsGroupGeneralMappingByImages",
- "IsActionHomomorphism"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: imprim matrix wreath product embedding",
- "filters": [
- [
- "IsEmbeddingImprimitiveWreathProductMatrixGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: matrix direct product projection",
- "filters": [
- [
- "IsProjectionDirectProductMatrixGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: matrix direct product embedding",
- "filters": [
- [
- "IsEmbeddingDirectProductMatrixGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: perm subdirect product projection",
- "filters": [
- [
- "IsProjectionSubdirectProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: perm direct product projection",
- "filters": [
- [
- "IsProjectionDirectProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: perm direct product embedding",
- "filters": [
- [
- "IsEmbeddingDirectProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: blocks homomorphism",
- "filters": [
- [
- "IsBlocksHomomorphism"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: Constituent homomorphism",
- "filters": [
- [
- "IsConstituentHomomorphism"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "ImagesRepresentative: for conjugator isomorphism",
- "filters": [
- [
- "IsConjugatorIsomorphism",
- "Tester(IsConjugatorIsomorphism)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "aka": [
- "ImageElmActionHomomorphism"
- ],
- "comment": "ImagesRepresentative: for action hom",
- "filters": [
- [
- "IsActionHomomorphism"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "ImagesRepresentative: for Frobenius automorphism and source element",
- "filters": [
- [
- "IsFrobeniusAutomorphism"
- ],
- []
- ],
- "rank": 26
- },
- {
- "comment": "ImagesRepresentative: for polring g.m.b.i., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsPolynomialRingDefaultGeneratorMapping"
- ],
- []
- ],
- "rank": 26
- },
- {
- "comment": "ImagesRepresentative: for algebra g.m.b.i., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ],
- []
- ],
- "rank": 25
- },
- {
- "comment": "ImagesRepresentative",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsFromAffineCrystGroupToPcpGroup",
- "Tester(IsFromAffineCrystGroupToPcpGroup)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ImagesRepresentative",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsFromAffineCrystGroupToFpGroup",
- "Tester(IsFromAffineCrystGroupToFpGroup)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ImagesRepresentative",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsPointHomomorphism",
- "Tester(IsPointHomomorphism)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ImagesRepresentative: word decomp hom",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsWordDecompHomomorphism",
- "Tester(IsWordDecompHomomorphism)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ImagesRepresentative: perm group hom",
- "filters": [
- [
- "IsPermGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ImagesRepresentative: for SC ring g.m.b.i., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "IsSCRingGeneralMappingByImagesDefaultRep"
- ],
- []
- ],
- "rank": 24
- },
- {
- "comment": "ImagesRepresentative: for `ByAsGroupGeneralMapping' hom",
- "filters": [
- [
- "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "ImagesRepresentative: for left module m.b.m., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLinearMappingByMatrixDefaultRep"
- ],
- []
- ],
- "rank": 23
- },
- {
- "comment": "ImagesRepresentative: for left module g.m.b.i., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLinearGeneralMappingByImagesDefaultRep"
- ],
- []
- ],
- "rank": 23
- },
- {
- "comment": "ImagesRepresentative: for nilpotent Lie algebra automorphisms",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsNilpotentLieAutomorphismRep"
- ],
- []
- ],
- "rank": 22
- },
- {
- "comment": "ImagesRepresentative: for group automorphisms",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsPGAutomorphismRep"
- ],
- []
- ],
- "rank": 22
- },
- {
- "aka": [
- "ImagesRepresentativeGMBIByElementsList"
- ],
- "comment": "ImagesRepresentative: parallel enumeration of source and range",
- "filters": [
- [
- "IsGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "ImagesRepresentative: for embedding of magma into magma ring, and mult. element",
- "filters": [
- [
- "IsEmbeddingMagmaMagmaRing"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "ImagesRepresentative: equivalence relations",
- "filters": [
- [
- "IsEquivalenceRelation",
- "Tester(IsEquivalenceRelation)"
- ],
- []
- ],
- "rank": 21
- },
- {
- "comment": "ImagesRepresentative: for semigroup homomorphism by images",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "IsSemigroupHomomorphismByImagesRep"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "ImagesRepresentative: for mapping by function",
- "filters": [
- [
- "IsMappingByFunctionRep"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "ImagesRepresentative: for a restricted mapping, and an element",
- "filters": [
- [
- "IsGeneralRestrictedMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "ImagesRepresentative: for a composition mapping, and an element",
- "filters": [
- [
- "IsCompositionMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "ImagesRepresentative: for an inverse mapping and an element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsInverseGeneralMappingRep"
- ],
- []
- ],
- "rank": 9
- },
- {
- "comment": "ImagesRepresentative: for non s.p. general mapping, and element",
- "filters": [
- [
- "IsNonSPGeneralMapping"
- ],
- []
- ],
- "rank": 8
- },
- {
- "comment": "ImagesRepresentative: for s.p. general mapping, and element",
- "filters": [
- [
- "IsSPGeneralMapping"
- ],
- []
- ],
- "rank": 8
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "ImagesRepresentative",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "ImagesSet"
- ],
- "filters": [
- [
- [
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 799
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "ImagesSet: for zero mapping and collection",
- "filters": [
- [
- "IsZero",
- "Tester(IsZero)",
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 10019
- },
- {
- "comment": "ImagesSet: for identity mapping and collection",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 10019
- },
- {
- "comment": "ImagesSet: for ANF automorphism and field",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ]
- ],
- "rank": 80
- },
- {
- "comment": "ImagesSet: for Frobenius automorphism and field contained in the source",
- "filters": [
- [
- "IsFrobeniusAutomorphism"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ]
- ],
- "rank": 80
- },
- {
- "comment": "ImagesSet: constituent homomorphism",
- "filters": [
- [
- "IsConstituentHomomorphism"
- ],
- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "Tester(StabChainMutable)"
- ]
- ],
- "rank": 79
- },
- {
- "comment": "ImagesSet: for blocks homomorphism and perm. group",
- "filters": [
- [
- "IsBlocksHomomorphism"
- ],
- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 78
- },
- {
- "comment": "ImagesSet: for field homomorphism and field",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ]
- ],
- "rank": 77
- },
- {
- "comment": "ImagesSet: for conjugator isomorphism, and group",
- "filters": [
- [
- "IsConjugatorIsomorphism",
- "Tester(IsConjugatorIsomorphism)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 58
- },
- {
- "comment": "ImagesSet: method for algebra-with-one hom. and FLMLOR-with-one",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 56
- },
- {
- "comment": "ImagesSet: method for injective s.p. mapping respecting mult. & inv., and group",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsInjective",
- "Tester(IsInjective)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 54
- },
- {
- "comment": "ImagesSet: for polring g.m.b.i., and ring",
- "filters": [
- [
- "IsGeneralMapping",
- "IsPolynomialRingDefaultGeneratorMapping"
- ],
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 52
- },
- {
- "comment": "ImagesSet: method for algebra hom. and FLMLOR",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 52
- },
- {
- "comment": "ImagesSet: method for s.p. general mapping respecting mult. & inv., and group",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 48
- },
- {
- "comment": "ImagesSet: method for linear mapping and left module",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "ImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "ImagesSet: for general mapping, and empty list",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "ImagesSet: for a restricted mapping, and an collection",
- "filters": [
- [
- "IsGeneralRestrictedMappingRep"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "ImagesSet: for a composition mapping, and an collection",
- "filters": [
- [
- "IsCompositionMappingRep"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "ImagesSet: for an inverse mapping and a collection",
- "filters": [
- [
- "IsGeneralMapping",
- "IsInverseGeneralMappingRep"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "ImagesSet: for general mapping, and finite collection",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 9
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "ImagesSet",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "ImageElm"
- ],
- "filters": [
- [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ],
- []
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 822
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "ImageElm: for zero mapping and object",
- "filters": [
- [
- "IsZero",
- "Tester(IsZero)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "ImageElm: for identity mapping and object",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "ImageElm: for ANF automorphism and scalar",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsCyc"
- ]
- ],
- "rank": 42
- },
- {
- "comment": "ImageElm: for Fp to SCA mapping, and element",
- "filters": [
- [
- "IsFptoSCAMorphism"
- ],
- [
- "IsElementOfFpAlgebra"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "ImageElm: for Frobenius automorphism and source element",
- "filters": [
- [
- "IsFrobeniusAutomorphism"
- ],
- []
- ],
- "rank": 26
- },
- {
- "comment": "ImageElm: for mapping by function",
- "filters": [
- [
- "IsMappingByFunctionRep"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "ImageElm: for an inverse mapping and an element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsInverseGeneralMappingRep"
- ],
- []
- ],
- "rank": 13
- },
- {
- "comment": "ImageElm: for mapping, and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)"
- ],
- []
- ],
- "rank": 11
- },
- {
- "comment": "ImageElm: for general mapping, and element",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 7
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "ImageElm",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "PreImagesElm"
- ],
- "filters": [
- [
- [
- "IsGeneralMapping"
- ],
- []
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 949
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "PreImagesElm: for zero mapping and object",
- "filters": [
- [
- "IsZero",
- "Tester(IsZero)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "PreImagesElm: for identity mapping and object",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "PreImagesElm: for embedding of ring into magma ring, and free magma ring element",
- "filters": [
- [
- "IsEmbeddingRingMagmaRing"
- ],
- [
- "IsElementOfFreeMagmaRing"
- ]
- ],
- "rank": 37
- },
- {
- "comment": "PreImagesElm: for ANF automorphism and scalar",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "PreImagesElm: for embedding of magma into magma ring, and free magma ring element",
- "filters": [
- [
- "IsEmbeddingMagmaMagmaRing"
- ],
- [
- "IsElementOfFreeMagmaRing"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PreImagesElm: for binary rels over [1..n] with images list",
- "filters": [
- [
- "IsEndoGeneralMapping",
- "Tester(IsEndoGeneralMapping)",
- "IsBinaryRelationOnPointsRep"
- ],
- [
- "IsInt",
- "IsPosRat"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PreImagesElm: for field homomorphism and element",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)"
- ],
- []
- ],
- "rank": 23
- },
- {
- "comment": "PreImagesElm: for Lie embedding and Lie object in default representation",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLieEmbeddingRep"
- ],
- [
- "IsPackedElementDefaultRep",
- "IsLieObject"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PreImagesElm: equivalence relations with parition and element",
- "filters": [
- [
- "IsEquivalenceRelation",
- "Tester(IsEquivalenceRelation)",
- "Tester(EquivalenceRelationPartition)"
- ],
- []
- ],
- "rank": 22
- },
- {
- "comment": "PreImagesElm: for mapping by function",
- "filters": [
- [
- "IsMappingByFunctionWithInverseRep"
- ],
- []
- ],
- "rank": 19
- },
- {
- "comment": "PreImagesElm: method for s.p. gen. mapping respecting add. & add.inv., and element",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "PreImagesElm: method for s.p. general mapping respecting mult. & inv., and element",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "PreImagesElm: for a restricted mapping, and an element",
- "filters": [
- [
- "IsGeneralRestrictedMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "PreImagesElm: for a composition mapping, and an element",
- "filters": [
- [
- "IsCompositionMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "PreImagesElm: for an inverse mapping and an element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsInverseGeneralMappingRep"
- ],
- []
- ],
- "rank": 9
- },
- {
- "comment": "PreImagesElm: for constant time access general mapping, and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsConstantTimeAccessGeneralMapping",
- "Tester(IsConstantTimeAccessGeneralMapping)"
- ],
- []
- ],
- "rank": 9
- },
- {
- "comment": "PreImagesElm: for general mapping with finite source, and element",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 7
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "PreImagesElm",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "PreImageElm"
- ],
- "filters": [
- [
- [
- "IsGeneralMapping",
- "IsInjective",
- "Tester(IsInjective)",
- "IsSurjective",
- "Tester(IsSurjective)"
- ],
- []
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 973
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "PreImageElm: for identity mapping and object",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "PreImageElm: for ANF automorphism and scalar",
- "filters": [
- [
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsInjective",
- "Tester(IsInjective)",
- "IsSurjective",
- "Tester(IsSurjective)",
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 40
- },
- {
- "comment": "PreImageElm: for mapping by function",
- "filters": [
- [
- "IsMappingByFunctionWithInverseRep"
- ],
- []
- ],
- "rank": 19
- },
- {
- "comment": "PreImageElm: for an inj. & surj. inverse mapping, and an element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsInjective",
- "Tester(IsInjective)",
- "IsSurjective",
- "Tester(IsSurjective)",
- "IsInverseGeneralMappingRep"
- ],
- []
- ],
- "rank": 13
- },
- {
- "aka": [
- "PreImagesRepresentative"
- ],
- "comment": "PreImageElm: for inj. & surj. general mapping, and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsInjective",
- "Tester(IsInjective)",
- "IsSurjective",
- "Tester(IsSurjective)"
- ],
- []
- ],
- "rank": 11
- },
- {
- "comment": "PreImageElm: for general mapping, and element",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 7
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "PreImageElm",
- "type": "GAP_Operation"
- },
- {
- "filters": [
- [
- [
- "IsGeneralMapping"
- ],
- []
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 999
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "PreImagesRepresentative: for zero mapping and object",
- "filters": [
- [
- "IsZero",
- "Tester(IsZero)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "comment": "PreImagesRepresentative: for identity mapping and object",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- []
- ],
- "rank": 10017
- },
- {
- "aka": [
- "PreImagesRepresentativeOperationAlgebraHomomorphism"
- ],
- "comment": "PreImagesRepresentative: for an alg. hom. from f. p. algebra, and an element",
- "filters": [
- [
- "IsAlgebraHomomorphismFromFpRep"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "PreImagesRepresentative: for an operation algebra homomorphism, and an element",
- "filters": [
- [
- "IsOperationAlgebraHomomorphismDefaultRep"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 59
- },
- {
- "comment": "PreImagesRepresentative: for a blow up isomorphism, and a matrix in the range",
- "filters": [
- [
- "IsBlowUpIsomorphism"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 47
- },
- {
- "comment": "PreImagesRepresentative: for embedding of ring into magma ring, and free magma ring element",
- "filters": [
- [
- "IsEmbeddingRingMagmaRing"
- ],
- [
- "IsElementOfFreeMagmaRing"
- ]
- ],
- "rank": 37
- },
- {
- "comment": "PreImagesRepresentative: for ANF automorphism and scalar",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 36
- },
- {
- "comment": "PreImagesRepresentative: for ToPcpGHBI",
- "filters": [
- [
- "IsToPcpGHBI"
- ],
- [
- "IsPcpElement"
- ]
- ],
- "rank": 35
- },
- {
- "comment": "PreImagesRepresentative: for Fp to SCA mapping, and element",
- "filters": [
- [
- "IsFptoSCAMorphism"
- ],
- [
- "IsSCAlgebraObj"
- ]
- ],
- "rank": 33
- },
- {
- "comment": "PreImagesRepresentative: AutomGroup Niceomorphism",
- "filters": [
- [
- "IsActionHomomorphismAutomGroup"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 32
- },
- {
- "comment": "PreImagesRepresentative: IsProjectiveActionHomomorphism",
- "filters": [
- [
- "IsProjectiveActionHomomorphism"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PreImagesRepresentative: IsLinearActionHomomorphism",
- "filters": [
- [
- "IsLinearActionHomomorphism"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PreImagesRepresentative: constituent homomorphism",
- "filters": [
- [
- "IsConstituentHomomorphism"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PreImagesRepresentative: for embedding of magma into magma ring, and free magma ring element",
- "filters": [
- [
- "IsEmbeddingMagmaMagmaRing"
- ],
- [
- "IsElementOfFreeMagmaRing"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "PreImagesRepresentative",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsPcgsToPcgsGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "PreImagesRepresentative: imprim perm wreath product embedding",
- "filters": [
- [
- "IsEmbeddingImprimitiveWreathProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 29
- },
- {
- "comment": "PreImagesRepresentative: hom. to standard generators of fp group, using 'MappedWord'",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsToFpGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: imprim matrix wreath product embedding",
- "filters": [
- [
- "IsEmbeddingImprimitiveWreathProductMatrixGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: matrix direct product projection",
- "filters": [
- [
- "IsProjectionDirectProductMatrixGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: matrix direct product embedding",
- "filters": [
- [
- "IsEmbeddingDirectProductMatrixGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: perm subdirect product projection",
- "filters": [
- [
- "IsProjectionSubdirectProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: perm direct product projection",
- "filters": [
- [
- "IsProjectionDirectProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: perm direct product embedding",
- "filters": [
- [
- "IsEmbeddingDirectProductPermGroup"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: blocks homomorphism",
- "filters": [
- [
- "IsBlocksHomomorphism"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: for conjugator isomorphism",
- "filters": [
- [
- "IsConjugatorIsomorphism",
- "Tester(IsConjugatorIsomorphism)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "PreImagesRepresentative: method for pcgs hom",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsToPcGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "PreImagesRepresentative: for algebra g.m.b.i. knowing inverse, and element",
- "filters": [
- [
- "IsGeneralMapping",
- "Tester(InverseGeneralMapping)",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ],
- []
- ],
- "rank": 26
- },
- {
- "comment": "PreImagesRepresentative: for homomorphisms of free groups",
- "filters": [
- [
- "IsToFpGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse",
- "IsAssociativeElement",
- "IsWord"
- ]
- ],
- "rank": 25
- },
- {
- "comment": "PreImagesRepresentative: for algebra g.m.b.i., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsAlgebraGeneralMappingByImagesDefaultRep"
- ],
- []
- ],
- "rank": 25
- },
- {
- "comment": "PreImagesRepresentative",
- "filters": [
- [
- "IsGroupGeneralMappingByImages",
- "IsPointHomomorphism",
- "Tester(IsPointHomomorphism)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "PreImagesRepresentative: for PBG-Niceo",
- "filters": [
- [
- "IsPreimagesByAsGroupGeneralMappingByImages",
- "IsNiceMonomorphism"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PreImagesRepresentative",
- "filters": [
- [
- "IsToPermGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 23
- },
- {
- "comment": "PreImagesRepresentative: for ring g.m.b.i., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "IsRingGeneralMappingByImagesDefaultRep"
- ],
- []
- ],
- "rank": 23
- },
- {
- "comment": "PreImagesRepresentative: for left module m.b.m., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLinearMappingByMatrixDefaultRep"
- ],
- []
- ],
- "rank": 23
- },
- {
- "comment": "PreImagesRepresentative: for left module g.m.b.i., and element",
- "filters": [
- [
- "IsGeneralMapping",
- "IsLinearGeneralMappingByImagesDefaultRep"
- ],
- []
- ],
- "rank": 23
- },
- {
- "comment": "PreImagesRepresentative: for GHBI and mult.-elm.-with-inverse",
- "filters": [
- [
- "IsGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PreImagesRepresentative: for PBG-Hom",
- "filters": [
- [
- "IsPreimagesByAsGroupGeneralMappingByImages"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 22
- },
- {
- "comment": "PreImagesRepresentative: equivalence relations",
- "filters": [
- [
- "IsEquivalenceRelation",
- "Tester(IsEquivalenceRelation)"
- ],
- []
- ],
- "rank": 21
- },
- {
- "comment": "PreImagesRepresentative: for semigroup homomorphism by images",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "IsSemigroupHomomorphismByImagesRep"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 20
- },
- {
- "comment": "PreImagesRepresentative: for mapping by function with inverse",
- "filters": [
- [
- "IsMappingByFunctionWithInverseRep"
- ],
- []
- ],
- "rank": 19
- },
- {
- "comment": "PreImagesRepresentative: for mapping by function",
- "filters": [
- [
- "IsMappingByFunctionRep"
- ],
- []
- ],
- "rank": 14
- },
- {
- "comment": "PreImagesRepresentative: for a restricted mapping, and an element",
- "filters": [
- [
- "IsGeneralRestrictedMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "PreImagesRepresentative: for a composition mapping, and an element",
- "filters": [
- [
- "IsCompositionMappingRep"
- ],
- []
- ],
- "rank": 10
- },
- {
- "comment": "PreImagesRepresentative: for an inverse mapping and an element",
- "filters": [
- [
- "IsInverseGeneralMappingRep"
- ],
- []
- ],
- "rank": 9
- },
- {
- "comment": "PreImagesRepresentative: for total non-s.p. general mapping, and element",
- "filters": [
- [
- "IsNonSPGeneralMapping"
- ],
- []
- ],
- "rank": 8
- },
- {
- "comment": "PreImagesRepresentative: for s.p. general mapping, and element",
- "filters": [
- [
- "IsSPGeneralMapping"
- ],
- []
- ],
- "rank": 8
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "PreImagesRepresentative",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "PreImagesSet"
- ],
- "filters": [
- [
- [
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 1021
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "PreImagesSet: for zero mapping and collection",
- "filters": [
- [
- "IsZero",
- "Tester(IsZero)",
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 10019
- },
- {
- "comment": "PreImagesSet: for identity mapping and collection",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 10019
- },
- {
- "comment": "PreImagesSet: for PcpGHBI",
- "filters": [
- [
- "IsFromPcpGHBI",
- "IsToPcpGHBI"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsPcpElement)"
- ]
- ],
- "rank": 91
- },
- {
- "comment": "PreImagesSet: for ANF automorphism and scalar",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)",
- "IsANFAutomorphismRep"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ]
- ],
- "rank": 80
- },
- {
- "comment": "PreImagesSet",
- "filters": [
- [
- "IsBlocksHomomorphism"
- ],
- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 78
- },
- {
- "comment": "PreImagesSet: constituent homomorphism",
- "filters": [
- [
- "IsConstituentHomomorphism"
- ],
- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 78
- },
- {
- "comment": "PreImagesSet: for field homomorphism and field",
- "filters": [
- [
- "IsFieldHomomorphism",
- "Tester(IsFieldHomomorphism)"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ]
- ],
- "rank": 77
- },
- {
- "comment": "PreImagesSet: map from (sub)group of fp group",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsFromFpGroupGeneralMapping"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 63
- },
- {
- "comment": "PreImagesSet: for conjugator isomorphism, and group",
- "filters": [
- [
- "IsConjugatorIsomorphism",
- "Tester(IsConjugatorIsomorphism)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 58
- },
- {
- "comment": "PreImagesSet: method for algebra-with-one hom. and FLMLOR-with-one",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsOne",
- "Tester(RespectsOne)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 56
- },
- {
- "comment": "PreImagesSet: method for injective s.p. mapping respecting mult. & inv., and group",
- "filters": [
- [
- "IsGeneralMapping",
- "IsSPGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsInjective",
- "Tester(IsInjective)",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 54
- },
- {
- "comment": "PreImagesSet: method for permgroup homs",
- "filters": [
- [
- "IsGeneralMapping",
- "IsTotal",
- "Tester(IsTotal)",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "IsPermGroupGeneralMapping"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 53
- },
- {
- "comment": "PreImagesSet: method for algebra hom. and FLMLOR",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 52
- },
- {
- "comment": "PreImagesSet: method for s.p. general mapping respecting mult. & inv., and group",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsMultiplication",
- "Tester(RespectsMultiplication)",
- "RespectsInverses",
- "Tester(RespectsInverses)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 48
- },
- {
- "comment": "PreImagesSet: method for linear mapping and left module",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)",
- "RespectsScalarMultiplication",
- "Tester(RespectsScalarMultiplication)"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 38
- },
- {
- "comment": "PreImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group",
- "filters": [
- [
- "IsSPGeneralMapping",
- "RespectsAddition",
- "Tester(RespectsAddition)",
- "RespectsAdditiveInverses",
- "Tester(RespectsAdditiveInverses)"
- ],
- [
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 30
- },
- {
- "comment": "PreImagesSet: for general mapping, and empty list",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ]
- ],
- "rank": 24
- },
- {
- "comment": "PreImagesSet: for a restricted mapping, and an collection",
- "filters": [
- [
- "IsGeneralRestrictedMappingRep"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PreImagesSet: for a composition mapping, and an collection",
- "filters": [
- [
- "IsCompositionMappingRep"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "PreImagesSet: for an inverse mapping and a collection",
- "filters": [
- [
- "IsGeneralMapping",
- "IsInverseGeneralMappingRep"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "PreImagesSet: for general mapping, and finite collection",
- "filters": [
- [
- "IsGeneralMapping"
- ],
- [
- "IsCollection"
- ]
- ],
- "rank": 9
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "PreImagesSet",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "CompositionMapping2"
- ],
- "filters": [
- [
- [
- "IsGeneralMapping"
- ],
- [
- "IsGeneralMapping"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/mapping.gd",
- "line": 1157
- }
- ],
- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "CompositionMapping2: for zero mapping and single-valued gen. mapping that resp. zero",
- "filters": [
- [
- "IsZero",
- "Tester(IsZero)",
- "IsGeneralMapping"
- ],
- [
- "IsGeneralMapping",
- "IsSingleValued",
- "Tester(IsSingleValued)",
- "RespectsZero",
- "Tester(RespectsZero)"
- ]
- ],
- "rank": 10028
- },
- {
- "comment": "CompositionMapping2: for identity mapping and general mapping",
- "filters": [
- [
- "IsOne",
- "Tester(IsOne)",
- "IsGeneralMapping"
- ],
- [
- "IsGeneralMapping"
- ]
- ],
- "rank": 10025
- },
- {
- "comment": "CompositionMapping2: for general mapping and identity mapping",
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- "Tester(IsOne)",
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- {
- "comment": "CompositionMapping2: for general mapping and zero mapping",
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- [
- "IsGeneralMapping"
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- [
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- "IsGeneralMapping"
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- "rank": 10024
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- {
- "comment": "CompositionMapping2: method for two pc group automorphisms",
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- [
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- "IsTotal",
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- "rank": 56
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- {
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- "rank": 54
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- {
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- [
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- "rank": 52
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- {
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- "rank": 52
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- {
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- {
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- {
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- {
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- {
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- {
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- {
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- {
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- {
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- {
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- {
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- "rank": 39
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- {
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- "rank": 34
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- {
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- {
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- {
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- {
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- "rank": 29
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- {
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- [
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- {
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- "rank": 54
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- {
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- {
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- {
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- "rank": 79
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- {
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- "rank": 78
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- {
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- "rank": 78
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- {
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- [
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- "rank": 78
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- {
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- "rank": 70
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- {
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- {
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- {
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- {
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- "rank": 65
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- {
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- [
- "IsMagma",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 60
- },
- {
- "comment": "IsCentral: for two magmas-with-inverses",
- "filters": [
- [
- "IsMagmaWithInverses"
- ],
- [
- "IsMagmaWithInverses"
- ]
- ],
- "rank": 34
- },
- {
- "comment": "IsCentral: for two magmas-with-one",
- "filters": [
- [
- "IsMagmaWithOne"
- ],
- [
- "IsMagmaWithOne"
- ]
- ],
- "rank": 28
- },
- {
- "comment": "IsCentral: for two magmas",
- "filters": [
- [
- "IsMagma"
- ],
- [
- "IsMagma"
- ]
- ],
- "rank": 22
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "IsCentral",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "CentraliserOp",
- "CentralizerOp"
- ],
- "filters": [
- [
- [
- "IsMagma"
- ],
- []
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/magma.gd",
- "line": 705
- }
- ],
- "methods": {
- "0args": [],
- "1args": [
- {
- "comment": "CentralizerOp",
- "filters": [
- [
- "IsRationalClassGroupRep"
- ]
- ],
- "rank": 11
- },
- {
- "comment": "CentralizerOp",
- "filters": [
- [
- "IsRationalClassGroupRep"
- ]
- ],
- "rank": 11
- }
- ],
- "2args": [
- {
- "comment": "CentralizerOp: for two magmas, the first being commutative",
- "filters": [
- [
- "IsMagma",
- "IsCommutative",
- "Tester(IsCommutative)"
- ],
- [
- "IsMagma"
- ]
- ],
- "rank": 10024
- },
- {
- "comment": "CentralizerOp: for a commutative magma, and a mult. element",
- "filters": [
- [
- "IsMagma",
- "IsCommutative",
- "Tester(IsCommutative)"
- ],
- [
- "IsMultiplicativeElement"
- ]
- ],
- "rank": 10016
- },
- {
- "comment": "CentralizerOp: TF method:subgroup",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "Tester(FittingFreeLiftSetup)"
- ],
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsMagmaWithInverses",
- "Tester(GeneratorsOfMagmaWithInverses)",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 866
- },
- {
- "comment": "CentralizerOp: handled by nice monomorphism: Subgroup CollColl",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsHandledByNiceMonomorphism",
- "Tester(IsHandledByNiceMonomorphism)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsHandledByNiceMonomorphism",
- "Tester(IsHandledByNiceMonomorphism)"
- ]
- ],
- "rank": 740
- },
- {
- "comment": "CentralizerOp: TF method:elm",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "Tester(FittingFreeLiftSetup)"
- ],
- [
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 438
- },
- {
- "comment": "CentralizerOp: handled by nice monomorphism: subgroup CollElm",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsHandledByNiceMonomorphism",
- "Tester(IsHandledByNiceMonomorphism)"
- ],
- []
- ],
- "rank": 370
- },
- {
- "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and FLMLOR",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsFullMatrixModule",
- "Tester(IsFullMatrixModule)",
- "IsGaussianSpace"
- ],
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 123
- },
- {
- "comment": "CentralizerOp: perm group, perm group",
- "filters": [
- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ],
- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 116
- },
- {
- "comment": "CentralizerOp: two AffineCrystGroupsOnLeft",
- "filters": [
- [
- "IsAffineCrystGroupOnLeft",
- "Tester(IsAffineCrystGroupOnLeft)"
- ],
- [
- "IsAffineCrystGroupOnLeft",
- "Tester(IsAffineCrystGroupOnLeft)"
- ]
- ],
- "rank": 110
- },
- {
- "comment": "CentralizerOp: two AffineCrystGroupsOnRight",
- "filters": [
- [
- "IsAffineCrystGroupOnRight",
- "Tester(IsAffineCrystGroupOnRight)"
- ],
- [
- "IsAffineCrystGroupOnRight",
- "Tester(IsAffineCrystGroupOnRight)"
- ]
- ],
- "rank": 110
- },
- {
- "aka": [
- "CentralizerNilpotentPcpGroup"
- ],
- "comment": "CentralizerOp: for a pcp group",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNilpotentGroup",
- "Tester(IsNilpotentGroup)",
- "CategoryCollections(IsPcpElement)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsPcpElement)"
- ]
- ],
- "rank": 106
- },
- {
- "comment": "CentralizerOp",
- "filters": [
- [
- "IsNaturalGL",
- "Tester(IsNaturalGL)",
- "IsIntegerMatrixGroup",
- "Tester(IsIntegerMatrixGroup)"
- ],
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 104
- },
- {
- "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and left module",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsFullMatrixModule",
- "Tester(IsFullMatrixModule)",
- "IsGaussianSpace"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)"
- ]
- ],
- "rank": 101
- },
- {
- "aka": [
- "CentralizerPcpGroup"
- ],
- "comment": "CentralizerOp: for a pcp group",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsPcpElement)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(IsPcpElement)"
- ]
- ],
- "rank": 100
- },
- {
- "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR-with-one, and FLMLOR",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsGaussianSpace"
- ],
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 100
- },
- {
- "comment": "CentralizerOp: for a subgroup of a free group",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
- ]
- ],
- "rank": 96
- },
- {
- "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR, and FLMLOR",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsGaussianSpace"
- ],
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 95
- },
- {
- "comment": "CentralizerOp: pcgs computable groups",
- "filters": [
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CanEasilyComputePcgs"
- ],
- [
- "IsFinite",
- "Tester(IsFinite)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "CanEasilyComputePcgs"
- ]
- ],
- "rank": 90
- },
- {
- "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR-with-one, and ordinary matrix",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsGaussianSpace"
- ],
- [
- "IsOrdinaryMatrix"
- ]
- ],
- "rank": 88
- },
- {
- "comment": "CentralizerOp: AffineCrystGroupOnLeft and element",
- "filters": [
- [
- "IsAffineCrystGroupOnLeft",
- "Tester(IsAffineCrystGroupOnLeft)"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 85
- },
- {
- "comment": "CentralizerOp: AffineCrystGroupOnRight and element",
- "filters": [
- [
- "IsAffineCrystGroupOnRight",
- "Tester(IsAffineCrystGroupOnRight)"
- ],
- [
- "IsTable",
- "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
- "CategoryCollections(CategoryCollections(IsAdditiveElement))",
- "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
- ]
- ],
- "rank": 85
- },
- {
- "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and empty list",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsFullMatrixModule",
- "Tester(IsFullMatrixModule)"
- ],
- [
- "IsList",
- "IsEmpty",
- "Tester(IsEmpty)"
- ]
- ],
- "rank": 84
- },
- {
- "comment": "CentralizerOp: for full (associative) matrix FLMLOR, and list of matrices",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsMagmaWithOne",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsFullMatrixModule",
- "Tester(IsFullMatrixModule)",
- "IsGaussianSpace"
- ],
- [
- "IsList",
- "IsCollection"
- ]
- ],
- "rank": 84
- },
- {
- "comment": "CentralizerOp: for associative Gaussian matrix FLMLOR, and ordinary matrix",
- "filters": [
- [
- "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
- "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule",
- "IsGaussianSpace"
- ],
- [
- "IsOrdinaryMatrix"
- ]
- ],
- "rank": 83
- },
- {
- "comment": "CentralizerOp: for a fin. dim. assoc. algebra and an algebra with parent",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "Tester(ParentAttr)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 77
- },
- {
- "comment": "CentralizerOp: for a fin. dim. assoc. algebra and an algebra",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 76
- },
- {
- "comment": "CentralizerOp: element in natural symmetric group",
- "filters": [
- [
- "IsNaturalSymmetricGroup",
- "Tester(IsNaturalSymmetricGroup)"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 70
- },
- {
- "comment": "CentralizerOp: element in natural alternating group",
- "filters": [
- [
- "IsNaturalAlternatingGroup",
- "Tester(IsNaturalAlternatingGroup)"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 70
- },
- {
- "comment": "CentralizerOp: generic method for two groups",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ],
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ]
- ],
- "rank": 70
- },
- {
- "comment": "CentralizerOp: perm group,elm",
- "filters": [
- [
- "CategoryCollections(IsPerm)",
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)"
- ],
- [
- "IsPerm"
- ]
- ],
- "rank": 66
- },
- {
- "comment": "CentralizerOp: for a pcp group",
- "filters": [
- [
- "IsMagmaWithInverses",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsNilpotentGroup",
- "Tester(IsNilpotentGroup)",
- "CategoryCollections(IsPcpElement)"
- ],
- [
- "IsPcpElement"
- ]
- ],
- "rank": 62
- },
- {
- "comment": "CentralizerOp: for a finite dimensional algebra and a vector space with parent",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
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- "Tester(IsAssociative)",
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- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ],
- [
- "IsFreeLeftModule"
- ]
- ],
- "rank": 61
- },
- {
- "comment": "IsLeftIdealOp: for SCRings",
- "filters": [
- [
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "CategoryCollections(IsSCRingObj)"
- ],
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- "IsRDistributive",
- "Tester(IsRDistributive)",
- "CategoryCollections(IsSCRingObj)"
- ]
- ],
- "rank": 58
- },
- {
- "comment": "IsLeftIdealOp: for FLMLOR and free left module",
- "filters": [
- [
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- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ],
- [
- "IsFreeLeftModule"
- ]
- ],
- "rank": 57
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "IsLeftIdealOp",
- "type": "GAP_Operation"
- },
- {
- "filters": [
- [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/ideal.gd",
- "line": 194
- }
- ],
- "methods": {
- "0args": [],
- "1args": [
- {
- "comment": "IsLeftIdealInParent: system getter",
- "filters": [
- [
- "IsAttributeStoringRep",
- "Tester(IsLeftIdealInParent)"
- ]
- ],
- "rank": 20029
- },
- {
- "comment": "IsLeftIdealInParent: method that calls the two-argument operation IsLeftIdealOp",
- "filters": [
- [
- "Tester(ParentAttr)",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
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- "IsRDistributive",
- "Tester(IsRDistributive)"
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- ],
- "rank": 27
- },
- {
- "comment": "IsLeftIdealInParent: default method requiring categories and checking properties",
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- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup"
- ]
- ],
- "rank": -14
- }
- ],
- "2args": [],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "IsLeftIdealInParent",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "SetIsLeftIdealInParent"
- ],
- "filters": [
- [
- [
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- "IsNearAdditiveMagma",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
- [
- "IsBool"
- ]
- ]
- ],
- "locations": [
- {
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- "line": 194
- }
- ],
- "methods": {
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- "1args": [],
- "2args": [
- {
- "comment": "Setter(IsLeftIdealInParent): system setter",
- "filters": [
- [
- "IsAttributeStoringRep"
- ],
- []
- ],
- "rank": 2
- },
- {
- "comment": "Setter(IsLeftIdealInParent): default method, does nothing",
- "filters": [
- [],
- []
- ],
- "rank": 0
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "Setter(IsLeftIdealInParent)",
- "type": "GAP_Operation"
- },
- {
- "filters": [
- [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
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- "1args": [],
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- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "Tester(IsLeftIdealInParent)",
- "type": "GAP_Operation"
- },
- {
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- [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
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- "IsAdditivelyCommutative",
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- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
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- ],
- "locations": [
- {
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- "line": 194
- }
- ],
- "methods": {
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- "1args": [],
- "2args": [
- {
- "comment": "IsLeftIdeal: left ideal in ring, naive",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
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- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "Tester(LeftActingRingOfIdeal)"
- ]
- ],
- "rank": 79
- },
- {
- "comment": "IsLeftIdeal: try to exploit the in-parent attribute IsLeftIdealInParent",
- "filters": [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
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- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 52
- }
- ],
- "3args": [],
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- "5args": [],
- "6args": []
- },
- "name": "IsLeftIdeal",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "IsRightIdealOp"
- ],
- "filters": [
- [
- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
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- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ]
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- "locations": [
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- "line": 195
- }
- ],
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- "2args": [
- {
- "comment": "IsRightIdealOp: for associative FLMLOR and FLMLOR",
- "filters": [
- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsAssociative",
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- "IsAdditivelyCommutative",
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- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ],
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- "IsDistributiveLOpDSum",
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ]
- ],
- "rank": 72
- },
- {
- "comment": "IsRightIdealOp: for associative FLMLOR-with-one and free left module",
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- [
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsDistributiveLOpDSum",
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- "Tester(IsAssociative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
- ],
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- "IsFreeLeftModule"
- ]
- ],
- "rank": 66
- },
- {
- "comment": "IsRightIdealOp: for associative FLMLOR and free left module",
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- [
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- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
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- ],
- [
- "IsFreeLeftModule"
- ]
- ],
- "rank": 61
- },
- {
- "comment": "IsRightIdealOp: for SCRings",
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- [
- "IsMagma",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsFreeLeftModule"
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- [
- "IsFreeLeftModule"
- ]
- ],
- "rank": 57
- }
- ],
- "3args": [],
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- "5args": [],
- "6args": []
- },
- "name": "IsRightIdealOp",
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- {
- "filters": [
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- [
- "IsMagma",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ]
- ],
- "locations": [
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- "methods": {
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- "1args": [
- {
- "comment": "IsRightIdealInParent: system getter",
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- [
- "IsAttributeStoringRep",
- "Tester(IsRightIdealInParent)"
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- "rank": 20029
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- {
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- [
- "Tester(ParentAttr)",
- "IsMagma",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)"
- ]
- ],
- "rank": 27
- },
- {
- "comment": "IsRightIdealInParent: default method requiring categories and checking properties",
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- [
- "IsMagma",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup"
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- ],
- "rank": -14
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- ],
- "2args": [],
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- "5args": [],
- "6args": []
- },
- "name": "IsRightIdealInParent",
- "type": "GAP_Operation"
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- {
- "aka": [
- "SetIsRightIdealInParent"
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- "filters": [
- [
- [
- "IsMagma",
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- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
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- "IsBool"
- ]
- ]
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- ],
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- "1args": [],
- "2args": [
- {
- "comment": "Setter(IsRightIdealInParent): system setter",
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- [
- "IsAttributeStoringRep"
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- []
- ],
- "rank": 2
- },
- {
- "comment": "Setter(IsRightIdealInParent): default method, does nothing",
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- [],
- []
- ],
- "rank": 0
- }
- ],
- "3args": [],
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- "5args": [],
- "6args": []
- },
- "name": "Setter(IsRightIdealInParent)",
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- [
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- "Tester(IsLDistributive)",
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- "Tester(IsRDistributive)"
- ]
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- "locations": [
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- "name": "Tester(IsRightIdealInParent)",
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- {
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- [
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- ],
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- "locations": [
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- "2args": [
- {
- "comment": "IsRightIdeal: try to exploit the in-parent attribute IsRightIdealInParent",
- "filters": [
- [
- "IsMagma",
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- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
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- "IsRDistributive",
- "Tester(IsRDistributive)"
- ],
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- {
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- ],
- "comment": "TwoSidedIdealByGenerators: for Lie algebra and collection of Lie objects",
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- ]
- ],
- "rank": 65
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- "filters": [
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- "IsZeroSquaredRing",
- "Tester(IsZeroSquaredRing)"
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- [
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- "Tester(IsEmpty)"
- ]
- ],
- "rank": 59
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- [
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- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "IsMagmaWithInversesIfNonzero",
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- "Tester(IsCommutative)",
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- [
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- "Tester(IsPolynomial)",
- "IsUnivariateRationalFunction",
- "Tester(IsUnivariateRationalFunction)"
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- ],
- "rank": 73
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- ],
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- },
- "name": "FieldExtension",
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- {
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- [
- [
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- "IsLeftActedOnByDivisionRing",
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- [
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- ],
- "locations": [
- {
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- {
- "file": "/home/makx/ac/gap/lib/field.gd",
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- },
- {
- "file": "/home/makx/ac/gap/lib/field.gd",
- "line": 568
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- {
- "comment": "Conjugates: system getter",
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- [
- "IsAttributeStoringRep",
- "Tester(Conjugates)"
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- ],
- "rank": 20013
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- {
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- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
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- "rank": 10
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- ],
- "2args": [
- {
- "comment": "Conjugates: for a field and a scalar (delegate to version with two fields)",
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- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
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- "Tester(IsCommutative)",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
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- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
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- ],
- "rank": 64
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- ],
- "3args": [
- {
- "comment": "Conjugates: for two fields of FFEs, and a FFE",
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- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsFinite",
- "Tester(IsFinite)",
- "CategoryCollections(IsFFE)",
- "IsExtLSet",
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- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
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- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "IsLDistributive",
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- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
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- "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"
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- ],
- "rank": 879
- },
- {
- "comment": "Conjugates: for Rationals, Rationals, and a rational",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "CategoryCollections(IsCyclotomic)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing",
- "IsPrimeField",
- "Tester(IsPrimeField)"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "CategoryCollections(IsCyclotomic)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing",
- "IsPrimeField",
- "Tester(IsPrimeField)"
- ],
- [
- "IsRat"
- ]
- ],
- "rank": 155
- },
- {
- "comment": "Conjugates: for cycl. field of cyclotomics, ab. number field, and cyclotomic",
- "filters": [
- [
- "CategoryCollections(IsCyclotomic)",
- "IsCyclotomicField",
- "Tester(IsCyclotomicField)"
- ],
- [
- "CategoryCollections(IsCyclotomic)",
- "IsAbelianNumberField",
- "Tester(IsAbelianNumberField)"
- ],
- [
- "IsCyc"
- ]
- ],
- "rank": 148
- },
- {
- "comment": "Conjugates: for two abelian number fields of cyclotomics, and cyclotomic",
- "filters": [
- [
- "CategoryCollections(IsCyclotomic)",
- "IsAbelianNumberField",
- "Tester(IsAbelianNumberField)"
- ],
- [
- "CategoryCollections(IsCyclotomic)",
- "IsAbelianNumberField",
- "Tester(IsAbelianNumberField)"
- ],
- [
- "IsCyc"
- ]
- ],
- "rank": 146
- },
- {
- "comment": "Conjugates: for two fields and a scalar (call `GaloisGroup')",
- "filters": [
- [
- "IsFieldControlledByGaloisGroup"
- ],
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
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- ],
- "rank": 119
- },
- {
- "comment": "Conjugates: for two fields and a scalar (call `TracePolynomial')",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
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- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
- "IsMagma",
- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
- "IsAssociative",
- "Tester(IsAssociative)",
- "IsCommutative",
- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
- "IsAdditivelyCommutative",
- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 118
- }
- ],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "Conjugates",
- "type": "GAP_Operation"
- },
- {
- "aka": [
- "SetConjugates"
- ],
- "filters": [
- [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ],
- []
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- ],
- "locations": [
- {
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- "methods": {
- "0args": [],
- "1args": [],
- "2args": [
- {
- "comment": "Setter(Conjugates): system setter",
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- [
- "IsAttributeStoringRep"
- ],
- []
- ],
- "rank": 2
- },
- {
- "comment": "Setter(Conjugates): default method, does nothing",
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- [],
- []
- ],
- "rank": 0
- }
- ],
- "3args": [],
- "4args": [],
- "5args": [],
- "6args": []
- },
- "name": "Setter(Conjugates)",
- "type": "GAP_Operation"
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- {
- "aka": [
- "HasConjugates"
- ],
- "filters": [
- [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
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- ],
- "locations": [
- {
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- "methods": {
- "0args": [],
- "1args": [],
- "2args": [],
- "3args": [],
- "4args": [],
- "5args": [],
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- },
- "name": "Tester(Conjugates)",
- "type": "GAP_Operation"
- },
- {
- "filters": [
- [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
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- ],
- [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "IsMagmaWithOne",
- "IsMagmaWithInversesIfNonzero",
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- "Tester(IsCommutative)",
- "IsNearAdditiveMagma",
- "IsNearAdditiveGroup",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
- "IsNearAdditiveElementWithInverse",
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- "IsMultiplicativeElementWithInverse"
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- ],
- [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
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- "IsAssociativeLOpEProd",
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- "IsDistributiveLOpESum",
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- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "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)",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
- "Tester(IsRDistributive)",
- "IsEuclideanRing"
- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- [
- [
- "IsClassFunction"
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- ],
- [
- [
- "IsOrdinaryTable"
- ],
- [
- "IsHomogeneousList"
- ]
- ]
- ],
- "locations": [
- {
- "file": "/home/makx/ac/gap/lib/field.gd",
- "line": 592
- },
- {
- "file": "/home/makx/ac/gap/lib/field.gd",
- "line": 593
- },
- {
- "file": "/home/makx/ac/gap/lib/field.gd",
- "line": 594
- },
- {
- "file": "/home/makx/ac/gap/lib/ctblfuns.gd",
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- }
- ],
- "methods": {
- "0args": [],
- "1args": [
- {
- "comment": "Norm: system getter",
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- [
- "IsAttributeStoringRep",
- "Tester(Norm)"
- ]
- ],
- "rank": 20013
- },
- {
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- "filters": [
- [
- "IsClassFunction"
- ]
- ],
- "rank": 31
- },
- {
- "comment": "Norm: for floats",
- "filters": [
- [
- "IsFloat"
- ]
- ],
- "rank": 12
- },
- {
- "comment": "Norm: for a scalar (delegate to version with default field)",
- "filters": [
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 10
- }
- ],
- "2args": [
- {
- "comment": "Norm: for matrix fields",
- "filters": [
- [
- "IsNumberFieldByMatrices",
- "Tester(IsNumberFieldByMatrices)"
- ],
- [
- "IsMultiplicativeElement"
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- ],
- "rank": 10061
- },
- {
- "comment": "Norm: for a field and a scalar (delegate to version with two fields)",
- "filters": [
- [
- "IsNonTrivial",
- "Tester(IsNonTrivial)",
- "IsExtLSet",
- "IsAssociativeLOpDProd",
- "IsAssociativeLOpEProd",
- "IsDistributiveLOpDSum",
- "IsDistributiveLOpESum",
- "IsTrivialLOpEOne",
- "IsLeftActedOnByRing",
- "IsLeftActedOnByDivisionRing",
- "Tester(IsLeftActedOnByDivisionRing)",
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- "Tester(IsAdditivelyCommutative)",
- "IsLDistributive",
- "Tester(IsLDistributive)",
- "IsRDistributive",
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- ],
- [
- "IsNearAdditiveElementWithInverse",
- "IsAdditiveElement",
- "IsMultiplicativeElementWithInverse"
- ]
- ],
- "rank": 64
- },
- {
- "comment": "Norm: for an ordinary character table and a homogeneous list",
- "filters": [
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