diff --git a/gaptypes.json b/gaptypes.json
new file mode 100644
index 0000000000000000000000000000000000000000..ab822e66e9b721f1f2dbb7d0a76845190e0bef03
--- /dev/null
+++ b/gaptypes.json
@@ -0,0 +1,352183 @@
+[
+ {
+ "name": "IsObject",
+ "type": "Category",
+ "implied": []
+ },
+ {
+ "name": "ViewObj",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/oper.g",
+ "line": 1627
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 10050,
+ "comment": "ViewObj: for a pcp group",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsPcpElement)"
+ ]
+ ]
+ },
+ {
+ "rank": 10038,
+ "comment": "ViewObj: for a Lie matrix in default representation",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsLieMatrix"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for groups with known structure description",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasStructureDescription"
+ ]
+ ]
+ },
+ {
+ "rank": 10036,
+ "comment": "ViewObj: for full hom space of linear mappings",
+ "filters": [
+ [
+ "CategoryCollections(IsGeneralMapping)",
+ "IsFreeLeftModule",
+ "IsFullHomModule",
+ "HasIsFullHomModule"
+ ]
+ ],
+ "aka": [
+ "ViewFullHomModule"
+ ]
+ },
+ {
+ "rank": 10023,
+ "comment": "ViewObj: for full ring Z/nZ",
+ "filters": [
+ [
+ "IsWholeFamily",
+ "HasIsWholeFamily",
+ "CategoryCollections(IsZmodnZObjNonprime)"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for nilpotent Lie algebra automorphisms",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsNilpotentLieAutomorphismRep"
+ ]
+ ]
+ },
+ {
+ "rank": 10022,
+ "comment": "ViewObj: for group automorphisms",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsPGAutomorphismRep"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for zero mapping",
+ "filters": [
+ [
+ "IsZero",
+ "HasIsZero",
+ "IsGeneralMapping"
+ ]
+ ]
+ },
+ {
+ "rank": 10017,
+ "comment": "ViewObj: for identity mapping",
+ "filters": [
+ [
+ "IsOne",
+ "HasIsOne",
+ "IsGeneralMapping"
+ ]
+ ]
+ },
+ {
+ "rank": 10009,
+ "comment": "ViewObj: for a canonical basis",
+ "filters": [
+ [
+ "IsBasis",
+ "IsCanonicalBasis",
+ "HasIsCanonicalBasis"
+ ]
+ ]
+ },
+ {
+ "rank": 10007,
+ "comment": "ViewObj: for an enumerator that perhaps has its own `ViewObj' function",
+ "filters": [
+ [
+ "IsList",
+ "IsDenseList",
+ "IsDuplicateFree",
+ "HasIsDuplicateFree",
+ "IsEnumeratorByFunctionsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 10001,
+ "comment": "ViewObj",
+ "filters": [
+ [
+ "IsPcp"
+ ]
+ ],
+ "aka": [
+ "PRINT_OBJ",
+ "PrintObj"
+ ]
+ },
+ {
+ "rank": 10001,
+ "comment": "ViewObj: for an object with name",
+ "filters": [
+ [
+ "HasName"
+ ]
+ ]
+ },
+ {
+ "rank": 10000,
+ "comment": "ViewObj",
+ "filters": [
+ []
+ ]
+ },
+ {
+ "rank": 136,
+ "comment": "ViewObj: subgroup by property",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasElementTestFunction"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for a two-sided ideal with known generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfTwoSidedIdeal",
+ "HasLeftActingRingOfIdeal",
+ "HasRightActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for a right ideal with known generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfRightIdeal",
+ "HasRightActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 128,
+ "comment": "ViewObj: for a left ideal with known generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfLeftIdeal",
+ "HasLeftActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for a restricted mapping",
+ "filters": [
+ [
+ "IsGeneralRestrictedMappingRep"
+ ]
+ ]
+ },
+ {
+ "rank": 110,
+ "comment": "ViewObj: for a composition mapping",
+ "filters": [
+ [
+ "IsCompositionMappingRep"
+ ]
+ ]
+ },
+ {
+ "rank": 109,
+ "comment": "ViewObj: for an inverse mapping",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsInverseGeneralMappingRep"
+ ]
+ ]
+ },
+ {
+ "rank": 107,
+ "comment": "ViewObj: objects with memory",
+ "filters": [
+ [
+ "IsObjWithMemory"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: straight line program elements",
+ "filters": [
+ [
+ "IsStraightLineProgElm"
+ ]
+ ]
+ },
+ {
+ "rank": 72,
+ "comment": "ViewObj: for a field of FFEs",
+ "filters": [
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "CategoryCollections(IsFFE)",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 68,
+ "comment": "ViewObj: for cyclotomic field of cyclotomics",
+ "filters": [
+ [
+ "CategoryCollections(IsCyclotomic)",
+ "IsCyclotomicField",
+ "HasIsCyclotomicField"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "ViewObj: for abelian number field of cyclotomics",
+ "filters": [
+ [
+ "CategoryCollections(IsCyclotomic)",
+ "IsAbelianNumberField",
+ "HasIsAbelianNumberField"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "ViewObj: pc group",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for natural symmetric group",
+ "filters": [
+ [
+ "IsNaturalSymmetricGroup",
+ "HasIsNaturalSymmetricGroup"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for natural alternating group",
+ "filters": [
+ [
+ "IsNaturalAlternatingGroup",
+ "HasIsNaturalAlternatingGroup"
+ ]
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+ {
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+ "comment": "ViewObj: for function field",
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+ [
+ "IsFunctionField"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for a polynomial ring",
+ "filters": [
+ [
+ "IsPolynomialRing"
+ ]
+ ]
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+ {
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+ "comment": "ViewObj: for a matrix field",
+ "filters": [
+ [
+ "IsNumberFieldByMatrices",
+ "HasIsNumberFieldByMatrices"
+ ]
+ ]
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+ {
+ "rank": 58,
+ "comment": "ViewObj: for algebraic extension",
+ "filters": [
+ [
+ "IsNumberField",
+ "HasIsNumberField",
+ "IsAlgebraicExtension"
+ ]
+ ]
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+ "comment": "ViewObj: for full matrix module",
+ "filters": [
+ [
+ "IsFreeLeftModule",
+ "IsFullMatrixModule",
+ "HasIsFullMatrixModule"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for full row module",
+ "filters": [
+ [
+ "IsFreeLeftModule",
+ "IsFullRowModule",
+ "HasIsFullRowModule"
+ ]
+ ]
+ },
+ {
+ "rank": 48,
+ "comment": "ViewObj: subgroup of free group",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
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+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+ ]
+ ]
+ },
+ {
+ "rank": 47,
+ "comment": "ViewObj: fp group",
+ "filters": [
+ [
+ "IsSubgroupFpGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 46,
+ "comment": "ViewObj: for a matrix group with stored generators",
+ "filters": [
+ [
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+ "IsMagmaWithInverses",
+ "HasGeneratorsOfMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
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+ "comment": "ViewObj: for a matrix group",
+ "filters": [
+ [
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
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+ "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 44,
+ "comment": "ViewObj: for GF2 matrix",
+ "filters": [
+ [
+ "IsTable",
+ "IsFinite",
+ "HasIsFinite",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "IsGF2MatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 44,
+ "comment": "ViewObj: for a Lie algebra with known dimension",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
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+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsJacobianRing",
+ "HasIsJacobianRing",
+ "IsZeroSquaredRing",
+ "HasIsZeroSquaredRing",
+ "HasDimension"
+ ]
+ ]
+ },
+ {
+ "rank": 43,
+ "comment": "ViewObj: for a Lie algebra with known generators",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsJacobianRing",
+ "HasIsJacobianRing",
+ "IsZeroSquaredRing",
+ "HasIsZeroSquaredRing",
+ "HasGeneratorsOfLeftOperatorRing"
+ ]
+ ]
+ },
+ {
+ "rank": 42,
+ "comment": "ViewObj: for a Lie algebra",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsJacobianRing",
+ "HasIsJacobianRing",
+ "IsZeroSquaredRing",
+ "HasIsZeroSquaredRing"
+ ]
+ ]
+ },
+ {
+ "rank": 41,
+ "comment": "ViewObj: for an algebra-with-one with known dimension",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasDimension"
+ ]
+ ]
+ },
+ {
+ "rank": 40,
+ "comment": "ViewObj: for an algebra-with-one with known generators",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfLeftOperatorRingWithOne"
+ ]
+ ]
+ },
+ {
+ "rank": 39,
+ "comment": "ViewObj: for an algebra-with-one",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 39,
+ "comment": "ViewObj: for a FLMLOR-with-one with known dimension",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
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+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule",
+ "HasDimension"
+ ]
+ ]
+ },
+ {
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+ "comment": "ViewObj: for an algebra with known dimension",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasDimension"
+ ]
+ ]
+ },
+ {
+ "rank": 38,
+ "comment": "ViewObj: for a FLMLOR-with-one with known generators",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
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+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule",
+ "HasGeneratorsOfLeftOperatorRingWithOne"
+ ]
+ ]
+ },
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+ "comment": "ViewObj: for an ordinary block matrix",
+ "filters": [
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ]
+ ]
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+ {
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+ "comment": "ViewObj: for an algebra with known generators",
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+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
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+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
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+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfLeftOperatorRing"
+ ]
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+ {
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+ "comment": "ViewObj: for a FLMLOR-with-one",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
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+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 36,
+ "comment": "ViewObj: for an algebra",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
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+ {
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+ "comment": "ViewObj: for a FLMLOR with known dimension",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule",
+ "HasDimension"
+ ]
+ ]
+ },
+ {
+ "rank": 35,
+ "comment": "ViewObj: for a character",
+ "filters": [
+ [
+ "IsClassFunction",
+ "IsCharacter",
+ "HasIsCharacter"
+ ]
+ ]
+ },
+ {
+ "rank": 35,
+ "comment": "ViewObj: for a FLMLOR with known generators",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule",
+ "HasGeneratorsOfLeftOperatorRing"
+ ]
+ ]
+ },
+ {
+ "rank": 35,
+ "comment": "ViewObj: for a group",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 35,
+ "comment": "ViewObj: for null map matrix",
+ "filters": [
+ [
+ "IsNullMapMatrix"
+ ]
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "ViewObj: for a FLMLOR",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
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+ "IsElementOfMagmaRingModuloRelations"
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+ "IsKnuthBendixRewritingSystemRep"
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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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+ [
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+ ]
+ ]
+ },
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+ ],
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+ "HasIsJacobianRing",
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+ ]
+ },
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+ "filters": [
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+ ],
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+ ]
+ ]
+ },
+ {
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+ "filters": [
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+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
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+ ]
+ ]
+ },
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+ ],
+ [
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+ "HasIsFullSCAlgebra"
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+ ]
+ },
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+ "HasIsWholeFamily",
+ "IsMagmaWithInverses",
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+ ]
+ },
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+ "IsFullMatrixModule",
+ "HasIsFullMatrixModule"
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+ },
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+ ],
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+ "CanEasilyComputePcgs"
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+ ]
+ },
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+ "CategoryCollections(IsRationalFunction)"
+ ]
+ ]
+ },
+ {
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+ ],
+ [
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+ "IsAssociative",
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+ "CanEasilyComputePcgs"
+ ]
+ ]
+ },
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+ "HasIsAssociative"
+ ],
+ [
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+ ]
+ ]
+ },
+ {
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+ "comment": "in: for ring element, and magma ring",
+ "filters": [
+ [
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+ ],
+ [
+ "IsMagmaRingModuloRelations"
+ ]
+ ]
+ },
+ {
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+ "filters": [
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+ ],
+ [
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+ "IsAssociative",
+ "HasIsAssociative",
+ "HasComputedInducedPcgses",
+ "CanEasilyComputePcgs"
+ ]
+ ]
+ },
+ {
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+ "comment": "in: for nonnegative integers",
+ "filters": [
+ [
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+ ],
+ [
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+ ]
+ ]
+ },
+ {
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+ "filters": [
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+ ],
+ [
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+ "IsSubgroupOfWholeGroupByQuotientRep"
+ ]
+ ]
+ },
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+ "comment": "in: for full hom space of linear mappings",
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+ ],
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+ "IsFreeLeftModule",
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+ ]
+ },
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+ "filters": [
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+ ],
+ [
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+ ]
+ ]
+ },
+ {
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+ "filters": [
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+ ],
+ [
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+ ]
+ ]
+ },
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+ "filters": [
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+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject"
+ ],
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+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
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+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsRowModule",
+ "HasIsRowModule",
+ "IsGaussianSpace"
+ ]
+ ]
+ },
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+ "comment": "in: SC Rings",
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+ ],
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+ "HasIsLDistributive",
+ "IsRDistributive",
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+ "HasGeneratorsOfRing",
+ "CategoryCollections(IsSCRingObj)"
+ ]
+ ]
+ },
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+ ],
+ [
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+ ]
+ ]
+ },
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+ "filters": [
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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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+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement"
+ ],
+ [
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+ "IsHandledByNiceBasis"
+ ]
+ ]
+ },
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+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement"
+ ],
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+ "IsFiniteDimensional",
+ "HasIsFiniteDimensional"
+ ]
+ ]
+ },
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+ "filters": [
+ [
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+ ],
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+ "HasIsEquivalenceRelation",
+ "HasEquivalenceRelationPartition"
+ ]
+ ]
+ },
+ {
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+ "comment": "in: for a transformation and a full transformation semigroup",
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+ ],
+ [
+ "IsFullTransformationSemigroup",
+ "HasIsFullTransformationSemigroup"
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+ ]
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+ ]
+ },
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+ "comment": "in: for a right coset with representative",
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+ "HasActingDomain",
+ "HasFunctionAction",
+ "IsRightCosetDefaultRep"
+ ]
+ ]
+ },
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+ ],
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+ "filters": [
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+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
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+ "filters": [
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+ [
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+ "IsExternalSet"
+ ]
+ ]
+ },
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+ "filters": [
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+ ],
+ [
+ "IsAdditiveCoset"
+ ]
+ ]
+ },
+ {
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+ "comment": "in: by CanonicalRepresentativeDeterminator",
+ "filters": [
+ [],
+ [
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+ "HasCanonicalRepresentativeDeterminatorOfExternalSet"
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+ },
+ {
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+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
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+ "IsAssociativeElement",
+ "IsWord"
+ ],
+ [
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+ ]
+ ]
+ },
+ {
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+ "filters": [
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+ ],
+ [
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+ ]
+ ]
+ },
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+ "filters": [
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+ [
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+ "IsExternalOrbit"
+ ]
+ ]
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+ ],
+ [
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+ ]
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+ "IsClass"
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+ "filters": [
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+ "IsExternalOrbit"
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+ "filters": [
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+ "IsExternalOrbit"
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+ [
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+ "filters": [
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+ "IsExternalOrbit"
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+ "filters": [
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+ ]
+ ]
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+ "filters": [
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+ ]
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+ },
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+ "IsResidueClassUnionClassListRep"
+ ]
+ ]
+ },
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+ "IsResidueClassUnionResidueListRep"
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+ ]
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+ "filters": [
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+ ]
+ ]
+ },
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+ "filters": [
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+ "IsDenseList",
+ "IsDuplicateFree",
+ "HasIsDuplicateFree",
+ "IsEnumeratorByFunctionsRep"
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+ "filters": [
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+ ]
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+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 33,
+ "comment": "PrintObj: for Z_(pi) (ResClasses)",
+ "filters": [
+ [
+ "IsZ_pi",
+ "HasIsZ_pi"
+ ]
+ ]
+ },
+ {
+ "rank": 33,
+ "comment": "PrintObj: for a virtual character",
+ "filters": [
+ [
+ "IsClassFunction",
+ "IsVirtualCharacter",
+ "HasIsVirtualCharacter"
+ ]
+ ]
+ },
+ {
+ "rank": 33,
+ "comment": "PrintObj: for a semigroup Congruence with known generating pairs",
+ "filters": [
+ [
+ "HasGeneratingPairsOfMagmaCongruence",
+ "IsSemigroupCongruence",
+ "HasIsSemigroupCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 32,
+ "comment": "PrintObj: for a semigroup congruence",
+ "filters": [
+ [
+ "IsSemigroupCongruence",
+ "HasIsSemigroupCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 31,
+ "comment": "PrintObj: for a class function",
+ "filters": [
+ [
+ "IsClassFunction"
+ ]
+ ]
+ },
+ {
+ "rank": 31,
+ "comment": "PrintObj: for an algebra-with-one hom. b.i",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsOne",
+ "HasRespectsOne",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "PrintObj: for a ring-with-one with generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfRingWithOne"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "PrintObj: for an alg. hom. from f. p. algebra",
+ "filters": [
+ [
+ "IsAlgebraHomomorphismFromFpRep"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "PrintObj: for an operation algebra homomorphism",
+ "filters": [
+ [
+ "IsOperationAlgebraHomomorphismDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "PrintObj: for an algebra hom. b.i.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "PrintObj: for a two-sided ideal with known generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfTwoSidedIdeal",
+ "HasLeftActingRingOfIdeal",
+ "HasRightActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "PrintObj: for a ring-with-one",
+ "filters": [
+ [
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "PrintObj: for a right semigroup congruence with known generating pairs",
+ "filters": [
+ [
+ "HasGeneratingPairsOfMagmaCongruence",
+ "IsRightSemigroupCongruence",
+ "HasIsRightSemigroupCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "PrintObj: for a left semigroup congruence with known generating pairs",
+ "filters": [
+ [
+ "HasGeneratingPairsOfMagmaCongruence",
+ "IsLeftSemigroupCongruence",
+ "HasIsLeftSemigroupCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "PrintObj: for a right ideal with known generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfRightIdeal",
+ "HasRightActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "PrintObj: for a left ideal with known generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfLeftIdeal",
+ "HasLeftActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for inner automorphism",
+ "filters": [
+ [
+ "IsInnerAutomorphism",
+ "HasIsInnerAutomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for a ring hom. b.i.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsRingGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for algebra module",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsAlgebraModule",
+ "HasIsAlgebraModule"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for an algebra-with-one g.m.b.i",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "RespectsOne",
+ "HasRespectsOne",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for a left module hom. b.i",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsLinearGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for a ring with generators",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasGeneratorsOfRing"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for a inverse monoid with known generators",
+ "filters": [
+ [
+ "IsMagmaWithOne",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsInverseSemigroup",
+ "HasIsInverseSemigroup",
+ "HasGeneratorsOfInverseMonoid"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for a magma Congruence with known generating pairs",
+ "filters": [
+ [
+ "IsMagmaCongruence",
+ "HasGeneratingPairsOfMagmaCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for a right magma congruence with known generating pairs",
+ "filters": [
+ [
+ "IsRightMagmaCongruence",
+ "HasGeneratingPairsOfMagmaCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PrintObj: for a left magma congruence with known generating pairs",
+ "filters": [
+ [
+ "IsLeftMagmaCongruence",
+ "HasGeneratingPairsOfMagmaCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "PrintObj: for ANF automorphism",
+ "filters": [
+ [
+ "IsFieldHomomorphism",
+ "HasIsFieldHomomorphism",
+ "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",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfLeftOperatorAdditiveGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "PrintObj: for a ring",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "PrintObj: for a magma congruence",
+ "filters": [
+ [
+ "IsMagmaCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "PrintObj: For a compressed MatFFE",
+ "filters": [
+ [
+ "IsSmallList",
+ "HasIsSmallList",
+ "Is8BitMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "PrintObj: for an algebra g.m.b.i",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "PrintObj: method for vector space",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "PrintObj: pcgs",
+ "filters": [
+ [
+ "IsPcgs",
+ "IsPcgsDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "PrintObj: for free left module with known generators",
+ "filters": [
+ [
+ "IsFreeLeftModule",
+ "HasGeneratorsOfLeftOperatorAdditiveGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "PrintObj: for a right semigroup congruence",
+ "filters": [
+ [
+ "IsRightSemigroupCongruence",
+ "HasIsRightSemigroupCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "PrintObj: for a left semigroup congruence",
+ "filters": [
+ [
+ "IsLeftSemigroupCongruence",
+ "HasIsLeftSemigroupCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "PrintObj: for saturated Fitting formation",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "ContainsTrivialGroup",
+ "HasContainsTrivialGroup",
+ "IsNormalSubgroupClosed",
+ "HasIsNormalSubgroupClosed",
+ "IsQuotientClosed",
+ "HasIsQuotientClosed",
+ "IsResiduallyClosed",
+ "HasIsResiduallyClosed",
+ "IsNormalProductClosed",
+ "HasIsNormalProductClosed",
+ "IsSaturated",
+ "HasIsSaturated",
+ "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",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsPcGroupGeneralMappingByImages"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "PrintObj: for nat. hom. of pc group",
+ "filters": [
+ [
+ "IsNaturalHomomorphismPcGroupRep"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "PrintObj: for conjugator isomorphism",
+ "filters": [
+ [
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "PrintObj: for a 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",
+ "HasGeneratorsOfMagma",
+ "IsMagmaWithZeroAdjoined"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "PrintObj: for a Brauer table",
+ "filters": [
+ [
+ "IsBrauerTable"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "PrintObj: for an ordinary table",
+ "filters": [
+ [
+ "IsOrdinaryTable"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "PrintObj: for action homomorphism",
+ "filters": [
+ [
+ "IsActionHomomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "PrintObj: for a inverse semigroup with known generators",
+ "filters": [
+ [
+ "IsInverseSemigroup",
+ "HasIsInverseSemigroup",
+ "HasGeneratorsOfInverseSemigroup"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "PrintObj: for a right magma congruence",
+ "filters": [
+ [
+ "IsRightMagmaCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "PrintObj: for a left magma congruence",
+ "filters": [
+ [
+ "IsLeftMagmaCongruence"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "PrintObj: for a Rees 0-matrix semigroup",
+ "filters": [
+ [
+ "IsWholeFamily",
+ "HasIsWholeFamily",
+ "IsReesZeroMatrixSemigroup",
+ "HasIsReesZeroMatrixSemigroup"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "PrintObj: for a Rees matrix semigroup",
+ "filters": [
+ [
+ "IsWholeFamily",
+ "HasIsWholeFamily",
+ "IsReesMatrixSemigroup",
+ "HasIsReesMatrixSemigroup"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "PrintObj: for GHBI",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsGroupGeneralMappingByImages"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "PrintObj: For a compressed VecFFE",
+ "filters": [
+ [
+ "IsSmallList",
+ "HasIsSmallList",
+ "Is8BitVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "PrintObj: for monoid with known generators",
+ "filters": [
+ [
+ "IsMagmaWithOne",
+ "HasGeneratorsOfMagmaWithOne",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "PrintObj: for an equivalence relation",
+ "filters": [
+ [
+ "IsEquivalenceRelation",
+ "HasIsEquivalenceRelation"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "PrintObj: for product of Fitting formations",
+ "filters": [
+ [
+ "IsFittingProductRep",
+ "IsFormationProductRep"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsUnicodeCharacter"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "PrintObj: modulo pcgs",
+ "filters": [
+ [
+ "IsModuloPcgs"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "PrintObj: combinatorial collector rep (32 Bits, up to date)",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "Is32BitsSingleCollectorRep",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "PrintObj: combinatorial collector rep (16 Bits, up to date)",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "Is16BitsSingleCollectorRep",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "PrintObj: combinatorial collector rep (8 Bits, up to date)",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "Is8BitsSingleCollectorRep",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj: for Fitting formation",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "ContainsTrivialGroup",
+ "HasContainsTrivialGroup",
+ "IsNormalSubgroupClosed",
+ "HasIsNormalSubgroupClosed",
+ "IsQuotientClosed",
+ "HasIsQuotientClosed",
+ "IsResiduallyClosed",
+ "HasIsResiduallyClosed",
+ "IsNormalProductClosed",
+ "HasIsNormalProductClosed",
+ "IsClassByPropertyRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj: for a saturated formation",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "ContainsTrivialGroup",
+ "HasContainsTrivialGroup",
+ "IsQuotientClosed",
+ "HasIsQuotientClosed",
+ "IsResiduallyClosed",
+ "HasIsResiduallyClosed",
+ "IsSaturated",
+ "HasIsSaturated",
+ "IsClassByPropertyRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj: combinatorial collector rep (32 Bits)",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "Is32BitsSingleCollectorRep",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj: combinatorial collector rep (16 Bits)",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "Is16BitsSingleCollectorRep",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj: combinatorial collector rep (8 Bits)",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "Is8BitsSingleCollectorRep",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj: combinatorial collector (up to date)",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "Is32BitsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "Is16BitsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "Is8BitsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "PrintObj: for mapping by function with inverse",
+ "filters": [
+ [
+ "IsMappingByFunctionWithInverseRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj: for a subsemigroup of a Rees 0-matrix semigroup",
+ "filters": [
+ [
+ "IsMagma",
+ "HasGeneratorsOfMagma",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsReesZeroMatrixSemigroupElement)"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj: for a subsemigroup of a Rees matrix semigroup",
+ "filters": [
+ [
+ "IsMagma",
+ "HasGeneratorsOfMagma",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsReesMatrixSemigroupElement)"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj: combinatorial collector",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsCombinatorialCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "Is32BitsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "Is16BitsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "Is8BitsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsUpToDatePolycyclicCollector",
+ "IsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "PrintObj: zmodnze : for full collection Z/nZ(m)",
+ "filters": [
+ [
+ "IsWholeFamily",
+ "HasIsWholeFamily",
+ "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",
+ "HasGeneratorsOfMagmaIdeal",
+ "IsSemigroupIdeal",
+ "HasIsSemigroupIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "PrintObj: for a Schunck class",
+ "filters": [
+ [
+ "IsSchunckClass",
+ "HasIsSchunckClass",
+ "IsClassByPropertyRep"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "PrintObj: for semigroup homomorphism by images",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsSPGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "IsSemigroupHomomorphismByImagesRep"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "PrintObj: for group general mapping b.i.",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsPowerConjugateCollector",
+ "IsSingleCollectorRep"
+ ]
+ ]
+ },
+ {
+ "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",
+ "HasIsLaurentPolynomial"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "PrintObj: for an add. magma-with-inverses with generators",
+ "filters": [
+ [
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfNearAdditiveGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "PrintObj: for a semigroup ideal",
+ "filters": [
+ [
+ "IsLeftActedOnBySuperset",
+ "IsRightActedOnBySuperset",
+ "IsMagma",
+ "IsSemigroupIdeal",
+ "HasIsSemigroupIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 16,
+ "comment": "PrintObj: for a Molien series",
+ "filters": [
+ [
+ "IsRationalFunction",
+ "IsUnivariateRationalFunction",
+ "HasIsUnivariateRationalFunction",
+ "HasMolienSeriesInfo"
+ ]
+ ]
+ },
+ {
+ "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",
+ "HasGeneratorsOfMagma",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 16,
+ "comment": "PrintObj: for a magma ideal with known generators",
+ "filters": [
+ [
+ "IsLeftActedOnBySuperset",
+ "IsRightActedOnBySuperset",
+ "IsMagma",
+ "HasGeneratorsOfMagmaIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 16,
+ "comment": "PrintObj: for -infinity",
+ "filters": [
+ [
+ "IsNegInfinity"
+ ]
+ ]
+ },
+ {
+ "rank": 16,
+ "comment": "PrintObj: for infinity",
+ "filters": [
+ [
+ "IsInfinity"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "PrintObj: for formation product",
+ "filters": [
+ [
+ "IsFormationProductRep"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "PrintObj: for formation",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "ContainsTrivialGroup",
+ "HasContainsTrivialGroup",
+ "IsQuotientClosed",
+ "HasIsQuotientClosed",
+ "IsResiduallyClosed",
+ "HasIsResiduallyClosed",
+ "IsClassByPropertyRep"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "PrintObj: for Fitting product",
+ "filters": [
+ [
+ "IsFittingProductRep"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "PrintObj: for Fitting class",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "ContainsTrivialGroup",
+ "HasContainsTrivialGroup",
+ "IsNormalSubgroupClosed",
+ "HasIsNormalSubgroupClosed",
+ "IsNormalProductClosed",
+ "HasIsNormalProductClosed",
+ "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",
+ "HasIsUnivariateRationalFunction"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "PrintObj: for an add. magma-with-zero with generators",
+ "filters": [
+ [
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveMagmaWithZero",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfNearAdditiveMagmaWithZero"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "PrintObj: for a magma ideal",
+ "filters": [
+ [
+ "IsLeftActedOnBySuperset",
+ "IsRightActedOnBySuperset",
+ "IsMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj: for Fitting set",
+ "filters": [
+ [
+ "IsClassByPropertyRep",
+ "IsFittingSetRep"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsPowerConjugateCollector",
+ "IsDeepThoughtCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsPadicExtensionNumber"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsPurePadicNumber"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj: polynomial",
+ "filters": [
+ [
+ "IsPolynomial",
+ "HasIsPolynomial"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj: for a right magma ideal with known generators",
+ "filters": [
+ [
+ "IsRightActedOnBySuperset",
+ "HasGeneratorsOfExtRSet",
+ "IsMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj: for a left magma ideal with known generators",
+ "filters": [
+ [
+ "IsLeftActedOnBySuperset",
+ "HasGeneratorsOfExtLSet",
+ "IsMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "PrintObj: for mapping by function",
+ "filters": [
+ [
+ "IsMappingByFunctionRep"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: for from-the-left collector",
+ "filters": [
+ [
+ "IsFromTheLeftCollectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: for floats",
+ "filters": [
+ [
+ "IsFloat"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep)",
+ "filters": [
+ [
+ "IsZmodnZepsObj",
+ "IsZmodnZepsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: rational function",
+ "filters": [
+ [
+ "IsRationalFunction"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: for UEALattice element",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsUEALatticeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: for an add. magma with generators",
+ "filters": [
+ [
+ "IsNearAdditiveMagma",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfNearAdditiveMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: for a right magma ideal",
+ "filters": [
+ [
+ "IsRightActedOnBySuperset",
+ "IsMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "PrintObj: for a left magma ideal",
+ "filters": [
+ [
+ "IsLeftActedOnBySuperset",
+ "IsMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsPowerCommutatorCollector"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsPowerConjugateCollector"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PrintObj: fp algebra elements",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsElementOfFpAlgebra"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PrintObj: for an additive coset",
+ "filters": [
+ [
+ "IsAdditiveCoset"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PrintObj: for an add. magma",
+ "filters": [
+ [
+ "IsNearAdditiveMagma",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PrintObj: for a binary relation on n points",
+ "filters": [
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsConjugacyClassSubgroupsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsRationalClassGroupRep"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsConjugacyClassGroupRep"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsPolycyclicCollector"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for a plist vector",
+ "filters": [
+ [
+ "IsPlistVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for GF2 vector",
+ "filters": [
+ [
+ "IsGF2VectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for s. c. ring element",
+ "filters": [
+ [
+ "IsSCRingObj"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for weight rep element",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsWeightRepElement"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for direct sum elements",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsDirectSumElement"
+ ]
+ ]
+ },
+ {
+ "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 algebra module element in packed representation",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsAlgebraModuleElement"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for s. c. algebra element",
+ "filters": [
+ [
+ "IsSCAlgebraObj"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for magma ring element",
+ "filters": [
+ [
+ "IsElementOfMagmaRingModuloRelations"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PrintObj: for a mapping",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "PrintObj: for an element of an f.p. group (default repres.)",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsElementOfFpGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "PrintObj: for external orbit",
+ "filters": [
+ [
+ "IsExternalOrbit"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "PrintObj: pcword",
+ "filters": [
+ [
+ "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+ "IsNBitsPcWordRep"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsRewritingSystem",
+ "IsBuiltFromGroup",
+ "HasIsBuiltFromGroup"
+ ]
+ ]
+ },
+ {
+ "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",
+ "HasIsSemiEchelonized",
+ "HasBasisVectors"
+ ]
+ ]
+ },
+ {
+ "rank": 9,
+ "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: 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",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsMultiplicativeElementWithInverseByRws"
+ ]
+ ]
+ },
+ {
+ "rank": 9,
+ "comment": "PrintObj: for a semi-echelonized basis",
+ "filters": [
+ [
+ "IsBasis",
+ "IsSemiEchelonized",
+ "HasIsSemiEchelonized"
+ ]
+ ]
+ },
+ {
+ "rank": 9,
+ "comment": "PrintObj: for right transversal",
+ "filters": [
+ [
+ "IsList",
+ "IsRightTransversalRep"
+ ]
+ ]
+ },
+ {
+ "rank": 8,
+ "comment": "PrintObj: for a partial perm",
+ "filters": [
+ [
+ "IsPartialPerm"
+ ]
+ ]
+ },
+ {
+ "rank": 8,
+ "comment": "PrintObj: for sparse hash tables",
+ "filters": [
+ [
+ "IsSparseHashRep"
+ ]
+ ]
+ },
+ {
+ "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",
+ "HasBasisVectors"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "PrintObj: for IsGroupClass and IsClassByPropertyRep",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "IsClassByPropertyRep"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "PrintObj",
+ "filters": [
+ [
+ "IsUnicodeString"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "PrintObj: for a Green's class",
+ "filters": [
+ [
+ "IsGreensClass"
+ ]
+ ]
+ },
+ {
+ "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 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: method for a weak pointer object",
+ "filters": [
+ [
+ "IsWeakPointerObject"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "PrintObj: for an enumerator that perhaps has its own `PrintObj' function",
+ "filters": [
+ [
+ "IsList",
+ "IsDenseList",
+ "IsDuplicateFree",
+ "HasIsDuplicateFree",
+ "IsEnumeratorByFunctionsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "PrintObj: for ioTCPstream",
+ "filters": [
+ [
+ "IsInputOutputStream",
+ "IsInputOutputTCPStreamRep"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "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": [
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+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "PrintObj: External Set",
+ "filters": [
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+ "IsExternalSet"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "PrintObj: assoc word in letter rep",
+ "filters": [
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+ "IsAssociativeElement",
+ "IsWord",
+ "IsLetterAssocWordRep"
+ ]
+ ]
+ },
+ {
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+ "comment": "PrintObj: for an eq. class",
+ "filters": [
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+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "PrintObj: iostream",
+ "filters": [
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+ "IsInputOutputStreamByPtyRep"
+ ]
+ ]
+ },
+ {
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+ "comment": "PrintObj: for IsGroupClassByListRep",
+ "filters": [
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+ ]
+ ]
+ },
+ {
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+ "comment": "PrintObj: for IsClassByUnionRep",
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+ ]
+ ]
+ },
+ {
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+ "comment": "PrintObj: for IsClassByIntersectionRep",
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+ ]
+ ]
+ },
+ {
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+ "comment": "PrintObj: for IsClassByComplementRep",
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+ ]
+ },
+ {
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+ ]
+ },
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+ "comment": "PrintObj: for a Rees 0-matrix semigroup element",
+ "filters": [
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+ ]
+ ]
+ },
+ {
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+ "comment": "PrintObj: for a Rees matrix semigroup element",
+ "filters": [
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+ ]
+ },
+ {
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+ "comment": "PrintObj: for an f.p. semigroup element",
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+ ]
+ },
+ {
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+ "comment": "PrintObj: for a presentation in default representation",
+ "filters": [
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+ "IsPresentationDefaultRep"
+ ]
+ ]
+ },
+ {
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+ "filters": [
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+ ]
+ },
+ {
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+ ]
+ },
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+ "comment": "PrintObj: wrapped additive elements",
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+ },
+ {
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+ "comment": "PrintObj: for an infinite list of generators",
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+ ]
+ },
+ {
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+ "comment": "PrintObj: for an infinite list of names",
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+ ]
+ },
+ {
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+ "comment": "PrintObj: for an enumerator",
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+ },
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+ },
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+ "comment": "PrintObj: for mutable basis with underlying mutable basis",
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+ },
+ {
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+ "comment": "PrintObj: for a mutable basis of a Gaussian matrix space",
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+ "IsMutableBasisOfGaussianMatrixSpaceRep"
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+ ]
+ },
+ {
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+ "comment": "PrintObj: for a mutable basis of a Gaussian row space",
+ "filters": [
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+ "IsMutableBasisOfGaussianRowSpaceRep"
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+ ]
+ },
+ {
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+ "comment": "PrintObj: for mutable basis represented by a nice mutable basis",
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+ "IsMutableBasisViaNiceMutableBasisRep"
+ ]
+ ]
+ },
+ {
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+ "comment": "PrintObj: for mutable basis represented by an immutable basis",
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+ ]
+ },
+ {
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+ "comment": "PrintObj: for an iterator that perhaps has its own `PrintObj' function",
+ "filters": [
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+ ]
+ },
+ {
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+ },
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+ },
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+ "comment": "PrintObj: output text file",
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+ },
+ {
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+ },
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+ },
+ {
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+ "comment": "PRINT_OBJ: for a type",
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+ "comment": "PRINT_OBJ: for a family",
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+ {
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+ "comment": "PrintObj: default method delegating to PrintString",
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+ }
+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
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+ },
+ {
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+ "type": "Operation",
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+ },
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+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
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+ "comment": "PrintString: for a group with generators",
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+ "HasGeneratorsOfMagmaWithInverses",
+ "IsAssociative",
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+ "comment": "PrintString: for a inverse monoid with known generators",
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+ ]
+ },
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+ "comment": "PrintString: for a Brauer table",
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+ },
+ {
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+ "comment": "PrintString: for an ordinary table",
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+ ]
+ },
+ {
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+ "comment": "PrintString: for a inverse semigroup with known generators",
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+ "HasIsInverseSemigroup",
+ "HasGeneratorsOfInverseSemigroup"
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+ },
+ {
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+ "comment": "PrintString: for monoid with known generators",
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+ },
+ {
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+ "comment": "PrintString: for a direct product element",
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+ ]
+ },
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+ "HasGeneratorsOfMagma",
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+ },
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+ "comment": "PrintString: default method delegating to String",
+ "filters": [
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+ ],
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+ "comment": "PrintString: for an object, and zero",
+ "filters": [
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+ "comment": "PrintString: for an object, and a negative integer",
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+ "comment": "Display: for matrix of FFEs",
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+ "comment": "Display: for matrix over Integers mod n",
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+ ]
+ },
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+ {
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+ "comment": "Display: generic: use DisplayString or otherwise PrintObj",
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+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfRightOperatorAdditiveGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "Representative: for left operator additive group with known generators",
+ "filters": [
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+ "IsDistributiveLOpDSum",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfLeftOperatorAdditiveGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "Representative: for magma-with-inverses with generators",
+ "filters": [
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+ "IsMagmaWithInverses",
+ "HasGeneratorsOfMagmaWithInverses"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "Representative: for a Rees 0-matrix semigroup",
+ "filters": [
+ [
+ "IsReesZeroMatrixSemigroup",
+ "HasIsReesZeroMatrixSemigroup"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "Representative: for a Rees matrix semigroup",
+ "filters": [
+ [
+ "IsReesMatrixSemigroup",
+ "HasIsReesMatrixSemigroup"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "Representative: for additive-magma-with-inverses with known generators",
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+ [
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfNearAdditiveGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "Representative: for additive-magma-with-zero with stored parent",
+ "filters": [
+ [
+ "HasParentAttr",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveMagmaWithZero",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "Representative: for additive-magma-with-zero with known generators",
+ "filters": [
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+ "IsNearAdditiveMagma",
+ "IsNearAdditiveMagmaWithZero",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfNearAdditiveMagmaWithZero"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "Representative: for magma-with-one with stored parent",
+ "filters": [
+ [
+ "HasParentAttr",
+ "IsMagmaWithOne"
+ ]
+ ]
+ },
+ {
+ "rank": 15,
+ "comment": "Representative: for magma-with-one with generators",
+ "filters": [
+ [
+ "IsMagmaWithOne",
+ "HasGeneratorsOfMagmaWithOne"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "Representative: for additive magma with known generators",
+ "filters": [
+ [
+ "IsNearAdditiveMagma",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "HasGeneratorsOfNearAdditiveMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "Representative: for magma with generators",
+ "filters": [
+ [
+ "IsMagma",
+ "HasGeneratorsOfMagma"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "Representative: External Set",
+ "filters": [
+ [
+ "IsExternalSet"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "Representative: for a domain with known domain generators",
+ "filters": [
+ [
+ "IsCollection",
+ "IsGeneralizedDomain",
+ "HasGeneratorsOfDomain"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "Representative: for a domain with known elements list",
+ "filters": [
+ [
+ "IsCollection",
+ "HasAsList",
+ "IsGeneralizedDomain"
+ ]
+ ]
+ },
+ {
+ "rank": 5,
+ "comment": "Representative: for a collection that is a list",
+ "filters": [
+ [
+ "IsList",
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 2,
+ "comment": "Representative: for a list",
+ "filters": [
+ [
+ "IsList"
+ ]
+ ]
+ }
+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "Representative"
+ ]
+ },
+ {
+ "name": "SetRepresentative",
+ "type": "Operation",
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+ {
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+ "line": 1563
+ }
+ ],
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+ "IsAttributeStoringRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetRepresentative: default method, does nothing",
+ "filters": [
+ [],
+ []
+ ]
+ }
+ ],
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+ "4args": [],
+ "5args": [],
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+ ]
+ },
+ {
+ "name": "HasRepresentative",
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+ ]
+ },
+ {
+ "name": "RepresentativeSmallest",
+ "type": "Attribute",
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+ "line": 1593
+ }
+ ],
+ "filters": [],
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+ "HasRepresentativeSmallest"
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+ ]
+ },
+ {
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+ "comment": "RepresentativeSmallest: for an empty list",
+ "filters": [
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
+ {
+ "rank": 8,
+ "comment": "RepresentativeSmallest: for a strictly sorted list",
+ "filters": [
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+ "HasIS_SSORT_LIST"
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+ },
+ {
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+ {
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+ "IsCollection",
+ "HasEnumeratorSorted"
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+ {
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+ "filters": [
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+ "IsList"
+ ]
+ ],
+ "aka": [
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+ ]
+ },
+ {
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+ ]
+ },
+ {
+ "name": "SetRepresentativeSmallest",
+ "type": "Operation",
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+ {
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+ "line": 1593
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+ ],
+ "filters": [],
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+ "IsAttributeStoringRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetRepresentativeSmallest: default method, does nothing",
+ "filters": [
+ [],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "SetRepresentativeSmallest"
+ ]
+ },
+ {
+ "name": "HasRepresentativeSmallest",
+ "type": "Filter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/coll.gd",
+ "line": 1593
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "HasRepresentativeSmallest"
+ ]
+ },
+ {
+ "name": "Random",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/coll.gd",
+ "line": 1654
+ },
+ {
+ "file": "/home/mp397/git/gap/lib/coll.gd",
+ "line": 1655
+ },
+ {
+ "file": "/home/mp397/git/gap/lib/random.gd",
+ "line": 72
+ },
+ {
+ "file": "/home/mp397/git/gap/lib/random.gd",
+ "line": 73
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 403,
+ "comment": "Random: for natural SL",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNaturalSL",
+ "HasIsNaturalSL"
+ ]
+ ]
+ },
+ {
+ "rank": 401,
+ "comment": "Random: for natural GL",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNaturalGL",
+ "HasIsNaturalGL"
+ ]
+ ]
+ },
+ {
+ "rank": 372,
+ "comment": "Random: for a group handled by nice monomorphism",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsHandledByNiceMonomorphism",
+ "HasIsHandledByNiceMonomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 116,
+ "comment": "Random: for an internal list",
+ "filters": [
+ [
+ "IsList",
+ "IsInternalRep"
+ ]
+ ]
+ },
+ {
+ "rank": 108,
+ "comment": "Random: for sparse hash tables",
+ "filters": [
+ [
+ "IsHash",
+ "IsSparseHashRep"
+ ]
+ ]
+ },
+ {
+ "rank": 107,
+ "comment": "Random: for dense hash tables",
+ "filters": [
+ [
+ "IsHash",
+ "IsDenseHashRep"
+ ]
+ ]
+ },
+ {
+ "rank": 75,
+ "comment": "Random: for a natural alternating group: floyd's algorithm",
+ "filters": [
+ [
+ "IsNaturalAlternatingGroup",
+ "HasIsNaturalAlternatingGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 75,
+ "comment": "Random: for a natural symmetric group: floyd's algorithm",
+ "filters": [
+ [
+ "IsNaturalSymmetricGroup",
+ "HasIsNaturalSymmetricGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 71,
+ "comment": "Random: for a permutation group",
+ "filters": [
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 70,
+ "comment": "Random: for Rationals",
+ "filters": [
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "CategoryCollections(IsCyclotomic)",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing",
+ "IsPrimeField",
+ "HasIsPrimeField"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "Random: for a large non-prime finite field",
+ "filters": [
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsFinite",
+ "HasIsFinite",
+ "CategoryCollections(IsFFE)",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 61,
+ "comment": "Random: for a finite prime field",
+ "filters": [
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsFinite",
+ "HasIsFinite",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing",
+ "IsPrimeField",
+ "HasIsPrimeField"
+ ]
+ ]
+ },
+ {
+ "rank": 60,
+ "comment": "Random: for a finite field with known primitive root",
+ "filters": [
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsFinite",
+ "HasIsFinite",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing",
+ "HasPrimitiveRoot"
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+ ]
+ },
+ {
+ "rank": 56,
+ "comment": "Random: for an algebraic extension",
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+ "IsAlgebraicExtension"
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+ ]
+ },
+ {
+ "rank": 55,
+ "comment": "Random: for a pcgs computable groups",
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+ "IsFinite",
+ "HasIsFinite",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CanEasilyComputePcgs"
+ ]
+ ]
+ },
+ {
+ "rank": 50,
+ "comment": "Random: for a pcp group",
+ "filters": [
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsPcpElement)"
+ ]
+ ]
+ },
+ {
+ "rank": 49,
+ "comment": "Random: for full ring Z/nZ",
+ "filters": [
+ [
+ "IsWholeFamily",
+ "HasIsWholeFamily",
+ "CategoryCollections(IsZmodnZObjNonprime)"
+ ]
+ ]
+ },
+ {
+ "rank": 49,
+ "comment": "Random: for an fp group",
+ "filters": [
+ [
+ "IsFinite",
+ "HasIsFinite",
+ "IsSubgroupFpGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 48,
+ "comment": "Random: for a full matrix module",
+ "filters": [
+ [
+ "IsFreeLeftModule",
+ "IsFullMatrixModule",
+ "HasIsFullMatrixModule"
+ ]
+ ]
+ },
+ {
+ "rank": 48,
+ "comment": "Random: for a full row module",
+ "filters": [
+ [
+ "IsFreeLeftModule",
+ "IsFullRowModule",
+ "HasIsFullRowModule"
+ ]
+ ]
+ },
+ {
+ "rank": 48,
+ "comment": "Random: for a free group",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+ ]
+ ]
+ },
+ {
+ "rank": 43,
+ "comment": "Random: LAGUNA: for a Lie algebra coming from an associative algebra",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsJacobianRing",
+ "HasIsJacobianRing",
+ "IsZeroSquaredRing",
+ "HasIsZeroSquaredRing",
+ "IsLieAlgebraByAssociativeAlgebra"
+ ]
+ ]
+ },
+ {
+ "rank": 40,
+ "comment": "Random: for `Integers'",
+ "filters": [
+ [
+ "IsIntegers"
+ ]
+ ]
+ },
+ {
+ "rank": 37,
+ "comment": "Random: LAGUNA: for full ot normalized unit group of group ring",
+ "filters": [
+ [
+ "IsGroupOfUnitsOfMagmaRing",
+ "HasIsGroupOfUnitsOfMagmaRing"
+ ]
+ ]
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+ {
+ "rank": 36,
+ "comment": "Random: for full hom space of linear mappings",
+ "filters": [
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+ "CategoryCollections(IsGeneralMapping)",
+ "IsFreeLeftModule",
+ "IsFullHomModule",
+ "HasIsFullHomModule"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "Random: for a free monoid",
+ "filters": [
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+ "IsMagmaWithOne",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "Random: for a free left module",
+ "filters": [
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+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "Random: for a free semigroup",
+ "filters": [
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+ "IsMagma",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections((IsWord and IsAssociativeElement))"
+ ]
+ ]
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+ "rank": 18,
+ "comment": "Random: for the full collection Z/nZ(m)",
+ "filters": [
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+ "IsWholeFamily",
+ "HasIsWholeFamily",
+ "CategoryCollections(IsZmodnZepsObj)"
+ ]
+ ]
+ },
+ {
+ "rank": 16,
+ "comment": "Random: for a RightCoset",
+ "filters": [
+ [
+ "IsRightCoset"
+ ]
+ ]
+ },
+ {
+ "rank": 13,
+ "comment": "Random: for a free magma",
+ "filters": [
+ [
+ "IsMagma",
+ "CategoryCollections(IsNonassocWord)"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "Random: for an additive coset",
+ "filters": [
+ [
+ "IsAdditiveCoset"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "Random: for for an external orbit: via acting domain",
+ "filters": [
+ [
+ "IsExternalOrbit"
+ ]
+ ]
+ },
+ {
+ "rank": 8,
+ "comment": "Random: for a double coset",
+ "filters": [
+ [
+ "IsDoubleCoset"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "Random: for a dense small list",
+ "filters": [
+ [
+ "IsList",
+ "IsDenseList",
+ "IsSmallList",
+ "HasIsSmallList"
+ ]
+ ],
+ "aka": [
+ "RandomList"
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+ {
+ "rank": 5,
+ "comment": "Random: for p-adic extension family",
+ "filters": [
+ [
+ "CategoryFamily(IsPadicExtensionNumber)"
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+ ]
+ },
+ {
+ "rank": 5,
+ "comment": "Random: for a pure p-adic family",
+ "filters": [
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+ "CategoryFamily(IsPurePadicNumber)"
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+ {
+ "rank": 4,
+ "comment": "Random: for an infinite list of generators",
+ "filters": [
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+ "IsList",
+ "IsInfiniteListOfGeneratorsRep"
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+ {
+ "rank": 3,
+ "comment": "Random: for a dense (small) list",
+ "filters": [
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+ "IsList",
+ "IsDenseList"
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+ {
+ "rank": 0,
+ "comment": "Random: for a (finite) collection",
+ "filters": [
+ [
+ "IsCollection",
+ "IsFinite",
+ "HasIsFinite"
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+ {
+ "rank": 0,
+ "comment": "Random: fallback method to test conditions",
+ "filters": [
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+ "comment": "Enumerator: finite pc computable groups",
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+ ]
+ },
+ {
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+ "comment": "Enumerator: for AffineCrystGroup",
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+ "IsAffineCrystGroupOnLeftOrRight",
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+ },
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+ "comment": "Enumerator: for enumerator of a free group",
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+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
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+ ]
+ },
+ {
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+ "comment": "Enumerator: fp gp.",
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+ [
+ "IsFinite",
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+ "IsSubgroupFpGroup"
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+ },
+ {
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+ "comment": "Enumerator: for trivial magma-with-one",
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+ "HasIsTrivial",
+ "IsMagmaWithOne"
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+ ],
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+ },
+ {
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+ "comment": "Enumerator: for integers",
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+ },
+ {
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+ "comment": "Enumerator: generic method for a group",
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+ },
+ {
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+ "IsRDistributive",
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+ "HasGeneratorsOfRingWithOne"
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+ ],
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+ "IsFullTransformationSemigroup",
+ "HasIsFullTransformationSemigroup"
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+ "IsTrivial",
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+ ],
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+ "IsReesZeroMatrixSemigroup",
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+ "comment": "Enumerator: zmodnze : for full collection Z/nZ(m)",
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+ "comment": "Enumerator: for a Rees matrix semigroup",
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+ {
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+ "comment": "Enumerator: for a left semigroup ideal",
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+ {
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+ "comment": "Enumerator: for a right semigroup ideal",
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+ "comment": "Enumerator: for a generic semigroup",
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+ "comment": "Enumerator: for a free magma",
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+ {
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+ "comment": "Enumerator: generic method for an add. magma",
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+ "comment": "Enumerator",
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+ ]
+ },
+ {
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+ "comment": "Enumerator",
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+ },
+ {
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+ "comment": "Enumerator: for an additive coset",
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+ {
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+ "comment": "Enumerator",
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+ },
+ {
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+ "comment": "Enumerator: xorb by stabilizer",
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+ {
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+ "comment": "Enumerator: <xorb by pcgs>",
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+ {
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+ "comment": "Enumerator: for external subset with home enumerator",
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+ "comment": "Enumerator: for dense hash tables",
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+ "comment": "Enumerator: for list dictionaries",
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+ "comment": "Enumerator: for equivalence classes",
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+ {
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+ "comment": "Enumerator: for a domain with stored domain generators",
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+ "HasIsNonTrivial",
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+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
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+ "IsMagmaWithOne",
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+ "IsAssociative",
+ "HasIsAssociative",
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+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
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+ "HasIsLDistributive",
+ "IsRDistributive",
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+ [
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+ "IsDistributiveLOpESum",
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+ "IsLeftActedOnByDivisionRing",
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+ "IsRDistributive",
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+ "IsPrimeField",
+ "HasIsPrimeField"
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+ ]
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+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "CategoryCollections(IsCyclotomic)",
+ "IsExtLSet",
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+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
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+ "IsLeftActedOnByDivisionRing",
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+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
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+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
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+ "IsAdditivelyCommutative",
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+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
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+ "IsPrimeField",
+ "HasIsPrimeField"
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+ [
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+ "HasIsZ_pi"
+ ]
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+ {
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+ "comment": "IsSubset: for subgroups of free groups",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsFinitelyGeneratedGroup",
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+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsFinitelyGeneratedGroup",
+ "HasIsFinitelyGeneratedGroup",
+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+ ]
+ ]
+ },
+ {
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+ "comment": "IsSubset: for certain cyclotomic semirings",
+ "filters": [
+ [
+ "CategoryCollections(IsCyclotomic)",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
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+ "IsNearAdditiveMagma",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
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+ "comment": "IsSubset: 2-sided ideal in ring, naive",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
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+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasLeftActingRingOfIdeal",
+ "HasRightActingRingOfIdeal"
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+ ]
+ },
+ {
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+ "comment": "IsSubset: subgroups of fp group by quot. rep",
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+ "IsSubgroupFpGroup",
+ "IsSubgroupOfWholeGroupByQuotientRep"
+ ],
+ [
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+ "IsSubgroupOfWholeGroupByQuotientRep"
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+ },
+ {
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+ "comment": "IsSubset: pcgs computable groups",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasFamilyPcgs",
+ "CanEasilyComputePcgs"
+ ],
+ [
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+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
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+ "filters": [
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+ "IsSubgroupFpGroup"
+ ],
+ [
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+ "IsSubgroupFpGroup"
+ ]
+ ]
+ },
+ {
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+ "comment": "IsSubset: subgp fp group: via quotient rep",
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+ "IsSubgroupFpGroup"
+ ],
+ [
+ "IsSubgroupFpGroup"
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+ ]
+ },
+ {
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+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
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+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
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+ "HasIsRDistributive",
+ "IsFreeLeftModule"
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+ [
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+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
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+ "IsMagmaWithOne",
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+ "IsNearAdditiveGroup",
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+ "IsLDistributive",
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+ "HasIsRDistributive",
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+ ]
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+ "HasIsZ_pi"
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+ [
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+ },
+ {
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+ "comment": "IsSubset: generic method for two groups",
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+ "IsAssociative",
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+ ],
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+ "HasIsAssociative"
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+ ]
+ },
+ {
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+ "comment": "IsSubset: for two FLMLORs",
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+ "IsAssociativeLOpDProd",
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+ "IsNearAdditiveMagma",
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+ "IsFreeLeftModule"
+ ],
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+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
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+ ]
+ },
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+ "HasIsZ_pi"
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+ [
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+ "HasIsZ_pi"
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+ ]
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+ {
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+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
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+ "HasIsLDistributive",
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+ "HasIsRDistributive",
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+ },
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+ "IsNearAdditiveMagma",
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+ "HasIsAdditivelyCommutative",
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+ ]
+ },
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+ "filters": [
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+ [
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+ ]
+ },
+ {
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+ "comment": "IsSubset: for two collections that are internal lists",
+ "filters": [
+ [
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+ "IsInternalRep",
+ "IsCollection"
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+ "IsInternalRep",
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+ [
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+ {
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+ "filters": [
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+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
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+ "IsNearAdditiveGroup",
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+ ]
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+ {
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+ "IsInternalRep"
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+ [
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+ "IsInternalRep"
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+ ]
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+ "comment": "IsSubset: for two additive magmas with zero",
+ "filters": [
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+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
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+ [
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+ "IsNearAdditiveMagmaWithZero",
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+ ]
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+ {
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+ "comment": "IsSubset: for two magmas with one",
+ "filters": [
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+ [
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+ {
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+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
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+ ]
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+ [
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+ "HasIsEmpty"
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+ "comment": "IsSubset: for two unions of residue classes with fixed rep's (ResClasses)",
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+ [
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+ "comment": "IsSubset: for the base ring and a residue class union (ResClasses)",
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+ [
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+ "comment": "IsSubset: for two collections (loop over the elements of the second)",
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+ [
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+ [
+ "IsCollection"
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+ {
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+ "comment": "IsSubset: for two collections in different families",
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+ [
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+ "aka": [
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+ },
+ {
+ "name": "Intersection2",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/coll.gd",
+ "line": 3050
+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
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+ "comment": "Intersection2: domain and whole family",
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+ "IsCollection",
+ "IsGeneralizedDomain"
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+ [
+ "IsCollection",
+ "IsWholeFamily",
+ "HasIsWholeFamily"
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+ },
+ {
+ "rank": 10009,
+ "comment": "Intersection2: whole family and domain",
+ "filters": [
+ [
+ "IsCollection",
+ "IsWholeFamily",
+ "HasIsWholeFamily"
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+ "IsGeneralizedDomain"
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+ {
+ "rank": 10002,
+ "comment": "Intersection2: for two times the same ring (ResClasses)",
+ "filters": [
+ [
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+ [
+ "IsListOrCollection"
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+ {
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+ "comment": "Intersection2: handled by nice monomorphism:group CollColl",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
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+ [
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+ "IsAssociative",
+ "HasIsAssociative",
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+ "HasIsHandledByNiceMonomorphism"
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+ ]
+ },
+ {
+ "rank": 136,
+ "comment": "Intersection2: for two cyclotomic fields of cyclotomics",
+ "filters": [
+ [
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+ "IsCyclotomicField",
+ "HasIsCyclotomicField"
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+ "HasIsCyclotomicField"
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+ ]
+ },
+ {
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+ "comment": "Intersection2: for abelian number field and cyclotomic field",
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+ [
+ "CategoryCollections(IsCyclotomic)",
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+ [
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+ "IsCyclotomicField",
+ "HasIsCyclotomicField"
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+ },
+ {
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+ "comment": "Intersection2: for cyclotomic field and abelian number field",
+ "filters": [
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+ "CategoryCollections(IsCyclotomic)",
+ "IsCyclotomicField",
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+ ],
+ [
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+ "HasIsAbelianNumberField"
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+ ]
+ },
+ {
+ "rank": 132,
+ "comment": "Intersection2: for two abelian number fields",
+ "filters": [
+ [
+ "CategoryCollections(IsCyclotomic)",
+ "IsAbelianNumberField",
+ "HasIsAbelianNumberField"
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+ [
+ "CategoryCollections(IsCyclotomic)",
+ "IsAbelianNumberField",
+ "HasIsAbelianNumberField"
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+ ]
+ },
+ {
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+ "comment": "Intersection2",
+ "filters": [
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+ [
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+ "HasIsNaturalAlternatingGroup"
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+ {
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+ "comment": "Intersection2",
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+ "IsNaturalAlternatingGroup",
+ "HasIsNaturalAlternatingGroup"
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+ [
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+ "HasIsNaturalSymmetricGroup"
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+ {
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+ "comment": "Intersection2",
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+ [
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+ "HasIsNaturalSymmetricGroup"
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+ [
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+ "HasIsNaturalAlternatingGroup"
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+ ]
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+ {
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+ "comment": "Intersection2",
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+ "HasIsNaturalSymmetricGroup"
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+ },
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+ "comment": "Intersection2",
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+ ]
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+ {
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+ "comment": "Intersection2",
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+ [
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+ [
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+ },
+ {
+ "rank": 126,
+ "comment": "Intersection2",
+ "filters": [
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ],
+ [
+ "IsNaturalSymmetricGroup",
+ "HasIsNaturalSymmetricGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 126,
+ "comment": "Intersection2",
+ "filters": [
+ [
+ "IsNaturalSymmetricGroup",
+ "HasIsNaturalSymmetricGroup"
+ ],
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 124,
+ "comment": "Intersection2: for two fields of FFEs",
+ "filters": [
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "CategoryCollections(IsFFE)",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ],
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "CategoryCollections(IsFFE)",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 122,
+ "comment": "Intersection2: perm groups",
+ "filters": [
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ],
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 110,
+ "comment": "Intersection2: two AffineCrystGroupsOnLeft",
+ "filters": [
+ [
+ "IsAffineCrystGroupOnLeft",
+ "HasIsAffineCrystGroupOnLeft"
+ ],
+ [
+ "IsAffineCrystGroupOnLeft",
+ "HasIsAffineCrystGroupOnLeft"
+ ]
+ ]
+ },
+ {
+ "rank": 110,
+ "comment": "Intersection2: two AffineCrystGroupsOnRight",
+ "filters": [
+ [
+ "IsAffineCrystGroupOnRight",
+ "HasIsAffineCrystGroupOnRight"
+ ],
+ [
+ "IsAffineCrystGroupOnRight",
+ "HasIsAffineCrystGroupOnRight"
+ ]
+ ]
+ },
+ {
+ "rank": 103,
+ "comment": "Intersection2: for Z_(pi) and Rationals (ResClasses)",
+ "filters": [
+ [
+ "IsZ_pi",
+ "HasIsZ_pi"
+ ],
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "CategoryCollections(IsCyclotomic)",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing",
+ "IsPrimeField",
+ "HasIsPrimeField"
+ ]
+ ]
+ },
+ {
+ "rank": 103,
+ "comment": "Intersection2: for Rationals and Z_(pi) (ResClasses)",
+ "filters": [
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "CategoryCollections(IsCyclotomic)",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing",
+ "IsPrimeField",
+ "HasIsPrimeField"
+ ],
+ [
+ "IsZ_pi",
+ "HasIsZ_pi"
+ ]
+ ]
+ },
+ {
+ "rank": 100,
+ "comment": "Intersection2: for subgroups of free groups",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsFinitelyGeneratedGroup",
+ "HasIsFinitelyGeneratedGroup",
+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsFinitelyGeneratedGroup",
+ "HasIsFinitelyGeneratedGroup",
+ "CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
+ ]
+ ]
+ },
+ {
+ "rank": 100,
+ "comment": "Intersection2: for pcp groups",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsPcpElement)"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsPcpElement)"
+ ]
+ ]
+ },
+ {
+ "rank": 82,
+ "comment": "Intersection2: for certain cyclotomic semirings",
+ "filters": [
+ [
+ "CategoryCollections(IsCyclotomic)",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "CategoryCollections(IsCyclotomic)",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 76,
+ "comment": "Intersection2: subgroups of fp group by quotient",
+ "filters": [
+ [
+ "IsSubgroupFpGroup",
+ "IsSubgroupOfWholeGroupByQuotientRep"
+ ],
+ [
+ "IsSubgroupFpGroup",
+ "IsSubgroupOfWholeGroupByQuotientRep"
+ ]
+ ]
+ },
+ {
+ "rank": 74,
+ "comment": "Intersection2: subgroups of fp group",
+ "filters": [
+ [
+ "IsSubgroupFpGroup"
+ ],
+ [
+ "IsSubgroupFpGroup"
+ ]
+ ]
+ },
+ {
+ "rank": 74,
+ "comment": "Intersection2: generic method for two FLMLORs-with-one",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 72,
+ "comment": "Intersection2: groups with pcgs",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasHomePcgs"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasHomePcgs"
+ ]
+ ]
+ },
+ {
+ "rank": 70,
+ "comment": "Intersection2: for two spaces in a common s.c. algebra",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "CategoryCollections(IsSCAlgebraObj)"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "CategoryCollections(IsSCAlgebraObj)"
+ ]
+ ]
+ },
+ {
+ "rank": 70,
+ "comment": "Intersection2: generic method for two groups",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 68,
+ "comment": "Intersection2: generic method for two FLMLORs",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "Intersection2: for Z_(pi)'s (ResClasses)",
+ "filters": [
+ [
+ "IsZ_pi",
+ "HasIsZ_pi"
+ ],
+ [
+ "IsZ_pi",
+ "HasIsZ_pi"
+ ]
+ ]
+ },
+ {
+ "rank": 60,
+ "comment": "Intersection2: for two Gaussian row spaces",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsRowModule",
+ "HasIsRowModule",
+ "IsGaussianSpace"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsRowModule",
+ "HasIsRowModule",
+ "IsGaussianSpace"
+ ]
+ ]
+ },
+ {
+ "rank": 50,
+ "comment": "Intersection2: method for two vector spaces",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "Intersection2: for Fitting sets",
+ "filters": [
+ [
+ "IsFittingSetRep"
+ ],
+ [
+ "IsFittingSetRep"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "Intersection2: for Fitting class and Fitting set",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "ContainsTrivialGroup",
+ "HasContainsTrivialGroup",
+ "IsNormalSubgroupClosed",
+ "HasIsNormalSubgroupClosed",
+ "IsNormalProductClosed",
+ "HasIsNormalProductClosed"
+ ],
+ [
+ "IsFittingSetRep"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "Intersection2: for Fitting set and Fitting class",
+ "filters": [
+ [
+ "IsFittingSetRep"
+ ],
+ [
+ "IsGroupClass",
+ "HasIsGroupClass",
+ "ContainsTrivialGroup",
+ "HasContainsTrivialGroup",
+ "IsNormalSubgroupClosed",
+ "HasIsNormalSubgroupClosed",
+ "IsNormalProductClosed",
+ "HasIsNormalProductClosed"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "Intersection2: for two additive cosets",
+ "filters": [
+ [
+ "IsAdditiveCoset"
+ ],
+ [
+ "IsAdditiveCoset"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "Intersection2: for residue class unions of Z in sparse rep. (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnionOfZ",
+ "IsResidueClassUnionClassListRep"
+ ],
+ [
+ "IsResidueClassUnionOfZ",
+ "IsResidueClassUnionClassListRep"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "Intersection2: for the empty set and a set (ResClasses)",
+ "filters": [
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ],
+ [
+ "IsListOrCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "Intersection2: for a set and the empty set (ResClasses)",
+ "filters": [
+ [
+ "IsListOrCollection"
+ ],
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "Intersection2: for two residue class unions in different rep. (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionClassListRep"
+ ],
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionResidueListRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "Intersection2: for two residue class unions in different rep. (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionResidueListRep"
+ ],
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionClassListRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "Intersection2: for two residue class unions in standard rep. (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionResidueListRep"
+ ],
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionResidueListRep"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "Intersection2: for two unions of residue classes with fixed rep's (ResClasses)",
+ "filters": [
+ [
+ "IsUnionOfResidueClassesWithFixedRepresentatives"
+ ],
+ [
+ "IsUnionOfResidueClassesWithFixedRepresentatives"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "Intersection2: for the base ring and a residue class union (ResClasses)",
+ "filters": [
+ [
+ "IsCollection",
+ "IsGeneralizedDomain"
+ ],
+ [
+ "IsResidueClassUnion"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "Intersection2: for a residue class union and the base ring (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnion"
+ ],
+ [
+ "IsCollection",
+ "IsGeneralizedDomain"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "Intersection2: for a residue class union and a finite set (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionClassListRep"
+ ],
+ [
+ "IsList"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "Intersection2: for a residue class union and a finite set (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnion",
+ "IsResidueClassUnionResidueListRep"
+ ],
+ [
+ "IsList"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "Intersection2: for two group classes by list",
+ "filters": [
+ [
+ "IsGroupClassByListRep"
+ ],
+ [
+ "IsGroupClassByListRep"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "Intersection2: of two class intersections",
+ "filters": [
+ [
+ "IsClassByIntersectionRep"
+ ],
+ [
+ "IsClassByIntersectionRep"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "Intersection2: for two collections in the same family, both lists",
+ "filters": [
+ [
+ "IsList",
+ "IsCollection"
+ ],
+ [
+ "IsList",
+ "IsCollection"
+ ]
+ ],
+ "aka": [
+ "IntersectionSet"
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "Intersection2: for two lists or collections, the first being empty",
+ "filters": [
+ [
+ "IsListOrCollection",
+ "IsEmpty",
+ "HasIsEmpty"
+ ],
+ [
+ "IsListOrCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "Intersection2: for two lists or collections, the second being empty",
+ "filters": [
+ [
+ "IsListOrCollection"
+ ],
+ [
+ "IsListOrCollection",
+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
+ {
+ "rank": 9,
+ "comment": "Intersection2: for grp class and group class by list",
+ "filters": [
+ [
+ "IsGroupClass",
+ "HasIsGroupClass"
+ ],
+ [
+ "IsGroupClassByListRep"
+ ]
+ ]
+ },
+ {
+ "rank": 9,
+ "comment": "Intersection2: for group class by list and group class",
+ "filters": [
+ [
+ "IsGroupClassByListRep"
+ ],
+ [
+ "IsGroupClass",
+ "HasIsGroupClass"
+ ]
+ ]
+ },
+ {
+ "rank": 8,
+ "comment": "Intersection2: for a finite set and a residue class union (ResClasses)",
+ "filters": [
+ [
+ "IsList"
+ ],
+ [
+ "IsResidueClassUnion"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "Intersection2: of class and small list/coll",
+ "filters": [
+ [
+ "IsClass"
+ ],
+ [
+ "IsListOrCollection",
+ "IsFinite",
+ "HasIsFinite",
+ "HasSize"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "Intersection2: of small list/coll and class",
+ "filters": [
+ [
+ "IsListOrCollection",
+ "IsFinite",
+ "HasIsFinite",
+ "HasSize"
+ ],
+ [
+ "IsClass"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "Intersection2: for two collections in the same family, the first being a list",
+ "filters": [
+ [
+ "IsList",
+ "IsCollection"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 7,
+ "comment": "Intersection2: for two collections in the same family, the second being a list",
+ "filters": [
+ [
+ "IsCollection"
+ ],
+ [
+ "IsList",
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "Intersection2: of small list and class",
+ "filters": [
+ [
+ "IsList",
+ "IsFinite",
+ "HasIsFinite"
+ ],
+ [
+ "IsClass"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "Intersection2: of class and small list",
+ "filters": [
+ [
+ "IsClass"
+ ],
+ [
+ "IsList",
+ "IsFinite",
+ "HasIsFinite"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "Intersection2: of class intersection and class/list/coll",
+ "filters": [
+ [
+ "IsClassByIntersectionRep"
+ ],
+ [
+ "IsListOrCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "Intersection2: of class/list/coll and class intersection",
+ "filters": [
+ [
+ "IsListOrCollection"
+ ],
+ [
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+ "comment": "*: straight line program element with x",
+ "filters": [
+ [
+ "IsStraightLineProgElm"
+ ],
+ [
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 98,
+ "comment": "*: for two empty matrices",
+ "filters": [
+ [
+ "IsTable",
+ "IsEmpty",
+ "HasIsEmpty",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ],
+ [
+ "IsTable",
+ "IsEmpty",
+ "HasIsEmpty",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ]
+ ]
+ },
+ {
+ "rank": 98,
+ "comment": "*: More efficient non-recursive kernel method for vector*matrix of cyclotomics",
+ "filters": [
+ [
+ "IsPlistRep",
+ "IsSmallList",
+ "HasIsSmallList",
+ "CategoryCollections(IsCyclotomic)",
+ "IsListDefault"
+ ],
+ [
+ "IsPlistRep",
+ "IsSmallList",
+ "HasIsSmallList",
+ "CategoryCollections(CategoryCollections(IsCyclotomic))",
+ "IsListDefault",
+ "IsRectangularTable",
+ "HasIsRectangularTable"
+ ]
+ ]
+ },
+ {
+ "rank": 97,
+ "comment": "*: More efficient non-recursive method for matrix*matrix of cyclotomics",
+ "filters": [
+ [
+ "IsSmallList",
+ "HasIsSmallList",
+ "CategoryCollections(CategoryCollections(IsCyclotomic))",
+ "IsListDefault"
+ ],
+ [
+ "IsPlistRep",
+ "IsSmallList",
+ "HasIsSmallList",
+ "CategoryCollections(CategoryCollections(IsCyclotomic))",
+ "IsListDefault",
+ "IsRectangularTable",
+ "HasIsRectangularTable"
+ ]
+ ]
+ },
+ {
+ "rank": 90,
+ "comment": "*: for GF2 matrix and GF2 matrix",
+ "filters": [
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "IsListDefault",
+ "IsGF2MatrixRep"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "IsListDefault",
+ "IsGF2MatrixRep"
+ ]
+ ],
+ "aka": [
+ "PROD_GF2MAT_GF2MAT"
+ ]
+ },
+ {
+ "rank": 88,
+ "comment": "*: 8 bit matrix * 8 bit matrix",
+ "filters": [
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "Is8BitMatrixRep"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "Is8BitMatrixRep"
+ ]
+ ],
+ "aka": [
+ "PROD_MAT8BIT_MAT8BIT"
+ ]
+ },
+ {
+ "rank": 82,
+ "comment": "*: for two ordinary block matrices",
+ "filters": [
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ],
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 78,
+ "comment": "*: For an 8 bit vector and a compatible matrix",
+ "filters": [
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsSmallList",
+ "HasIsSmallList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "Is8BitVectorRep"
+ ],
+ [
+ "IsTable",
+ "IsPlistRep",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ]
+ ],
+ "aka": [
+ "PROD_VEC8BIT_MATRIX"
+ ]
+ },
+ {
+ "rank": 78,
+ "comment": "*: for GF2 vector and GF2 matrix",
+ "filters": [
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "IsListDefault",
+ "IsGF2VectorRep"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "IsListDefault",
+ "IsGF2MatrixRep"
+ ]
+ ],
+ "aka": [
+ "PROD_GF2VEC_GF2MAT"
+ ]
+ },
+ {
+ "rank": 77,
+ "comment": "*: 8 bit matrix * 8 bit vector",
+ "filters": [
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "Is8BitMatrixRep"
+ ],
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "Is8BitVectorRep"
+ ]
+ ],
+ "aka": [
+ "PROD_MAT8BIT_VEC8BIT"
+ ]
+ },
+ {
+ "rank": 77,
+ "comment": "*: 8 bit vector * 8 bit matrix",
+ "filters": [
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "Is8BitVectorRep"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "Is8BitMatrixRep"
+ ]
+ ],
+ "aka": [
+ "PROD_VEC8BIT_MAT8BIT"
+ ]
+ },
+ {
+ "rank": 75,
+ "comment": "*: For a GF2 vector and a compatible matrix",
+ "filters": [
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsSmallList",
+ "HasIsSmallList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "IsGF2VectorRep"
+ ],
+ [
+ "IsTable",
+ "IsPlistRep",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ]
+ ],
+ "aka": [
+ "PROD_GF2VEC_ANYMAT"
+ ]
+ },
+ {
+ "rank": 70,
+ "comment": "*: for two characters",
+ "filters": [
+ [
+ "IsCharacter",
+ "HasIsCharacter"
+ ],
+ [
+ "IsCharacter",
+ "HasIsCharacter"
+ ]
+ ]
+ },
+ {
+ "rank": 70,
+ "comment": "*: for two null map matrices",
+ "filters": [
+ [
+ "IsNullMapMatrix"
+ ],
+ [
+ "IsNullMapMatrix"
+ ]
+ ]
+ },
+ {
+ "rank": 69,
+ "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"
+ ]
+ ],
+ "aka": [
+ "PROD_GF2MAT_GF2VEC"
+ ]
+ },
+ {
+ "rank": 69,
+ "comment": "*: for empty list, and empty matrix",
+ "filters": [
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ],
+ [
+ "IsTable",
+ "IsEmpty",
+ "HasIsEmpty",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ]
+ ]
+ },
+ {
+ "rank": 69,
+ "comment": "*: for empty matrix, and empty list",
+ "filters": [
+ [
+ "IsTable",
+ "IsEmpty",
+ "HasIsEmpty",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ],
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
+ {
+ "rank": 69,
+ "comment": "*: for matrix and null map matrix",
+ "filters": [
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ],
+ [
+ "IsNullMapMatrix"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "*: for two virtual characters",
+ "filters": [
+ [
+ "IsVirtualCharacter",
+ "HasIsVirtualCharacter"
+ ],
+ [
+ "IsVirtualCharacter",
+ "HasIsVirtualCharacter"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "*: for GF2 vectors",
+ "filters": [
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "IsListDefault",
+ "IsGF2VectorRep"
+ ],
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "IsListDefault",
+ "IsGF2VectorRep"
+ ]
+ ],
+ "aka": [
+ "PROD_GF2VEC_GF2VEC"
+ ]
+ },
+ {
+ "rank": 64,
+ "comment": "*: For 2 8 bit vectors",
+ "filters": [
+ [
+ "IsList",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "CategoryCollections(IsAdditiveElement)",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "Is8BitVectorRep"
+ ],
+ [
+ "IsList",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "CategoryCollections(IsAdditiveElement)",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "Is8BitVectorRep"
+ ]
+ ],
+ "aka": [
+ "PROD_VEC8BIT_VEC8BIT"
+ ]
+ },
+ {
+ "rank": 64,
+ "comment": "*: for ffe and ordinary block matrix of integers",
+ "filters": [
+ [
+ "IsFFE"
+ ],
+ [
+ "IsOrdinaryMatrix",
+ "CategoryCollections(CategoryCollections(IsCyclotomic))",
+ "IsBlockMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 64,
+ "comment": "*: for ordinary block matrix of integers and ffe",
+ "filters": [
+ [
+ "IsOrdinaryMatrix",
+ "CategoryCollections(CategoryCollections(IsCyclotomic))",
+ "IsBlockMatrixRep"
+ ],
+ [
+ "IsFFE"
+ ]
+ ]
+ },
+ {
+ "rank": 63,
+ "comment": "*",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsRowModule",
+ "HasIsRowModule"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ]
+ ]
+ },
+ {
+ "rank": 62,
+ "comment": "*: for two class functions",
+ "filters": [
+ [
+ "IsClassFunction"
+ ],
+ [
+ "IsClassFunction"
+ ]
+ ]
+ },
+ {
+ "rank": 62,
+ "comment": "*: for two empty row vectors in the same family",
+ "filters": [
+ [
+ "IsHomogeneousList",
+ "IsEmpty",
+ "HasIsEmpty",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "IsEmptyRowVectorRep"
+ ],
+ [
+ "IsHomogeneousList",
+ "IsEmpty",
+ "HasIsEmpty",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "IsEmptyRowVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 60,
+ "comment": "*: for GF2 matrix and GF2 element",
+ "filters": [
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "IsListDefault",
+ "IsGF2MatrixRep"
+ ],
+ [
+ "IsFFE"
+ ]
+ ]
+ },
+ {
+ "rank": 60,
+ "comment": "*: for GF2 element and GF2 matrix",
+ "filters": [
+ [
+ "IsFFE"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "IsListDefault",
+ "IsGF2MatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 59,
+ "comment": "*: scalar * 8 bit matrix",
+ "filters": [
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "Is8BitMatrixRep"
+ ],
+ [
+ "IsFFE"
+ ]
+ ]
+ },
+ {
+ "rank": 59,
+ "comment": "*: scalar * 8 bit matrix",
+ "filters": [
+ [
+ "IsFFE"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
+ "Is8BitMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 57,
+ "comment": "*: for ring element, and empty matrix",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsTable",
+ "IsEmpty",
+ "HasIsEmpty",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ]
+ ]
+ },
+ {
+ "rank": 57,
+ "comment": "*: for empty matrix, and ring element",
+ "filters": [
+ [
+ "IsTable",
+ "IsEmpty",
+ "HasIsEmpty",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 56,
+ "comment": "*: for integer and ordinary block matrix",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 56,
+ "comment": "*: for ordinary block matrix and integer",
+ "filters": [
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ],
+ [
+ "IsInt"
+ ]
+ ]
+ },
+ {
+ "rank": 55,
+ "comment": "*: for GF2 vector and FFE",
+ "filters": [
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "IsGF2VectorRep"
+ ],
+ [
+ "IsFFE"
+ ]
+ ]
+ },
+ {
+ "rank": 55,
+ "comment": "*: for FFE and GF2 vector",
+ "filters": [
+ [
+ "IsFFE"
+ ],
+ [
+ "IsList",
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "CategoryCollections(IsNearAdditiveElementWithInverse)",
+ "IsAdditiveElement",
+ "CategoryCollections(IsAdditiveElement)",
+ "IsExtLElement",
+ "IsExtRElement",
+ "CategoryCollections(IsMultiplicativeElement)",
+ "IsOddAdditiveNestingDepthObject",
+ "IsGF2VectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 55,
+ "comment": "*: for empty list and null map matrix",
+ "filters": [
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ],
+ [
+ "IsNullMapMatrix"
+ ]
+ ]
+ },
+ {
+ "rank": 54,
+ "comment": "*: for character, and positive integer",
+ "filters": [
+ [
+ "IsCharacter",
+ "HasIsCharacter"
+ ],
+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 54,
+ "comment": "*: for positive integer, and character",
+ "filters": [
+ [
+ "IsInt",
+ "IsPosRat"
+ ],
+ [
+ "IsCharacter",
+ "HasIsCharacter"
+ ]
+ ]
+ },
+ {
+ "rank": 53,
+ "comment": "*: for ring and right ideal (construct a two-sided ideal)",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasRightActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 53,
+ "comment": "*: for left ideal and ring (construct a two-sided ideal)",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasLeftActingRingOfIdeal"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 51,
+ "comment": "*: for virtual character, and integer",
+ "filters": [
+ [
+ "IsVirtualCharacter",
+ "HasIsVirtualCharacter"
+ ],
+ [
+ "IsInt"
+ ]
+ ]
+ },
+ {
+ "rank": 51,
+ "comment": "*: for integer, and virtual character",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsVirtualCharacter",
+ "HasIsVirtualCharacter"
+ ]
+ ]
+ },
+ {
+ "rank": 50,
+ "comment": "*: for vector and ordinary block matrix",
+ "filters": [
+ [
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject"
+ ],
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 50,
+ "comment": "*: for ordinary block matrix and vector",
+ "filters": [
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ],
+ [
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject"
+ ]
+ ]
+ },
+ {
+ "rank": 49,
+ "comment": "*: for empty row vector, and integer",
+ "filters": [
+ [
+ "IsHomogeneousList",
+ "IsEmpty",
+ "HasIsEmpty",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "IsEmptyRowVectorRep"
+ ],
+ [
+ "IsInt"
+ ]
+ ]
+ },
+ {
+ "rank": 49,
+ "comment": "*: for integer, and empty row vector",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsHomogeneousList",
+ "IsEmpty",
+ "HasIsEmpty",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "IsEmptyRowVectorRep"
+ ]
+ ]
+ },
+ {
+ "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 a mgrv, and an ordinary block matrix",
+ "filters": [
+ [
+ "IsMultiplicativeGeneralizedRowVector"
+ ],
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 47,
+ "comment": "*: for an ordinary block matrix, and a mgrv",
+ "filters": [
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ],
+ [
+ "IsMultiplicativeGeneralizedRowVector"
+ ]
+ ]
+ },
+ {
+ "rank": 46,
+ "comment": "*: for ring element and ordinary block matrix",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 46,
+ "comment": "*: for ordinary block matrix and ring element",
+ "filters": [
+ [
+ "IsOrdinaryMatrix",
+ "IsBlockMatrixRep"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 45,
+ "comment": "*: for a scalar and Z^2 (ResClasses)",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsRowModule",
+ "HasIsRowModule"
+ ]
+ ]
+ },
+ {
+ "rank": 45,
+ "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": 45,
+ "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": 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": "*: for a null map matrix and a scalar",
+ "filters": [
+ [
+ "IsNullMapMatrix"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 45,
+ "comment": "*: for a scalar and a null map matrix",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ],
+ [
+ "IsNullMapMatrix"
+ ]
+ ]
+ },
+ {
+ "rank": 44,
+ "comment": "*",
+ "filters": [
+ [
+ "IsRat"
+ ],
+ [
+ "IsList",
+ "CategoryCollections(IsPadicNumber)"
+ ]
+ ]
+ },
+ {
+ "rank": 44,
+ "comment": "*",
+ "filters": [
+ [
+ "IsList",
+ "CategoryCollections(IsPadicNumber)"
+ ],
+ [
+ "IsRat"
+ ]
+ ]
+ },
+ {
+ "rank": 42,
+ "comment": "*: for vector and null map matrix",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement"
+ ],
+ [
+ "IsNullMapMatrix"
+ ]
+ ]
+ },
+ {
+ "rank": 41,
+ "comment": "*: for residue class union of Z^2 and matrix (ResClasses)",
+ "filters": [
+ [
+ "IsResidueClassUnionOfZxZ"
+ ],
+ [
+ "IsTable",
+ "CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
+ "CategoryCollections(CategoryCollections(IsAdditiveElement))",
+ "CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
+ ]
+ ]
+ },
+ {
+ "rank": 41,
+ "comment": "*: for list in `IsListDefault', and class function",
+ "filters": [
+ [
+ "IsListDefault"
+ ],
+ [
+ "IsClassFunction"
+ ]
+ ]
+ },
+ {
+ "rank": 41,
+ "comment": "*: for class function, and list in `IsListDefault'",
+ "filters": [
+ [
+ "IsClassFunction"
+ ],
+ [
+ "IsListDefault"
+ ]
+ ]
+ },
+ {
+ "rank": 41,
+ "comment": "*: For an FFE and an 8 bit vector ",
+ "filters": [
+ [
+ "IsFFE",
+ "IsInternalRep"
+ ],
+ [
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "Is8BitVectorRep"
+ ]
+ ],
+ "aka": [
+ "PROD_FFE_VEC8BIT"
+ ]
+ },
+ {
+ "rank": 41,
+ "comment": "*: For an 8 bit vector and an FFE",
+ "filters": [
+ [
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "Is8BitVectorRep"
+ ],
+ [
+ "IsFFE",
+ "IsInternalRep"
+ ]
+ ],
+ "aka": [
+ "PROD_VEC8BIT_FFE"
+ ]
+ },
+ {
+ "rank": 40,
+ "comment": "*: for two nearly character tables (call `CharacterTableDirectProduct')",
+ "filters": [
+ [
+ "IsNearlyCharacterTable"
+ ],
+ [
+ "IsNearlyCharacterTable"
+ ]
+ ],
+ "aka": [
+ "CharacterTableDirectProduct"
+ ]
+ },
+ {
+ "rank": 40,
+ "comment": "*: group times element",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 38,
+ "comment": "*: for two direct product elements",
+ "filters": [
+ [
+ "IsDirectProductElement"
+ ],
+ [
+ "IsDirectProductElement"
+ ]
+ ]
+ },
+ {
+ "rank": 37,
+ "comment": "*: for list and null map matrix",
+ "filters": [
+ [
+ "IsList"
+ ],
+ [
+ "IsNullMapMatrix"
+ ]
+ ]
+ },
+ {
+ "rank": 36,
+ "comment": "*: for a ring element and the base ring (ResClasses)",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsMagma",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 36,
+ "comment": "*: for internal FFE and element in Z/pZ (ModulusRep)",
+ "filters": [
+ [
+ "IsFFE",
+ "IsInternalRep"
+ ],
+ [
+ "IsFFE",
+ "IsLogOrderedFFE",
+ "IsZmodnZObj",
+ "IsModulusRep"
+ ]
+ ]
+ },
+ {
+ "rank": 36,
+ "comment": "*: for element in Z/pZ (ModulusRep) and internal FFE",
+ "filters": [
+ [
+ "IsFFE",
+ "IsLogOrderedFFE",
+ "IsZmodnZObj",
+ "IsModulusRep"
+ ],
+ [
+ "IsFFE",
+ "IsInternalRep"
+ ]
+ ]
+ },
+ {
+ "rank": 35,
+ "comment": "*: for the base module and a scalar / matrix (ResClasses)",
+ "filters": [
+ [
+ "IsRowModule",
+ "HasIsRowModule"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 35,
+ "comment": "*: internal ffe * (large) integer",
+ "filters": [
+ [
+ "IsFFE",
+ "IsInternalRep"
+ ],
+ [
+ "IsInt"
+ ]
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "*: for the base ring and a ring element (ResClasses)",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "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,
+ "comment": "*: laurent * laurent",
+ "filters": [
+ [
+ "IsPolynomialFunction",
+ "IsLaurentPolynomial",
+ "HasIsLaurentPolynomial"
+ ],
+ [
+ "IsPolynomialFunction",
+ "IsLaurentPolynomial",
+ "HasIsLaurentPolynomial"
+ ]
+ ],
+ "aka": [
+ "PRODUCT_LAURPOLS"
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "*: for ring and ring element (construct a left ideal)",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "*: for ring element and ring (construct a right ideal)",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "*: for empty row vector, and multiplicative element",
+ "filters": [
+ [
+ "IsHomogeneousList",
+ "IsEmpty",
+ "HasIsEmpty",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "IsEmptyRowVectorRep"
+ ],
+ [
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "*: for multiplicative element, and empty row vector",
+ "filters": [
+ [
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsHomogeneousList",
+ "IsEmpty",
+ "HasIsEmpty",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject",
+ "IsEmptyRowVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 33,
+ "comment": "*: for rational and element in Z/nZ (ModulusRep)",
+ "filters": [
+ [
+ "IsRat"
+ ],
+ [
+ "IsZmodnZObj",
+ "IsModulusRep"
+ ]
+ ]
+ },
+ {
+ "rank": 33,
+ "comment": "*: for element in Z/nZ (ModulusRep) and rational",
+ "filters": [
+ [
+ "IsZmodnZObj",
+ "IsModulusRep"
+ ],
+ [
+ "IsRat"
+ ]
+ ]
+ },
+ {
+ "rank": 32,
+ "comment": "*: for 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": 31,
+ "comment": "*: for s. c. ring element in dense vector rep. and integer",
+ "filters": [
+ [
+ "IsSCRingObj",
+ "IsDenseCoeffVectorRep"
+ ],
+ [
+ "IsInt"
+ ]
+ ]
+ },
+ {
+ "rank": 31,
+ "comment": "*: for integer and s. c. ring element in dense vector rep.",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsSCRingObj",
+ "IsDenseCoeffVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 31,
+ "comment": "*: for s. c. algebra element in dense vector rep. and integer",
+ "filters": [
+ [
+ "IsSCAlgebraObj",
+ "IsDenseCoeffVectorRep"
+ ],
+ [
+ "IsInt"
+ ]
+ ]
+ },
+ {
+ "rank": 31,
+ "comment": "*: for integer and s. c. algebra element in dense vector rep.",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsSCAlgebraObj",
+ "IsDenseCoeffVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "*: for two plist matrices",
+ "filters": [
+ [
+ "IsPlistMatrixRep"
+ ],
+ [
+ "IsPlistMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "*",
+ "filters": [
+ [
+ "IsRat"
+ ],
+ [
+ "IsPadicNumber"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "*",
+ "filters": [
+ [
+ "IsPadicNumber"
+ ],
+ [
+ "IsRat"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "*",
+ "filters": [
+ [
+ "IsFFE"
+ ],
+ [
+ "IsFFE"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "*: univariate * univariate",
+ "filters": [
+ [
+ "IsPolynomialFunction",
+ "IsUnivariateRationalFunction",
+ "HasIsUnivariateRationalFunction"
+ ],
+ [
+ "IsPolynomialFunction",
+ "IsUnivariateRationalFunction",
+ "HasIsUnivariateRationalFunction"
+ ]
+ ],
+ "aka": [
+ "PRODUCT_UNIVFUNCS"
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: for float and rational",
+ "filters": [
+ [
+ "IsFloat"
+ ],
+ [
+ "IsRat"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: for rational and float",
+ "filters": [
+ [
+ "IsRat"
+ ],
+ [
+ "IsFloat"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: zmodnze : for element x in Z/nZ and y in Z/nZ(m)",
+ "filters": [
+ [
+ "IsZmodnZObj",
+ "IsModulusRep"
+ ],
+ [
+ "IsZmodnZepsObj",
+ "IsZmodnZepsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: zmodnze : for element x in Z/nZ(m) and y in Z/nZ",
+ "filters": [
+ [
+ "IsZmodnZepsObj",
+ "IsZmodnZepsRep"
+ ],
+ [
+ "IsZmodnZObj",
+ "IsModulusRep"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: for s. c. algebra element and integer",
+ "filters": [
+ [
+ "IsSCAlgebraObj"
+ ],
+ [
+ "IsInt"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: for integer and s. c. algebra element",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsSCAlgebraObj"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: for a default list, and a direct product element",
+ "filters": [
+ [
+ "IsListDefault"
+ ],
+ [
+ "IsDirectProductElement"
+ ]
+ ],
+ "aka": [
+ "PROD_LIST_SCL_DEFAULT"
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "*: for a direct product element, and a default list",
+ "filters": [
+ [
+ "IsDirectProductElement"
+ ],
+ [
+ "IsListDefault"
+ ]
+ ],
+ "aka": [
+ "PROD_SCL_LIST_DEFAULT"
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*",
+ "filters": [
+ [
+ "IsPadicExtensionNumber"
+ ],
+ [
+ "IsPadicExtensionNumber"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*",
+ "filters": [
+ [
+ "IsPadicExtensionNumber"
+ ],
+ [
+ "IsPurePadicNumber"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*",
+ "filters": [
+ [
+ "IsPurePadicNumber"
+ ],
+ [
+ "IsPadicExtensionNumber"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*",
+ "filters": [
+ [
+ "IsPurePadicNumber"
+ ],
+ [
+ "IsPurePadicNumber"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*: zmodnze : for element x in Z/nZ(m) (ZmodnZepsRep) and cyclotomic y",
+ "filters": [
+ [
+ "IsZmodnZepsObj",
+ "IsZmodnZepsRep"
+ ],
+ [
+ "IsCyclotomic"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*: zmodnze : for cyclotomic x and element y in Z/nZ(m) (ZmodnZepsRep)",
+ "filters": [
+ [
+ "IsCyclotomic"
+ ],
+ [
+ "IsZmodnZepsObj",
+ "IsZmodnZepsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*: polynomial * polynomial",
+ "filters": [
+ [
+ "IsPolynomial",
+ "HasIsPolynomial"
+ ],
+ [
+ "IsPolynomial",
+ "HasIsPolynomial"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*: for two Lie objects in default representation",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsLieObject"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsLieObject"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*: for scalar and algebra g.m.b.i.",
+ "filters": [
+ [
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*: for rational, and magma ring element",
+ "filters": [
+ [
+ "IsRat"
+ ],
+ [
+ "IsElementOfMagmaRingModuloRelations"
+ ]
+ ],
+ "aka": [
+ "RingElmTimesElm"
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*: for magma ring element, and rational",
+ "filters": [
+ [
+ "IsElementOfMagmaRingModuloRelations"
+ ],
+ [
+ "IsRat"
+ ]
+ ],
+ "aka": [
+ "ElmTimesRingElm"
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "*",
+ "filters": [
+ [
+ "IsSmallList",
+ "HasIsSmallList",
+ "IsListDefault"
+ ],
+ [
+ "IsSmallList",
+ "HasIsSmallList",
+ "IsListDefault"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: for a plist vector and a plist matrix",
+ "filters": [
+ [
+ "IsPlistVectorRep"
+ ],
+ [
+ "IsPlistMatrixRep"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
+ "filters": [
+ [
+ "IsZmodnZepsObj",
+ "IsZmodnZepsRep"
+ ],
+ [
+ "IsZmodnZepsObj",
+ "IsZmodnZepsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: univariate * coeff",
+ "filters": [
+ [
+ "IsPolynomialFunction",
+ "IsUnivariateRationalFunction",
+ "HasIsUnivariateRationalFunction"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: coeff * univariate",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsPolynomialFunction",
+ "IsUnivariateRationalFunction",
+ "HasIsUnivariateRationalFunction"
+ ]
+ ],
+ "aka": [
+ "ProdCoeffUnivfunc"
+ ]
+ },
+ {
+ "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 UEALattice elements",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsUEALatticeElement"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsUEALatticeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: for row vector and Lie object",
+ "filters": [
+ [
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsLieObject"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: for Lie object and row vector",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsLieObject"
+ ],
+ [
+ "IsHomogeneousList",
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsExtLElement",
+ "IsExtRElement",
+ "IsOddAdditiveNestingDepthObject"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: for s. c. algebra elements in dense vector rep.",
+ "filters": [
+ [
+ "IsSCAlgebraObj",
+ "IsDenseCoeffVectorRep"
+ ],
+ [
+ "IsSCAlgebraObj",
+ "IsDenseCoeffVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: for scalar and linear m.b.m.",
+ "filters": [
+ [
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsLinearMappingByMatrixDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "*: for scalar and linear g.m.b.i.",
+ "filters": [
+ [
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsLinearGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "*: for an integer and a residue class union of Z^2 (ResClasses)",
+ "filters": [
+ [
+ "IsInt"
+ ],
+ [
+ "IsResidueClassUnionOfZxZ"
+ ]
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "*: for floats",
+ "filters": [
+ [
+ "IsFloat"
+ ],
+ [
+ "IsFloat"
+ ]
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "*: laurent * coeff",
+ "filters": [
+ [
+ "IsUnivariateRationalFunction",
+ "HasIsUnivariateRationalFunction",
+ "IsLaurentPolynomial",
+ "HasIsLaurentPolynomial"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "*: coeff * laurent",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsUnivariateRationalFunction",
+ "HasIsUnivariateRationalFunction",
+ "IsLaurentPolynomial",
+ "HasIsLaurentPolynomial"
+ ]
+ ],
+ "aka": [
+ "ProdCoeffLaurpol"
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "*: fp algebra elements",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsElementOfFpAlgebra"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsElementOfFpAlgebra"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "*: for binary relations on points",
+ "filters": [
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
+ ],
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: FElm*Alg",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsAlgebraicElement"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: Alg*FElm",
+ "filters": [
+ [
+ "IsAlgebraicElement"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: rat-fun * coeff",
+ "filters": [
+ [
+ "IsPolynomialFunction"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: coeff * rat-fun",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsPolynomialFunction"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: for UEALattice element and scalar",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsUEALatticeElement"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: for scalar and UEALattice element",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsUEALatticeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: for cochain and scalar",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsCochain"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse",
+ "IsZero",
+ "HasIsZero"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: for scalar and cochain",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse",
+ "IsZero",
+ "HasIsZero"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsCochain"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: additive element with inverse * negative integer",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse"
+ ],
+ [
+ "IsInt",
+ "IsNegRat"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "*: negative integer * additive element with inverse",
+ "filters": [
+ [
+ "IsInt",
+ "IsNegRat"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "*: for 0-cochain and scalar",
+ "filters": [
+ [
+ "IsCochain",
+ "IsZeroCochainRep"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "*: for scalar and 0-cochain",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ],
+ [
+ "IsCochain",
+ "IsZeroCochainRep"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "*: for ring element, and Lie object in default representation",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsLieObject"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "*: for Lie object in default representation, and ring element",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsLieObject"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "*: for s. c. algebra elements",
+ "filters": [
+ [
+ "IsSCAlgebraObj"
+ ],
+ [
+ "IsSCAlgebraObj"
+ ]
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "*: for two magma ring elements",
+ "filters": [
+ [
+ "IsElementOfMagmaRingModuloRelations"
+ ],
+ [
+ "IsElementOfMagmaRingModuloRelations"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: RightCoset with element",
+ "filters": [
+ [
+ "IsRightCoset"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for a scalar and a plist vector",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ],
+ [
+ "IsPlistVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for a plist vector and a scalar",
+ "filters": [
+ [
+ "IsPlistVectorRep"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for cochain and scalar",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsCochain"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for scalar and cochain",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsCochain"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for a scalar and an algebra module element in packed representation",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsAlgebraModuleElement"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for an algebra module element in packed representation and a scalar",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsAlgebraModuleElement"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for s. c. algebra element in dense vector rep. and ring element",
+ "filters": [
+ [
+ "IsSCAlgebraObj",
+ "IsDenseCoeffVectorRep"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: for ring element and s. c. algebra element in dense vector rep.",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsSCAlgebraObj",
+ "IsDenseCoeffVectorRep"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: additive element * positive integer",
+ "filters": [
+ [
+ "IsNearAdditiveElement"
+ ],
+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "*: positive integer * additive element",
+ "filters": [
+ [
+ "IsInt",
+ "IsPosRat"
+ ],
+ [
+ "IsNearAdditiveElement"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "*: generic method for n bits pc word rep",
+ "filters": [
+ [
+ "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+ "IsNBitsPcWordRep"
+ ],
+ [
+ "IsMultiplicativeElementWithInverseByPolycyclicCollector",
+ "IsNBitsPcWordRep"
+ ]
+ ],
+ "aka": [
+ "NBitsPcWord_Product"
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "*: fp algebra el*ring el",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsElementOfFpAlgebra"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "*: ring el *fp algebra el",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsElementOfFpAlgebra"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "*: for two magma congruence classes",
+ "filters": [
+ [
+ "IsCongruenceClass"
+ ],
+ [
+ "IsCongruenceClass"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "*: for permutation and binary relation on points",
+ "filters": [
+ [
+ "IsPerm"
+ ],
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "*: for binary relation on points and permutation",
+ "filters": [
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
+ ],
+ [
+ "IsPerm"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for weight rep element and a scalar",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsWeightRepElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for weight rep element and a scalar",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsWeightRepElement"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for a direct sum element and a scalar",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsDirectSumElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for a direct sum element and a scalar",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsDirectSumElement"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for a scalar and a sparse rowspace element",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsPackedElementDefaultRep",
+ "IsSparseRowSpaceElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for a sparse rowspace element and a scalar",
+ "filters": [
+ [
+ "IsPackedElementDefaultRep",
+ "IsSparseRowSpaceElement"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for s. c. algebra element and ring element",
+ "filters": [
+ [
+ "IsSCAlgebraObj"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for ring element and s. c. algebra element",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsSCAlgebraObj"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: 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",
+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
+ ],
+ [
+ "IsTransformation"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for transformation and binary relation on points",
+ "filters": [
+ [
+ "IsTransformation"
+ ],
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsBinaryRelationOnPointsRep"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for zero and total general mapping",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement",
+ "IsZero",
+ "HasIsZero"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for a non-list, and a direct product element",
+ "filters": [
+ [],
+ [
+ "IsDirectProductElement"
+ ]
+ ]
+ },
+ {
+ "rank": 19,
+ "comment": "*: for a direct product element, and a non-list",
+ "filters": [
+ [
+ "IsDirectProductElement"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "*: for a scalar and a monomial element",
+ "filters": [
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ],
+ [
+ "IsMonomialElement",
+ "IsMonomialElementRep"
+ ]
+ ]
+ },
+ {
+ "rank": 18,
+ "comment": "*: for a monomial element and a scalar",
+ "filters": [
+ [
+ "IsMonomialElement",
+ "IsMonomialElementRep"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 17,
+ "comment": "*: 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"
+ ]
+ ]
+ },
+ {
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+ [
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+ [
+ "IsList"
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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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+ "HasIsFieldHomomorphism"
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+ "HasIsZero",
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+ "IsOperationAlgebraHomomorphismDefaultRep"
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+ "IsSurjective",
+ "HasIsSurjective",
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+ "IsSurjective",
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+ "IsActionHomomorphism"
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+ "IsEmbeddingDirectProductPermGroup"
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+ "IsAttributeStoringRep",
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+ "aka": [
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+ {
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+ "rank": 35,
+ "comment": "ImagesRepresentative: map from fp group or free group, use 'MappedWord'",
+ "filters": [
+ [
+ "IsFromFpGroupStdGensGeneralMappingByImages"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "ImagesRepresentative: map from (sub)fp group, rewrite",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsFromFpGroupGeneralMappingByImages"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 33,
+ "comment": "ImagesRepresentative: for embedding of ring into magma ring, and ring element",
+ "filters": [
+ [
+ "IsEmbeddingRingMagmaRing"
+ ],
+ [
+ "IsNearAdditiveElementWithInverse",
+ "IsAdditiveElement",
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 31,
+ "comment": "ImagesRepresentative: for Fp to SCA mapping, and element",
+ "filters": [
+ [
+ "IsFptoSCAMorphism"
+ ],
+ [
+ "IsElementOfFpAlgebra"
+ ]
+ ],
+ "aka": [
+ "FptoSCAMorphismImageElm"
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "ImagesRepresentative",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsPcgsToPcgsGeneralMappingByImages"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "ImagesRepresentative: using `RepresentativeAction'",
+ "filters": [
+ [
+ "HasImagesSource",
+ "IsActionHomomorphismByBase"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 29,
+ "comment": "ImagesRepresentative: imprim perm wreath product embedding",
+ "filters": [
+ [
+ "IsEmbeddingImprimitiveWreathProductPermGroup"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "ImagesRepresentative: for isom by finite matrix groups (Polenta)",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsIsomorphismByFinitePolycyclicMatrixGroup",
+ "HasIsIsomorphismByFinitePolycyclicMatrixGroup"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "ImagesRepresentative: for isom by matrix groups (Polenta)",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsIsomorphismByPolycyclicMatrixGroup",
+ "HasIsIsomorphismByPolycyclicMatrixGroup"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "ImagesRepresentative: for group by field elems isom",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsMultGroupByFieldElemsIsomorphism",
+ "HasIsMultGroupByFieldElemsIsomorphism"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 28,
+ "comment": "ImagesRepresentative: for unit groups",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsUnitGroupIsomorphism",
+ "HasIsUnitGroupIsomorphism"
+ ],
+ [
+ "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",
+ "HasIsConjugatorIsomorphism"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "ImagesRepresentative: for action hom",
+ "filters": [
+ [
+ "IsActionHomomorphism"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ],
+ "aka": [
+ "ImageElmActionHomomorphism"
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "ImagesRepresentative: for Frobenius automorphism and source element",
+ "filters": [
+ [
+ "IsFrobeniusAutomorphism"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 26,
+ "comment": "ImagesRepresentative: for polring g.m.b.i., and element",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsPolynomialRingDefaultGeneratorMapping"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 25,
+ "comment": "ImagesRepresentative: for algebra g.m.b.i., and element",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "ImagesRepresentative",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsFromAffineCrystGroupToPcpGroup",
+ "HasIsFromAffineCrystGroupToPcpGroup"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "ImagesRepresentative",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsFromAffineCrystGroupToFpGroup",
+ "HasIsFromAffineCrystGroupToFpGroup"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "ImagesRepresentative",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsPointHomomorphism",
+ "HasIsPointHomomorphism"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 24,
+ "comment": "ImagesRepresentative: word decomp hom",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages",
+ "IsWordDecompHomomorphism",
+ "HasIsWordDecompHomomorphism"
+ ],
+ [
+ "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",
+ "HasRespectsMultiplication",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "IsSCRingGeneralMappingByImagesDefaultRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "ImagesRepresentative: for `ByAsGroupGeneralMapping' hom",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByAsGroupGeneralMappingByImages"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "ImagesRepresentative: for left module m.b.m., and element",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsLinearMappingByMatrixDefaultRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 23,
+ "comment": "ImagesRepresentative: for left module g.m.b.i., and element",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsLinearGeneralMappingByImagesDefaultRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "ImagesRepresentative: for nilpotent Lie algebra automorphisms",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsNilpotentLieAutomorphismRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "ImagesRepresentative: for group automorphisms",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsPGAutomorphismRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "ImagesRepresentative: parallel enumeration of source and range",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByImages"
+ ],
+ [
+ "IsMultiplicativeElementWithInverse"
+ ]
+ ],
+ "aka": [
+ "ImagesRepresentativeGMBIByElementsList"
+ ]
+ },
+ {
+ "rank": 22,
+ "comment": "ImagesRepresentative: for embedding of magma into magma ring, and mult. element",
+ "filters": [
+ [
+ "IsEmbeddingMagmaMagmaRing"
+ ],
+ [
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 21,
+ "comment": "ImagesRepresentative: equivalence relations",
+ "filters": [
+ [
+ "IsEquivalenceRelation",
+ "HasIsEquivalenceRelation"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 20,
+ "comment": "ImagesRepresentative: for semigroup homomorphism by images",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsSPGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "IsSemigroupHomomorphismByImagesRep"
+ ],
+ [
+ "IsMultiplicativeElement"
+ ]
+ ]
+ },
+ {
+ "rank": 14,
+ "comment": "ImagesRepresentative: for mapping by function",
+ "filters": [
+ [
+ "IsMappingByFunctionRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "ImagesRepresentative: for a restricted mapping, and an element",
+ "filters": [
+ [
+ "IsGeneralRestrictedMappingRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 10,
+ "comment": "ImagesRepresentative: for a composition mapping, and an element",
+ "filters": [
+ [
+ "IsCompositionMappingRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 9,
+ "comment": "ImagesRepresentative: for an inverse mapping and an element",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsInverseGeneralMappingRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 8,
+ "comment": "ImagesRepresentative: for non s.p. general mapping, and element",
+ "filters": [
+ [
+ "IsNonSPGeneralMapping"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 8,
+ "comment": "ImagesRepresentative: for s.p. general mapping, and element",
+ "filters": [
+ [
+ "IsSPGeneralMapping"
+ ],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "ImagesRepresentative"
+ ]
+ },
+ {
+ "name": "ImagesSet",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/mapping.gd",
+ "line": 833
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 10019,
+ "comment": "ImagesSet: for zero mapping and collection",
+ "filters": [
+ [
+ "IsZero",
+ "HasIsZero",
+ "IsGeneralMapping"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 10019,
+ "comment": "ImagesSet: for identity mapping and collection",
+ "filters": [
+ [
+ "IsOne",
+ "HasIsOne",
+ "IsGeneralMapping"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 85,
+ "comment": "ImagesSet: constituent homomorphism",
+ "filters": [
+ [
+ "IsConstituentHomomorphism"
+ ],
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasStabChainMutable"
+ ]
+ ]
+ },
+ {
+ "rank": 84,
+ "comment": "ImagesSet: for blocks homomorphism and perm. group",
+ "filters": [
+ [
+ "IsBlocksHomomorphism"
+ ],
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 81,
+ "comment": "ImagesSet: for ANF automorphism and field",
+ "filters": [
+ [
+ "IsFieldHomomorphism",
+ "HasIsFieldHomomorphism",
+ "IsANFAutomorphismRep"
+ ],
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 81,
+ "comment": "ImagesSet: for Frobenius automorphism and field contained in the source",
+ "filters": [
+ [
+ "IsFrobeniusAutomorphism"
+ ],
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 78,
+ "comment": "ImagesSet: for field homomorphism and field",
+ "filters": [
+ [
+ "IsFieldHomomorphism",
+ "HasIsFieldHomomorphism"
+ ],
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 58,
+ "comment": "ImagesSet: for conjugator isomorphism, and group",
+ "filters": [
+ [
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 57,
+ "comment": "ImagesSet: method for algebra-with-one hom. and FLMLOR-with-one",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsOne",
+ "HasRespectsOne",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 55,
+ "comment": "ImagesSet: method for injective s.p. mapping respecting mult. & inv., and group",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsSPGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsInjective",
+ "HasIsInjective",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 52,
+ "comment": "ImagesSet: for polring g.m.b.i., and ring",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsPolynomialRingDefaultGeneratorMapping"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": 52,
+ "comment": "ImagesSet: method for algebra hom. and FLMLOR",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 49,
+ "comment": "ImagesSet: method for s.p. general mapping respecting mult. & inv., and group",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 38,
+ "comment": "ImagesSet: method for linear mapping and left module",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "ImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses"
+ ],
+ [
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "ImagesSet: for general mapping, and empty list",
+ "filters": [
+ [
+ "IsGeneralMapping"
+ ],
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "ImagesSet: for a restricted mapping, and a collection",
+ "filters": [
+ [
+ "IsGeneralRestrictedMappingRep"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "ImagesSet: for a composition mapping, and a collection",
+ "filters": [
+ [
+ "IsCompositionMappingRep"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
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+ "comment": "PreImagesRepresentative: for s.p. general mapping, and element",
+ "filters": [
+ [
+ "IsSPGeneralMapping"
+ ],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ }
+ },
+ {
+ "name": "PreImagesSet",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/mapping.gd",
+ "line": 1055
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 10019,
+ "comment": "PreImagesSet: for zero mapping and collection",
+ "filters": [
+ [
+ "IsZero",
+ "HasIsZero",
+ "IsGeneralMapping"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 10019,
+ "comment": "PreImagesSet: for identity mapping and collection",
+ "filters": [
+ [
+ "IsOne",
+ "HasIsOne",
+ "IsGeneralMapping"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 91,
+ "comment": "PreImagesSet: for PcpGHBI",
+ "filters": [
+ [
+ "IsFromPcpGHBI",
+ "IsToPcpGHBI"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsPcpElement)"
+ ]
+ ]
+ },
+ {
+ "rank": 84,
+ "comment": "PreImagesSet",
+ "filters": [
+ [
+ "IsBlocksHomomorphism"
+ ],
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 84,
+ "comment": "PreImagesSet: constituent homomorphism",
+ "filters": [
+ [
+ "IsConstituentHomomorphism"
+ ],
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 81,
+ "comment": "PreImagesSet: for ANF automorphism and scalar",
+ "filters": [
+ [
+ "IsFieldHomomorphism",
+ "HasIsFieldHomomorphism",
+ "IsANFAutomorphismRep"
+ ],
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 78,
+ "comment": "PreImagesSet: for field homomorphism and field",
+ "filters": [
+ [
+ "IsFieldHomomorphism",
+ "HasIsFieldHomomorphism"
+ ],
+ [
+ "IsNonTrivial",
+ "HasIsNonTrivial",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsMagmaWithInversesIfNonzero",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsCommutative",
+ "HasIsCommutative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsEuclideanRing"
+ ]
+ ]
+ },
+ {
+ "rank": 63,
+ "comment": "PreImagesSet: map from (sub)group of fp group",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsFromFpGroupGeneralMapping"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 58,
+ "comment": "PreImagesSet: for conjugator isomorphism, and group",
+ "filters": [
+ [
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 57,
+ "comment": "PreImagesSet: method for algebra-with-one hom. and FLMLOR-with-one",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsOne",
+ "HasRespectsOne",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 55,
+ "comment": "PreImagesSet: method for injective s.p. mapping respecting mult. & inv., and group",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsSPGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsInjective",
+ "HasIsInjective",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 53,
+ "comment": "PreImagesSet: method for permgroup homs",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsPermGroupGeneralMapping"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 52,
+ "comment": "PreImagesSet: method for algebra hom. and FLMLOR",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 49,
+ "comment": "PreImagesSet: method for s.p. general mapping respecting mult. & inv., and group",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 38,
+ "comment": "PreImagesSet: method for linear mapping and left module",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 30,
+ "comment": "PreImagesSet: method for s.p. gen. mapping resp. add. & add.inv., and add. group",
+ "filters": [
+ [
+ "IsSPGeneralMapping",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses"
+ ],
+ [
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "PreImagesSet: for general mapping, and empty list",
+ "filters": [
+ [
+ "IsGeneralMapping"
+ ],
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PreImagesSet: for a restricted mapping, and a collection",
+ "filters": [
+ [
+ "IsGeneralRestrictedMappingRep"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "PreImagesSet: for a composition mapping, and a collection",
+ "filters": [
+ [
+ "IsCompositionMappingRep"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 11,
+ "comment": "PreImagesSet: for an inverse mapping and a collection",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsInverseGeneralMappingRep"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ },
+ {
+ "rank": 9,
+ "comment": "PreImagesSet: for general mapping, and finite collection",
+ "filters": [
+ [
+ "IsGeneralMapping"
+ ],
+ [
+ "IsCollection"
+ ]
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "PreImagesSet"
+ ]
+ },
+ {
+ "name": "CompositionMapping2",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/mapping.gd",
+ "line": 1190
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 10028,
+ "comment": "CompositionMapping2: for zero mapping and single-valued gen. mapping that resp. zero",
+ "filters": [
+ [
+ "IsZero",
+ "HasIsZero",
+ "IsGeneralMapping"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsZero",
+ "HasRespectsZero"
+ ]
+ ]
+ },
+ {
+ "rank": 10025,
+ "comment": "CompositionMapping2: for identity mapping and general mapping",
+ "filters": [
+ [
+ "IsOne",
+ "HasIsOne",
+ "IsGeneralMapping"
+ ],
+ [
+ "IsGeneralMapping"
+ ]
+ ]
+ },
+ {
+ "rank": 10025,
+ "comment": "CompositionMapping2: for general mapping and identity mapping",
+ "filters": [
+ [
+ "IsGeneralMapping"
+ ],
+ [
+ "IsOne",
+ "HasIsOne",
+ "IsGeneralMapping"
+ ]
+ ]
+ },
+ {
+ "rank": 10024,
+ "comment": "CompositionMapping2: for general mapping and zero mapping",
+ "filters": [
+ [
+ "IsGeneralMapping"
+ ],
+ [
+ "IsZero",
+ "HasIsZero",
+ "IsGeneralMapping"
+ ]
+ ]
+ },
+ {
+ "rank": 56,
+ "comment": "CompositionMapping2: method for two pc group automorphisms",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsInjective",
+ "HasIsInjective",
+ "IsSurjective",
+ "HasIsSurjective",
+ "IsPcGroupGeneralMappingByImages",
+ "IsToPcGroupGeneralMappingByImages"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsInjective",
+ "HasIsInjective",
+ "IsSurjective",
+ "HasIsSurjective",
+ "IsPcGroupGeneralMappingByImages",
+ "IsToPcGroupGeneralMappingByImages"
+ ]
+ ]
+ },
+ {
+ "rank": 54,
+ "comment": "CompositionMapping2: for two inner automorphisms",
+ "filters": [
+ [
+ "IsInnerAutomorphism",
+ "HasIsInnerAutomorphism"
+ ],
+ [
+ "IsInnerAutomorphism",
+ "HasIsInnerAutomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 52,
+ "comment": "CompositionMapping2: for two ANF automorphisms",
+ "filters": [
+ [
+ "IsFieldHomomorphism",
+ "HasIsFieldHomomorphism",
+ "IsANFAutomorphismRep"
+ ],
+ [
+ "IsFieldHomomorphism",
+ "HasIsFieldHomomorphism",
+ "IsANFAutomorphismRep"
+ ]
+ ]
+ },
+ {
+ "rank": 52,
+ "comment": "CompositionMapping2: for two Frobenius automorphisms",
+ "filters": [
+ [
+ "IsFrobeniusAutomorphism"
+ ],
+ [
+ "IsFrobeniusAutomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 51,
+ "comment": "CompositionMapping2: for gp. hom. and fp. hom, transferring the coset table",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses",
+ "IsFromFpGroupGeneralMappingByImages",
+ "HasCosetTableFpHom"
+ ]
+ ]
+ },
+ {
+ "rank": 50,
+ "comment": "CompositionMapping2: for two conjugator automorphisms",
+ "filters": [
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
+ ],
+ [
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 47,
+ "comment": "CompositionMapping2: fp hom. with perm group hom.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsSurjective",
+ "HasIsSurjective",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses",
+ "IsToFpGroupGeneralMappingByImages"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses",
+ "IsPermGroupGeneralMappingByImages"
+ ]
+ ]
+ },
+ {
+ "rank": 46,
+ "comment": "CompositionMapping2: for two conjugator isomorphisms",
+ "filters": [
+ [
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
+ ],
+ [
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 46,
+ "comment": "CompositionMapping2: for left module hom. and algebra g.m.b.i.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 46,
+ "comment": "CompositionMapping2: for left module hom. and linear m.b.m.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication",
+ "IsLinearMappingByMatrixDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 45,
+ "comment": "CompositionMapping2: for action homomorphism with blocks homomorphism",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses",
+ "IsBlocksHomomorphism"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses",
+ "IsActionHomomorphism"
+ ]
+ ]
+ },
+ {
+ "rank": 44,
+ "comment": "CompositionMapping2: for nilpotent Lie algebra automorphisms",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsNilpotentLieAutomorphismRep"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsNilpotentLieAutomorphismRep"
+ ]
+ ]
+ },
+ {
+ "rank": 44,
+ "comment": "CompositionMapping2: for group automorphisms",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsPGAutomorphismRep"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsPGAutomorphismRep"
+ ]
+ ]
+ },
+ {
+ "rank": 44,
+ "comment": "CompositionMapping2: for left module hom. and algebra g.m.b.i.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication",
+ "IsAlgebraGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 42,
+ "comment": "CompositionMapping2: for left module hom. and linear g.m.b.i.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication"
+ ],
+ [
+ "IsGeneralMapping",
+ "RespectsAddition",
+ "HasRespectsAddition",
+ "RespectsAdditiveInverses",
+ "HasRespectsAdditiveInverses",
+ "RespectsScalarMultiplication",
+ "HasRespectsScalarMultiplication",
+ "IsLinearGeneralMappingByImagesDefaultRep"
+ ]
+ ]
+ },
+ {
+ "rank": 40,
+ "comment": "CompositionMapping2: group hom. with perm group hom.",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses",
+ "IsPermGroupGeneralMappingByImages"
+ ]
+ ]
+ },
+ {
+ "rank": 39,
+ "comment": "CompositionMapping2: method for hom2 from pc group",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsGroupGeneralMappingByPcgs"
+ ]
+ ]
+ },
+ {
+ "rank": 34,
+ "comment": "CompositionMapping2: for semigroup homomorphism by images",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsSPGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "IsSemigroupHomomorphismByImagesRep"
+ ],
+ [
+ "IsGeneralMapping",
+ "IsSPGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "IsSemigroupHomomorphismByImagesRep"
+ ]
+ ]
+ },
+ {
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+ "comment": "CompositionMapping2: IsTransformationRepOfEndo, IsTransformationRepOfEndo",
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+ [
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+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsTotal",
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+ "IsSingleValued",
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+ "IsTransformationRepOfEndo"
+ ],
+ [
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+ "IsEndoGeneralMapping",
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+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsTransformationRepOfEndo"
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+ ]
+ },
+ {
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+ "comment": "CompositionMapping2: for gp. hom. and gp. gen. mapp., using `MappingGeneratorsImages'",
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+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
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+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
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+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
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+ ]
+ },
+ {
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+ "comment": "CompositionMapping2: IsTransformationRepOfEndo, IsEndoMapping",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsTotal",
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+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsTransformationRepOfEndo"
+ ],
+ [
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+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued"
+ ]
+ ]
+ },
+ {
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+ "comment": "CompositionMapping2: IsEndoMapping, IsTransformationRepOfEndo",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
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+ "HasIsSingleValued"
+ ],
+ [
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+ "IsEndoGeneralMapping",
+ "HasIsEndoGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsTransformationRepOfEndo"
+ ]
+ ]
+ },
+ {
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+ "comment": "CompositionMapping2: for two general mappings",
+ "filters": [
+ [
+ "IsGeneralMapping"
+ ],
+ [
+ "IsGeneralMapping"
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+ ],
+ "aka": [
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+ }
+ ],
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+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
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+ ]
+ },
+ {
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+ {
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+ }
+ ],
+ "filters": [],
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+ "1args": [],
+ "2args": [
+ {
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+ "comment": "ZeroMapping: for collection and additive-magma-with-zero",
+ "filters": [
+ [
+ "IsCollection"
+ ],
+ [
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+ "IsNearAdditiveMagmaWithZero",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative"
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+ ]
+ }
+ ],
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+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
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+ "ZeroMapping"
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+ },
+ {
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+ "type": "Operation",
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+ {
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+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [
+ {
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+ "comment": "RestrictedMapping: try if restriction is proper",
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+ [
+ "IsGeneralMapping",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
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+ [
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+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 10015,
+ "comment": "RestrictedMapping: for mapping that is already restricted",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsGeneralRestrictedMappingRep"
+ ],
+ [
+ "IsCollection",
+ "IsGeneralizedDomain"
+ ]
+ ]
+ },
+ {
+ "rank": 57,
+ "comment": "RestrictedMapping: action homomorphism",
+ "filters": [
+ [
+ "IsActionHomomorphism"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
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+ "comment": "RestrictedMapping: injective case: use GeneralRestrictedMapping",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "IsInjective",
+ "HasIsInjective",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
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+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 52,
+ "comment": "RestrictedMapping: create new GHBI",
+ "filters": [
+ [
+ "IsGeneralMapping",
+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
+ "HasIsSingleValued",
+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
+ ],
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
+ ]
+ ]
+ },
+ {
+ "rank": 12,
+ "comment": "RestrictedMapping: use GeneralRestrictedMapping",
+ "filters": [
+ [
+ "IsGeneralMapping"
+ ],
+ [
+ "IsCollection",
+ "IsGeneralizedDomain"
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+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "RestrictedMapping"
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+ },
+ {
+ "name": "Embedding",
+ "type": "Operation",
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+ {
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+ }
+ ],
+ "filters": [],
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+ "1args": [],
+ "2args": [
+ {
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+ "comment": "Embedding: of semidirect pc group and integer",
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+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+ "HasSemidirectProductInfo"
+ ],
+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 86,
+ "comment": "Embedding: of pc group and integer",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)",
+ "HasDirectProductInfo"
+ ],
+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 81,
+ "comment": "Embedding: generic method for perm semidirect products",
+ "filters": [
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasSemidirectProductInfo"
+ ],
+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 81,
+ "comment": "Embedding: perm wreath product",
+ "filters": [
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasWreathProductInfo"
+ ],
+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 81,
+ "comment": "Embedding: perm direct product",
+ "filters": [
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
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+ "HasDirectProductInfo"
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+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 79,
+ "comment": "Embedding: LAGUNA: from group to pc-presented normalized unit group of group ring",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
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+ [
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+ "HasIsNormalizedUnitGroupOfGroupRing"
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+ ]
+ },
+ {
+ "rank": 70,
+ "comment": "Embedding: pcp wreath product",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasWreathProductInfo",
+ "CategoryCollections(IsPcpElement)"
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+ [
+ "IsInt",
+ "IsPosRat"
+ ]
+ ]
+ },
+ {
+ "rank": 70,
+ "comment": "Embedding",
+ "filters": [
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasDirectProductInfo",
+ "CategoryCollections(IsPcpElement)"
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+ [
+ "IsInt",
+ "IsPosRat"
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+ ]
+ },
+ {
+ "rank": 65,
+ "comment": "Embedding: matrix wreath product",
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+ [
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasWreathProductInfo"
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+ [
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+ "IsPosRat"
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+ },
+ {
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+ "comment": "Embedding: matrix direct product",
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+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
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+ "HasDirectProductInfo"
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+ [
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+ "IsPosRat"
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+ },
+ {
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+ "comment": "Embedding: for ring and magma ring",
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+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
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+ [
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+ ]
+ },
+ {
+ "rank": 59,
+ "comment": "Embedding: generic wreath product",
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+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasWreathProductInfo",
+ "CategoryCollections(IsWreathProductElement)"
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+ [
+ "IsInt",
+ "IsPosRat"
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+ ]
+ },
+ {
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+ "comment": "Embedding: LAGUNA: from a group to the Lie algebra of the group ring",
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+ "IsMagma"
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+ [
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+ "HasIsLieAlgebraOfGroupRing"
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+ },
+ {
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+ "comment": "Embedding: free products",
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+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasFreeProductInfo"
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+ [
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+ "IsPosRat"
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+ },
+ {
+ "rank": 55,
+ "comment": "Embedding: vectorspace semidirect products",
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+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasSemidirectProductInfo"
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+ [
+ "IsInt",
+ "IsPosRat"
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+ },
+ {
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+ "comment": "Embedding: of semidirect product and integer",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasSemidirectProductInfo"
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+ [
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+ "IsPosRat"
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+ ]
+ },
+ {
+ "rank": 55,
+ "comment": "Embedding: group direct product and integer",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasDirectProductInfo"
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+ [
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+ "IsPosRat"
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+ {
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+ "comment": "Embedding: for magma and magma ring",
+ "filters": [
+ [
+ "IsMagma"
+ ],
+ [
+ "IsFreeMagmaRing"
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+ ]
+ },
+ {
+ "rank": 3,
+ "comment": "Embedding: for two families, the first with known Lie family",
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+ [
+ "IsFamily",
+ "HasLieFamily"
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+ [
+ "IsFamily"
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+ ]
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+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "Embedding"
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+ },
+ {
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+ "methods": {
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+ "1args": [
+ {
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+ "comment": "Projection: of semidirect pc group",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
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+ },
+ {
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+ "comment": "Projection: generic method for perm semidirect products",
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+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
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+ {
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+ "comment": "Projection: perm wreath product",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasWreathProductInfo"
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+ },
+ {
+ "rank": 46,
+ "comment": "Projection: matrix wreath product",
+ "filters": [
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+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasWreathProductInfo"
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+ ]
+ },
+ {
+ "rank": 40,
+ "comment": "Projection: generic wreath product",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasWreathProductInfo",
+ "CategoryCollections(IsWreathProductElement)"
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+ },
+ {
+ "rank": 36,
+ "comment": "Projection: of semidirect product",
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+ "IsAssociative",
+ "HasIsAssociative",
+ "HasSemidirectProductInfo"
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+ "2args": [
+ {
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+ "comment": "Projection: of pc group and integer",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
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+ "HasDirectProductInfo"
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+ [
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+ "IsPosRat"
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+ },
+ {
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+ "comment": "Projection: perm subdirect product",
+ "filters": [
+ [
+ "CategoryCollections(IsPerm)",
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasSubdirectProductInfo"
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+ [
+ "IsInt",
+ "IsPosRat"
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+ },
+ {
+ "rank": 81,
+ "comment": "Projection: perm direct product",
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+ [
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+ "IsMagmaWithInverses",
+ "IsAssociative",
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+ "HasDirectProductInfo"
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+ [
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+ "IsPosRat"
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+ },
+ {
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+ "comment": "Projection",
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+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
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+ "CategoryCollections(IsPcpElement)"
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+ [
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+ "IsPosRat"
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+ },
+ {
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+ "comment": "Projection: matrix direct product",
+ "filters": [
+ [
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
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+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasDirectProductInfo"
+ ],
+ [
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+ "IsPosRat"
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+ },
+ {
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+ "comment": "Projection: pc subdirect product",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative",
+ "HasSubdirectProductInfo"
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+ [
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+ "IsPosRat"
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+ },
+ {
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+ "comment": "Projection: group direct product and integer",
+ "filters": [
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+ [
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+ "IsPosRat"
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+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
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+ {
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+ "locations": [
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+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
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+ "comment": "MappingGeneratorsImages: system getter",
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+ [
+ "IsAttributeStoringRep",
+ "HasMappingGeneratorsImages"
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+ ]
+ },
+ {
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+ "comment": "MappingGeneratorsImages: for action hom that is `ByAsGroup'",
+ "filters": [
+ [
+ "IsGroupGeneralMappingByAsGroupGeneralMappingByImages",
+ "IsActionHomomorphism"
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+ ]
+ },
+ {
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+ "comment": "MappingGeneratorsImages: for conjugator isomorphism",
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+ [
+ "IsConjugatorIsomorphism",
+ "HasIsConjugatorIsomorphism"
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+ },
+ {
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+ "comment": "MappingGeneratorsImages: for group homomorphism",
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+ [
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+ "IsTotal",
+ "HasIsTotal",
+ "IsSingleValued",
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+ "RespectsMultiplication",
+ "HasRespectsMultiplication",
+ "RespectsInverses",
+ "HasRespectsInverses"
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+ ]
+ },
+ {
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+ "comment": "MappingGeneratorsImages: fallback method to test conditions",
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+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "MappingGeneratorsImages"
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+ },
+ {
+ "name": "SetMappingGeneratorsImages",
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+ "locations": [
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+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [
+ {
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+ "comment": "SetMappingGeneratorsImages: system setter",
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+ [
+ "IsAttributeStoringRep"
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+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetMappingGeneratorsImages: default method, does nothing",
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+ [],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "SetMappingGeneratorsImages"
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+ },
+ {
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+ "locations": [
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+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "HasMappingGeneratorsImages"
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+ },
+ {
+ "name": "RespectsMultiplication",
+ "type": "Property",
+ "locations": [
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+ "line": 60
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
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+ "comment": "RespectsMultiplication: system getter",
+ "filters": [
+ [
+ "IsAttributeStoringRep",
+ "HasRespectsMultiplication"
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+ ]
+ },
+ {
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+ "comment": "RespectsMultiplication: method for a general mapping",
+ "filters": [
+ [
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+ ]
+ }
+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "RespectsMultiplication"
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+ },
+ {
+ "name": "SetRespectsMultiplication",
+ "type": "Setter",
+ "locations": [
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+ "line": 60
+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [
+ {
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+ "comment": "SetRespectsMultiplication: system setter",
+ "filters": [
+ [
+ "IsAttributeStoringRep"
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+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetRespectsMultiplication: default method, does nothing",
+ "filters": [
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+ []
+ ]
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+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": -14,
+ "comment": "IsTwoSidedIdealInParent: default method requiring categories and checking properties",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup"
+ ]
+ ]
+ }
+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "IsIdealInParent",
+ "IsTwoSidedIdealInParent"
+ ]
+ },
+ {
+ "name": "SetIsTwoSidedIdealInParent",
+ "type": "Setter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 193
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 2,
+ "comment": "SetIsTwoSidedIdealInParent: system setter",
+ "filters": [
+ [
+ "IsAttributeStoringRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetIsTwoSidedIdealInParent: default method, does nothing",
+ "filters": [
+ [],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "SetIsIdealInParent",
+ "SetIsTwoSidedIdealInParent"
+ ]
+ },
+ {
+ "name": "HasIsTwoSidedIdealInParent",
+ "type": "Filter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 193
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "HasIsIdealInParent",
+ "HasIsTwoSidedIdealInParent"
+ ]
+ },
+ {
+ "name": "IsTwoSidedIdeal",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 193
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 52,
+ "comment": "IsTwoSidedIdeal: try to exploit the in-parent attribute IsTwoSidedIdealInParent",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "IsIdeal",
+ "IsTwoSidedIdeal"
+ ]
+ },
+ {
+ "name": "IsLeftIdealOp",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 194
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 72,
+ "comment": "IsLeftIdealOp: for associative FLMLOR and FLMLOR",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "IsLeftIdealOp: for associative FLMLOR-with-one and free left module",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 61,
+ "comment": "IsLeftIdealOp: for associative FLMLOR and free left module",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 58,
+ "comment": "IsLeftIdealOp: for SCRings",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "CategoryCollections(IsSCRingObj)"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "CategoryCollections(IsSCRingObj)"
+ ]
+ ]
+ },
+ {
+ "rank": 57,
+ "comment": "IsLeftIdealOp: for FLMLOR and free left module",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsFreeLeftModule"
+ ]
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "IsLeftIdealOp"
+ ]
+ },
+ {
+ "name": "IsLeftIdealInParent",
+ "type": "Property",
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+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 194
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 20029,
+ "comment": "IsLeftIdealInParent: system getter",
+ "filters": [
+ [
+ "IsAttributeStoringRep",
+ "HasIsLeftIdealInParent"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "IsLeftIdealInParent: method that calls the two-argument operation IsLeftIdealOp",
+ "filters": [
+ [
+ "HasParentAttr",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": -14,
+ "comment": "IsLeftIdealInParent: default method requiring categories and checking properties",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup"
+ ]
+ ]
+ }
+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "IsLeftIdealInParent"
+ ]
+ },
+ {
+ "name": "SetIsLeftIdealInParent",
+ "type": "Setter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 194
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 2,
+ "comment": "SetIsLeftIdealInParent: system setter",
+ "filters": [
+ [
+ "IsAttributeStoringRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetIsLeftIdealInParent: default method, does nothing",
+ "filters": [
+ [],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "SetIsLeftIdealInParent"
+ ]
+ },
+ {
+ "name": "HasIsLeftIdealInParent",
+ "type": "Filter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 194
+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "HasIsLeftIdealInParent"
+ ]
+ },
+ {
+ "name": "IsLeftIdeal",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 194
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 79,
+ "comment": "IsLeftIdeal: left ideal in ring, naive",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "HasLeftActingRingOfIdeal"
+ ]
+ ]
+ },
+ {
+ "rank": 52,
+ "comment": "IsLeftIdeal: try to exploit the in-parent attribute IsLeftIdealInParent",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ }
+ },
+ {
+ "name": "IsRightIdealOp",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 195
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 72,
+ "comment": "IsRightIdealOp: for associative FLMLOR and FLMLOR",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 66,
+ "comment": "IsRightIdealOp: for associative FLMLOR-with-one and free left module",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsMagmaWithOne",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 61,
+ "comment": "IsRightIdealOp: for associative FLMLOR and free left module",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsAssociative",
+ "HasIsAssociative",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsFreeLeftModule"
+ ]
+ ]
+ },
+ {
+ "rank": 58,
+ "comment": "IsRightIdealOp: for SCRings",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "CategoryCollections(IsSCRingObj)"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "CategoryCollections(IsSCRingObj)"
+ ]
+ ]
+ },
+ {
+ "rank": 57,
+ "comment": "IsRightIdealOp: for FLMLOR and free left module",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsFreeLeftModule"
+ ]
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "IsRightIdealOp"
+ ]
+ },
+ {
+ "name": "IsRightIdealInParent",
+ "type": "Property",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 195
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 20029,
+ "comment": "IsRightIdealInParent: system getter",
+ "filters": [
+ [
+ "IsAttributeStoringRep",
+ "HasIsRightIdealInParent"
+ ]
+ ]
+ },
+ {
+ "rank": 27,
+ "comment": "IsRightIdealInParent: method that calls the two-argument operation IsRightIdealOp",
+ "filters": [
+ [
+ "HasParentAttr",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ },
+ {
+ "rank": -14,
+ "comment": "IsRightIdealInParent: default method requiring categories and checking properties",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup"
+ ]
+ ]
+ }
+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "IsRightIdealInParent"
+ ]
+ },
+ {
+ "name": "SetIsRightIdealInParent",
+ "type": "Setter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 195
+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [
+ {
+ "rank": 2,
+ "comment": "SetIsRightIdealInParent: system setter",
+ "filters": [
+ [
+ "IsAttributeStoringRep"
+ ],
+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetIsRightIdealInParent: default method, does nothing",
+ "filters": [
+ [],
+ []
+ ]
+ }
+ ],
+ "3args": [],
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+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "SetIsRightIdealInParent"
+ ]
+ },
+ {
+ "name": "HasIsRightIdealInParent",
+ "type": "Filter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 195
+ }
+ ],
+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "HasIsRightIdealInParent"
+ ]
+ },
+ {
+ "name": "IsRightIdeal",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 195
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 52,
+ "comment": "IsRightIdeal: try to exploit the in-parent attribute IsRightIdealInParent",
+ "filters": [
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ],
+ [
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive"
+ ]
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "IsRightIdeal"
+ ]
+ },
+ {
+ "name": "TwoSidedIdealByGenerators",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/ideal.gd",
+ "line": 230
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [],
+ "2args": [
+ {
+ "rank": 65,
+ "comment": "TwoSidedIdealByGenerators: for Lie algebra and collection of Lie objects",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsAssociativeLOpEProd",
+ "IsDistributiveLOpDSum",
+ "IsDistributiveLOpESum",
+ "IsTrivialLOpEOne",
+ "IsLeftActedOnByRing",
+ "IsLeftActedOnByDivisionRing",
+ "HasIsLeftActedOnByDivisionRing",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsJacobianRing",
+ "HasIsJacobianRing",
+ "IsZeroSquaredRing",
+ "HasIsZeroSquaredRing"
+ ],
+ [
+ "IsList",
+ "CategoryCollections(IsLieObject)"
+ ]
+ ],
+ "aka": [
+ "IdealByGeneratorsForLieAlgebra"
+ ]
+ },
+ {
+ "rank": 64,
+ "comment": "TwoSidedIdealByGenerators: for matrix algebra and empty list",
+ "filters": [
+ [
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
+ "CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
+ "IsDistributiveLOpDSum",
+ "IsMagma",
+ "IsNearAdditiveMagma",
+ "IsNearAdditiveGroup",
+ "IsAdditivelyCommutative",
+ "HasIsAdditivelyCommutative",
+ "IsLDistributive",
+ "HasIsLDistributive",
+ "IsRDistributive",
+ "HasIsRDistributive",
+ "IsFreeLeftModule"
+ ],
+ [
+ "IsList",
+ "IsEmpty",
+ "HasIsEmpty"
+ ]
+ ]
+ },
+ {
+ "rank": 62,
+ "comment": "TwoSidedIdealByGenerators: for Lie algebra and empty list",
+ "filters": [
+ [
+ "IsExtLSet",
+ "IsAssociativeLOpDProd",
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+ "type": "Filter",
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+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
+ "line": 339
+ }
+ ],
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+ "5args": [],
+ "6args": []
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+ "aka": [
+ "HasCanonicalRepresentativeOfExternalSet"
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+ },
+ {
+ "name": "CanonicalRepresentativeDeterminatorOfExternalSet",
+ "type": "Attribute",
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+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
+ "line": 364
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 20011,
+ "comment": "CanonicalRepresentativeDeterminatorOfExternalSet: system getter",
+ "filters": [
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+ ],
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+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "CanonicalRepresentativeDeterminatorOfExternalSet"
+ ]
+ },
+ {
+ "name": "SetCanonicalRepresentativeDeterminatorOfExternalSet",
+ "type": "Operation",
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+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ }
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+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [
+ {
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+ "filters": [
+ [
+ "IsAttributeStoringRep"
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+ []
+ ]
+ },
+ {
+ "rank": 0,
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+ [],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
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+ "aka": [
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+ },
+ {
+ "name": "HasCanonicalRepresentativeDeterminatorOfExternalSet",
+ "type": "Filter",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ "4args": [],
+ "5args": [],
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+ },
+ "aka": [
+ "HasCanonicalRepresentativeDeterminatorOfExternalSet"
+ ]
+ },
+ {
+ "name": "CanEasilyDetermineCanonicalRepresentativeExternalSet",
+ "type": "Property",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
+ "line": 380
+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 20009,
+ "comment": "CanEasilyDetermineCanonicalRepresentativeExternalSet: system getter",
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+ [
+ "IsAttributeStoringRep",
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+ ]
+ }
+ ],
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+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
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+ },
+ {
+ "name": "SetCanEasilyDetermineCanonicalRepresentativeExternalSet",
+ "type": "Setter",
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+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
+ "line": 380
+ }
+ ],
+ "filters": [],
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+ "filters": [
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+ {
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+ []
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+ },
+ {
+ "name": "HasCanEasilyDetermineCanonicalRepresentativeExternalSet",
+ "type": "Filter",
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+ "5args": [],
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+ },
+ {
+ "name": "ActorOfExternalSet",
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+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ }
+ ],
+ "filters": [],
+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 20009,
+ "comment": "ActorOfExternalSet: system getter",
+ "filters": [
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+ "IsAttributeStoringRep",
+ "HasActorOfExternalSet"
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+ {
+ "rank": 11,
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+ [
+ "IsConjugacyClassGroupRep"
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+ {
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+ "IsExternalOrbit",
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+ {
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+ "comment": "ActorOfExternalSet",
+ "filters": [
+ [
+ "IsExternalSet"
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+ }
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+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "ActorOfExternalSet",
+ "OperatorOfExternalSet"
+ ]
+ },
+ {
+ "name": "SetActorOfExternalSet",
+ "type": "Operation",
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+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ }
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+ "filters": [],
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+ "1args": [],
+ "2args": [
+ {
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+ "filters": [
+ [
+ "IsAttributeStoringRep"
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+ []
+ ]
+ },
+ {
+ "rank": 0,
+ "comment": "SetActorOfExternalSet: default method, does nothing",
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+ [],
+ []
+ ]
+ }
+ ],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
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+ "SetOperatorOfExternalSet"
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+ },
+ {
+ "name": "HasActorOfExternalSet",
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+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ "methods": {
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+ "1args": [],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "HasActorOfExternalSet",
+ "HasOperatorOfExternalSet"
+ ]
+ },
+ {
+ "name": "PreOrbishProcessing",
+ "type": "Operation",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ }
+ ],
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+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 35,
+ "comment": "PreOrbishProcessing",
+ "filters": [
+ [
+ "IsMagmaWithInverses",
+ "IsAssociative",
+ "HasIsAssociative"
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+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "PreOrbishProcessing"
+ ]
+ },
+ {
+ "name": "ActionHomomorphismAttr",
+ "type": "Attribute",
+ "locations": [
+ {
+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ ],
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+ "methods": {
+ "0args": [],
+ "1args": [
+ {
+ "rank": 20009,
+ "comment": "ActionHomomorphismAttr: system getter",
+ "filters": [
+ [
+ "IsAttributeStoringRep",
+ "HasActionHomomorphismAttr"
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+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "ActionHomomorphismAttr: call OpHomConstructor",
+ "filters": [
+ [
+ "IsExternalSet"
+ ]
+ ]
+ }
+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
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+ {
+ "name": "SetActionHomomorphismAttr",
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+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ "1args": [],
+ "2args": [
+ {
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+ [
+ "IsAttributeStoringRep"
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+ []
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+ {
+ "rank": 0,
+ "comment": "SetActionHomomorphismAttr: default method, does nothing",
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+ [],
+ []
+ ]
+ }
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+ "4args": [],
+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "SetActionHomomorphismAttr"
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+ {
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+ "6args": []
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+ "aka": [
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+ {
+ "name": "SurjectiveActionHomomorphismAttr",
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+ "locations": [
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+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ "methods": {
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+ "1args": [
+ {
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+ [
+ "IsAttributeStoringRep",
+ "HasSurjectiveActionHomomorphismAttr"
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+ ]
+ },
+ {
+ "rank": 6,
+ "comment": "SurjectiveActionHomomorphismAttr: call Ac.Hom.Constructor",
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+ [
+ "IsExternalSet"
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+ ]
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+ ],
+ "2args": [],
+ "3args": [],
+ "4args": [],
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+ "IsAttributeStoringRep"
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+ {
+ "rank": 0,
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+ [],
+ []
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+ {
+ "name": "HasSurjectiveActionHomomorphismAttr",
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+ "methods": {
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+ "2args": [],
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+ "4args": [],
+ "5args": [],
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+ "aka": [
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+ },
+ {
+ "name": "UnderlyingExternalSet",
+ "type": "Attribute",
+ "locations": [
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+ "file": "/home/mp397/git/gap/lib/oprt.gd",
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+ }
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+ "methods": {
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+ {
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+ {
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+ [],
+ []
+ ]
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+ {
+ "name": "HasUnderlyingExternalSet",
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+ []
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+ "HasIsAssociative"
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+ [],
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+ [],
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+ {
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+ }
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+ "filters": [],
+ "methods": {
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+ "1args": [],
+ "2args": [
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+ [
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+ "5args": [],
+ "6args": []
+ },
+ "aka": [
+ "RestrictedExternalSet"
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+ {
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+ "type": "Operation",
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+ "locations": [
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+ },
+ {
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+ "6args": []
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