[
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"name": "IsObject",
"type": "Category",
"implied": []
},
{
"name": "ViewObj",
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"line": 1626
}
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[]
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[
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[
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[
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{
"rank": 35,
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{
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"comment": "ViewObj: for a semigroup Congruence with known generating pairs",
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{
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"IsNilpotentLieAutomorphismRep"
]
]
},
{
"rank": 44,
"comment": "=: for group automorphisms",
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[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsPGAutomorphismRep"
],
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsPGAutomorphismRep"
]
]
},
{
"rank": 44,
"comment": "=: for GreensRelation",
"filters": [
[
"IsGreensRelation"
],
[
"IsGreensRelation"
]
]
},
{
"rank": 44,
"comment": "=: for an inverse semigroups with generators",
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[
"IsInverseSemigroup",
"HasIsInverseSemigroup",
"HasGeneratorsOfInverseSemigroup"
],
[
"IsInverseSemigroup",
"HasIsInverseSemigroup",
"HasGeneratorsOfInverseSemigroup"
]
]
},
{
"rank": 43,
"comment": "=: for ANF automorphism and identity mapping",
"filters": [
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
],
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 43,
"comment": "=: for identity mapping and ANF automorphism",
"filters": [
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
],
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
]
]
},
{
"rank": 43,
"comment": "=: for Frobenius automorphism and identity mapping",
"filters": [
[
"IsFrobeniusAutomorphism"
],
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 43,
"comment": "=: for identity mapping and Frobenius automorphism",
"filters": [
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
],
[
"IsFrobeniusAutomorphism"
]
]
},
{
"rank": 42,
"comment": "=: for GF2 vectors",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
]
],
"aka": [
"EQ_GF2VEC_GF2VEC"
]
},
{
"rank": 42,
"comment": "=: for eqivalence relations",
"filters": [
[
"IsEquivalenceRelation",
"HasIsEquivalenceRelation"
],
[
"IsEquivalenceRelation",
"HasIsEquivalenceRelation"
]
]
},
{
"rank": 42,
"comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,one,scal. mult.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsOne",
"HasRespectsOne",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsOne",
"HasRespectsOne",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
]
]
},
{
"rank": 40,
"comment": "=",
"filters": [
[
"IsUnicodeCharacter"
],
[
"IsUnicodeCharacter"
]
]
},
{
"rank": 40,
"comment": "=: for two underlying relations of general mappings",
"filters": [
[
"IsCollection",
"IsGeneralizedDomain",
"CategoryCollections(IsDirectProductElement)",
"HasUnderlyingGeneralMapping"
],
[
"IsCollection",
"IsGeneralizedDomain",
"CategoryCollections(IsDirectProductElement)",
"HasUnderlyingGeneralMapping"
]
]
},
{
"rank": 39,
"comment": "=: homomorphism by images with homomorphism: compare generator images",
"filters": [
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses",
"IsGroupGeneralMappingByImages"
],
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
]
]
},
{
"rank": 38,
"comment": "=: homomorphism with general mapping: test b=a",
"filters": [
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
],
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses",
"IsGroupGeneralMappingByImages"
]
]
},
{
"rank": 38,
"comment": "=: for ring ring general mapping and ring g.m.b.i.",
"filters": [
[
"IsGeneralMapping",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
],
[
"IsGeneralMapping",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"IsRingGeneralMappingByImagesDefaultRep"
]
]
},
{
"rank": 38,
"comment": "=: for ring g.m.b.i. and ring general mapping",
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[
"IsGeneralMapping",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"IsRingGeneralMappingByImagesDefaultRep"
],
[
"IsGeneralMapping",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
]
]
},
{
"rank": 38,
"comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,mult.,scal. mult.",
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[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
]
]
},
{
"rank": 38,
"comment": "=: method for two s.v. gen. mappings that respect mult.,one,add.,add.inv.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsOne",
"HasRespectsOne",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsOne",
"HasRespectsOne",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
]
]
},
{
"rank": 38,
"comment": "=: for two direct product elements",
"filters": [
[
"IsDirectProductElement"
],
[
"IsDirectProductElement"
]
]
},
{
"rank": 36,
"comment": "=: for two unknowns in default representation",
"filters": [
[
"IsUnknown",
"IsUnknownDefaultRep"
],
[
"IsUnknown",
"IsUnknownDefaultRep"
]
]
},
{
"rank": 35,
"comment": "=: for internal FFE and element in Z/pZ (ModulusRep)",
"filters": [
[
"IsFFE",
"IsInternalRep"
],
[
"IsFFE",
"IsZmodnZObj",
"IsModulusRep"
]
]
},
{
"rank": 35,
"comment": "=: for element in Z/pZ (ModulusRep) and internal FFE",
"filters": [
[
"IsFFE",
"IsZmodnZObj",
"IsModulusRep"
],
[
"IsFFE",
"IsInternalRep"
]
]
},
{
"rank": 34,
"comment": "=: for semigroup homomorphism by images",
"filters": [
[
"IsGeneralMapping",
"IsSPGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"IsSemigroupHomomorphismByImagesRep"
],
[
"IsGeneralMapping",
"IsSPGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"IsSemigroupHomomorphismByImagesRep"
]
]
},
{
"rank": 34,
"comment": "=",
"filters": [
[
"IsFFE",
"IsCoeffsModConwayPolRep"
],
[
"IsFFE",
"IsCoeffsModConwayPolRep"
]
]
},
{
"rank": 34,
"comment": "=: BFElm=BFElm",
"filters": [
[
"IsAlgBFRep"
],
[
"IsAlgBFRep"
]
]
},
{
"rank": 34,
"comment": "=: BFElm<AlgElm",
"filters": [
[
"IsAlgBFRep"
],
[
"IsKroneckerConstRep"
]
]
},
{
"rank": 34,
"comment": "=: AlgElm=BFElm",
"filters": [
[
"IsKroneckerConstRep"
],
[
"IsAlgBFRep"
]
]
},
{
"rank": 34,
"comment": "=: AlgElm=AlgElm",
"filters": [
[
"IsKroneckerConstRep"
],
[
"IsKroneckerConstRep"
]
]
},
{
"rank": 34,
"comment": "=: laurent",
"filters": [
[
"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
],
[
"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
]
]
},
{
"rank": 34,
"comment": "=: method for two s.v. gen. mappings that respect add.,add.inv.,scal. mult.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses",
"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
]
]
},
{
"rank": 34,
"comment": "=: method for two s.v. gen. mappings that respect mult.,add.,add.inv.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
]
]
},
{
"rank": 33,
"comment": "=: for a list and a class function",
"filters": [
[
"IsList"
],
[
"IsClassFunction"
]
]
},
{
"rank": 33,
"comment": "=: for a class function and a list",
"filters": [
[
"IsClassFunction"
],
[
"IsList"
]
]
},
{
"rank": 33,
"comment": "=: for a collection, and an empty row vector in the same family",
"filters": [
[
"IsCollection"
],
[
"IsHomogeneousList",
"IsEmpty",
"HasIsEmpty",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsEmptyRowVectorRep"
]
]
},
{
"rank": 33,
"comment": "=: for an empty row vector, and a collection in the same family",
"filters": [
[
"IsHomogeneousList",
"IsEmpty",
"HasIsEmpty",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsEmptyRowVectorRep"
],
[
"IsCollection"
]
]
},
{
"rank": 32,
"comment": "=: IsTransformationRepOfEndo, IsTransformationRepOfEndo",
"filters": [
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
],
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
]
]
},
{
"rank": 32,
"comment": "=: RightCosets",
"filters": [
[
"IsRightCoset"
],
[
"IsRightCoset"
]
]
},
{
"rank": 32,
"comment": "=",
"filters": [
[
"IsFFE"
],
[
"IsFFE",
"IsCoeffsModConwayPolRep"
]
]
},
{
"rank": 32,
"comment": "=",
"filters": [
[
"IsFFE",
"IsCoeffsModConwayPolRep"
],
[
"IsFFE"
]
]
},
{
"rank": 32,
"comment": "=: for two elements in Z/nZ (ModulusRep)",
"filters": [
[
"IsZmodnZObj",
"IsModulusRep"
],
[
"IsZmodnZObj",
"IsModulusRep"
]
]
},
{
"rank": 32,
"comment": "=: for cyclotomic and unknown",
"filters": [
[
"IsCyc"
],
[
"IsUnknown"
]
],
"aka": [
"IsAtomicList",
"IsReadOnlyObj",
"RETURN_FALSE",
"ReturnFalse"
]
},
{
"rank": 32,
"comment": "=: for unknown and cyclotomic",
"filters": [
[
"IsUnknown"
],
[
"IsCyc"
]
]
},
{
"rank": 32,
"comment": "=: for semigroup with generators and semigroup with generators",
"filters": [
[
"IsMagma",
"HasGeneratorsOfMagma",
"IsAssociative",
"HasIsAssociative"
],
[
"IsMagma",
"HasGeneratorsOfMagma",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 31,
"comment": "=: for `-infinity' and cyclotomic",
"filters": [
[
"IsNegInfinity"
],
[
"IsCyclotomic"
]
]
},
{
"rank": 31,
"comment": "=: for cyclotomic and `-infinity'",
"filters": [
[
"IsCyclotomic"
],
[
"IsNegInfinity"
]
]
},
{
"rank": 31,
"comment": "=: for `infinity' and cyclotomic",
"filters": [
[
"IsInfinity"
],
[
"IsCyclotomic"
]
]
},
{
"rank": 31,
"comment": "=: for cyclotomic and `infinity'",
"filters": [
[
"IsCyclotomic"
],
[
"IsInfinity"
]
]
},
{
"rank": 30,
"comment": "=: for two plist matrices",
"filters": [
[
"IsPlistMatrixRep"
],
[
"IsPlistMatrixRep"
]
]
},
{
"rank": 30,
"comment": "=: univariate = univariate",
"filters": [
[
"IsPolynomialFunction",
"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction"
],
[
"IsPolynomialFunction",
"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction"
]
]
},
{
"rank": 30,
"comment": "=: method for two s.v. gen. mappings that respect add. and add. inv.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
]
]
},
{
"rank": 30,
"comment": "=: method for two s.v. gen. mappings that respect mult. and inv.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
]
]
},
{
"rank": 29,
"comment": "=: for float and rational",
"filters": [
[
"IsFloat"
],
[
"IsRat"
]
],
"aka": [
"COMPARE_FLOAT_ANY"
]
},
{
"rank": 29,
"comment": "=: for rational and float",
"filters": [
[
"IsRat"
],
[
"IsFloat"
]
]
},
{
"rank": 29,
"comment": "=: IsEndoMapping, IsTransformationRepOfEndo",
"filters": [
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
],
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
]
]
},
{
"rank": 29,
"comment": "=: IsTransformationRepOfEndo, IsEndoMapping",
"filters": [
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
],
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 28,
"comment": "=",
"filters": [
[
"IsPadicExtensionNumber"
],
[
"IsPadicExtensionNumber"
]
]
},
{
"rank": 28,
"comment": "=",
"filters": [
[
"IsPurePadicNumber"
],
[
"IsPurePadicNumber"
]
]
},
{
"rank": 28,
"comment": "=: 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 additive group and additive coset",
"filters": [
[
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
],
[
"IsAdditiveCoset"
]
]
},
{
"rank": 28,
"comment": "=: for additive coset and additive group",
"filters": [
[
"IsAdditiveCoset"
],
[
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
]
]
},
{
"rank": 26,
"comment": "=: classes for perm group",
"filters": [
[
"IsConjugacyClassPermGroupRep"
],
[
"IsConjugacyClassPermGroupRep"
]
]
},
{
"rank": 26,
"comment": "=: compare source generator images",
"filters": [
[
"IsGeneralMapping",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
],
[
"IsGeneralMapping",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
]
]
},
{
"rank": 26,
"comment": "=: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
"filters": [
[
"IsZmodnZepsObj",
"IsZmodnZepsRep"
],
[
"IsZmodnZepsObj",
"IsZmodnZepsRep"
]
]
},
{
"rank": 26,
"comment": "=: rational functions",
"filters": [
[
"IsRationalFunction"
],
[
"IsRationalFunction"
]
]
},
{
"rank": 26,
"comment": "=: for s. c. ring elements in dense vector rep.",
"filters": [
[
"IsSCRingObj",
"IsDenseCoeffVectorRep"
],
[
"IsSCRingObj",
"IsDenseCoeffVectorRep"
]
]
},
{
"rank": 26,
"comment": "=: for two UEALattice elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsUEALatticeElement"
],
[
"IsPackedElementDefaultRep",
"IsUEALatticeElement"
]
]
},
{
"rank": 26,
"comment": "=: for s. c. algebra elements in dense vector rep.",
"filters": [
[
"IsSCAlgebraObj",
"IsDenseCoeffVectorRep"
],
[
"IsSCAlgebraObj",
"IsDenseCoeffVectorRep"
]
]
},
{
"rank": 26,
"comment": "=: method for two s.v. gen. mappings that respect add. and zero",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition",
"RespectsZero",
"HasRespectsZero"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition",
"RespectsZero",
"HasRespectsZero"
]
]
},
{
"rank": 26,
"comment": "=: method for two s.v. gen. mappings that respect mult. and one",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsOne",
"HasRespectsOne"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsOne",
"HasRespectsOne"
]
]
},
{
"rank": 25,
"comment": "=: for floats",
"filters": [
[
"IsFloat"
],
[
"IsFloat"
]
]
},
{
"rank": 25,
"comment": "=: FElm=BFElm",
"filters": [
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
],
[
"IsAlgBFRep"
]
]
},
{
"rank": 25,
"comment": "=: BFElm=FElm",
"filters": [
[
"IsAlgBFRep"
],
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
]
]
},
{
"rank": 25,
"comment": "=: FElm=AlgElm",
"filters": [
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
],
[
"IsKroneckerConstRep"
]
]
},
{
"rank": 25,
"comment": "=: AlgElm=FElm",
"filters": [
[
"IsKroneckerConstRep"
],
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
]
]
},
{
"rank": 24,
"comment": "=",
"filters": [
[
"IsRationalClassPermGroupRep"
],
[
"IsRationalClassPermGroupRep"
]
]
},
{
"rank": 24,
"comment": "=: xorbs with canonicalRepresentativeDeterminator",
"filters": [
[
"IsExternalOrbit",
"CanEasilyDetermineCanonicalRepresentativeExternalSet",
"HasCanEasilyDetermineCanonicalRepresentativeExternalSet"
],
[
"IsExternalOrbit",
"CanEasilyDetermineCanonicalRepresentativeExternalSet",
"HasCanEasilyDetermineCanonicalRepresentativeExternalSet"
]
]
},
{
"rank": 24,
"comment": "=: xorbs which know their size",
"filters": [
[
"HasSize",
"IsExternalOrbit"
],
[
"HasSize",
"IsExternalOrbit"
]
]
},
{
"rank": 24,
"comment": "=: for two additive cosets",
"filters": [
[
"IsAdditiveCoset"
],
[
"IsAdditiveCoset"
]
]
},
{
"rank": 24,
"comment": "=: for binary relss over [1..n] with images list",
"filters": [
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
],
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
]
]
},
{
"rank": 22,
"comment": "=",
"filters": [
[
"IsConjugacyClassSubgroupsRep"
],
[
"IsConjugacyClassSubgroupsRep"
]
]
},
{
"rank": 22,
"comment": "=",
"filters": [
[
"IsRationalClassGroupRep"
],
[
"IsRationalClassGroupRep"
]
]
},
{
"rank": 22,
"comment": "=: for two plist vectors",
"filters": [
[
"IsPlistVectorRep"
],
[
"IsPlistVectorRep"
]
]
},
{
"rank": 22,
"comment": "=: for two weight rep elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsWeightRepElement"
],
[
"IsPackedElementDefaultRep",
"IsWeightRepElement"
]
]
},
{
"rank": 22,
"comment": "=: for two cochains",
"filters": [
[
"IsPackedElementDefaultRep",
"IsCochain"
],
[
"IsPackedElementDefaultRep",
"IsCochain"
]
]
},
{
"rank": 22,
"comment": "=: for direct sum elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsDirectSumElement"
],
[
"IsPackedElementDefaultRep",
"IsDirectSumElement"
]
]
},
{
"rank": 22,
"comment": "=: for sparse rowspace elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsSparseRowSpaceElement"
],
[
"IsPackedElementDefaultRep",
"IsSparseRowSpaceElement"
]
]
},
{
"rank": 22,
"comment": "=: for two algebra module elements in packed representation",
"filters": [
[
"IsPackedElementDefaultRep",
"IsAlgebraModuleElement"
],
[
"IsPackedElementDefaultRep",
"IsAlgebraModuleElement"
]
]
},
{
"rank": 22,
"comment": "=: for s. c. algebra elements",
"filters": [
[
"IsSCAlgebraObj"
],
[
"IsSCAlgebraObj"
]
]
},
{
"rank": 22,
"comment": "=: for two normalized f.p. algebra elements",
"filters": [
[
"IsElementOfFpAlgebra",
"IsNormalForm",
"HasIsNormalForm"
],
[
"IsElementOfFpAlgebra",
"IsNormalForm",
"HasIsNormalForm"
]
]
},
{
"rank": 22,
"comment": "=: for two free magma ring elements",
"filters": [
[
"IsElementOfMagmaRingModuloRelations"
],
[
"IsElementOfMagmaRingModuloRelations"
]
]
},
{
"rank": 22,
"comment": "=: method for two s.v. gen. mappings that respect add.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsAddition",
"HasRespectsAddition"
]
]
},
{
"rank": 22,
"comment": "=: method for two s.v. gen. mappings that respect mult.",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication"
]
]
},
{
"rank": 20,
"comment": "=: xorbs",
"filters": [
[
"IsExternalOrbit"
],
[
"IsExternalOrbit"
]
]
},
{
"rank": 20,
"comment": "=: for monomial elements",
"filters": [
[
"IsMonomialElement",
"IsMonomialElementRep"
],
[
"IsMonomialElement",
"IsMonomialElementRep"
]
]
},
{
"rank": 18,
"comment": "=: for two residue class unions in different rep. (ResClasses)",
"filters": [
[
"IsResidueClassUnion",
"IsResidueClassUnionClassListRep"
],
[
"IsResidueClassUnion",
"IsResidueClassUnionResidueListRep"
]
]
},
{
"rank": 18,
"comment": "=: for two residue class unions in different rep. (ResClasses)",
"filters": [
[
"IsResidueClassUnion",
"IsResidueClassUnionResidueListRep"
],
[
"IsResidueClassUnion",
"IsResidueClassUnionClassListRep"
]
]
},
{
"rank": 18,
"comment": "=: for two residue class unions in sparse rep. (ResClasses)",
"filters": [
[
"IsResidueClassUnion",
"IsResidueClassUnionClassListRep"
],
[
"IsResidueClassUnion",
"IsResidueClassUnionClassListRep"
]
]
},
{
"rank": 18,
"comment": "=: for two residue class unions in standard rep. (ResClasses)",
"filters": [
[
"IsResidueClassUnion",
"IsResidueClassUnionResidueListRep"
],
[
"IsResidueClassUnion",
"IsResidueClassUnionResidueListRep"
]
]
},
{
"rank": 18,
"comment": "=: for two f.p. algebra elements (try nice monomorphism)",
"filters": [
[
"IsElementOfFpAlgebra"
],
[
"IsElementOfFpAlgebra"
]
]
},
{
"rank": 18,
"comment": "=: method for two s.v. gen. mappings",
"filters": [
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued"
],
[
"IsGeneralMapping",
"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 16,
"comment": "=: for fp monoid elts produced by the Froidure-Pin algorithm",
"filters": [
[
"IsFpMonoidReducedElt",
"HasIsFpMonoidReducedElt"
],
[
"IsFpMonoidReducedElt",
"HasIsFpMonoidReducedElt"
]
]
},
{
"rank": 16,
"comment": "=: DoubleCosets",
"filters": [
[
"IsDoubleCoset"
],
[
"IsDoubleCoset"
]
]
},
{
"rank": 16,
"comment": "=: for two inf. bits assoc. words",
"filters": [
[
"IsInfBitsAssocWord"
],
[
"IsInfBitsAssocWord"
]
],
"aka": [
"InfBits_Equal"
]
},
{
"rank": 16,
"comment": "=: for two 32 bits assoc. words",
"filters": [
[
"Is32BitsAssocWord"
],
[
"Is32BitsAssocWord"
]
]
},
{
"rank": 16,
"comment": "=: for two 16 bits assoc. words",
"filters": [
[
"Is16BitsAssocWord"
],
[
"Is16BitsAssocWord"
]
]
},
{
"rank": 16,
"comment": "=: for two 8 bits assoc. words",
"filters": [
[
"Is8BitsAssocWord"
],
[
"Is8BitsAssocWord"
]
]
},
{
"rank": 14,
"comment": "=",
"filters": [
[
"IsUnicodeString"
],
[
"IsUnicodeString"
]
]
},
{
"rank": 14,
"comment": "=: for fp semigp elts produced by the Froidure-Pin algorithm",
"filters": [
[
"IsFpSemigpReducedElt",
"HasIsFpSemigpReducedElt"
],
[
"IsFpSemigpReducedElt",
"HasIsFpSemigpReducedElt"
]
]
},
{
"rank": 14,
"comment": "=: for Green's classes",
"filters": [
[
"IsGreensClass"
],
[
"IsGreensClass"
]
]
},
{
"rank": 14,
"comment": "=: for two f.p. group elements",
"filters": [
[
"IsElementOfFpGroup"
],
[
"IsElementOfFpGroup"
]
]
},
{
"rank": 14,
"comment": "=: wreath elements",
"filters": [
[
"IsWreathProductElement"
],
[
"IsWreathProductElement"
]
]
},
{
"rank": 14,
"comment": "=: for two elements of magma by mult. table",
"filters": [
[
"IsMagmaByMultiplicationTableObj"
],
[
"IsMagmaByMultiplicationTableObj"
]
]
},
{
"rank": 14,
"comment": "=: for two elements of a magma with zero adjoined",
"filters": [
[
"IsMagmaWithZeroAdjoinedElementRep"
],
[
"IsMagmaWithZeroAdjoinedElementRep"
]
]
},
{
"rank": 14,
"comment": "=: for two general mappings",
"filters": [
[
"IsGeneralMapping"
],
[
"IsGeneralMapping"
]
]
},
{
"rank": 12,
"comment": "=: for two unions of residue classes with fixed rep's (ResClasses)",
"filters": [
[
"IsUnionOfResidueClassesWithFixedRepresentatives"
],
[
"IsUnionOfResidueClassesWithFixedRepresentatives"
]
]
},
{
"rank": 12,
"comment": "=: for pcp elements",
"filters": [
[
"IsPcpElement"
],
[
"IsPcpElement"
]
]
},
{
"rank": 12,
"comment": "=",
"filters": [
[
"IsMonoidByAdjoiningIdentityElt"
],
[
"IsMonoidByAdjoiningIdentityElt"
]
]
},
{
"rank": 12,
"comment": "=: for two elements of a f.p. monoid",
"filters": [
[
"IsElementOfFpMonoid"
],
[
"IsElementOfFpMonoid"
]
]
},
{
"rank": 12,
"comment": "=",
"filters": [
[
"IsMultiplicativeElementWithInverseByRws"
],
[
"IsMultiplicativeElementWithInverseByRws"
]
]
},
{
"rank": 12,
"comment": "=: assoc words in letter rep",
"filters": [
[
"IsAssociativeElement",
"IsWord",
"IsLetterAssocWordRep"
],
[
"IsAssociativeElement",
"IsWord",
"IsLetterAssocWordRep"
]
]
},
{
"rank": 12,
"comment": "=: for two equivalence classes",
"filters": [
[
"IsEquivalenceClass"
],
[
"IsEquivalenceClass"
]
]
},
{
"rank": 12,
"comment": "=: for two small lists",
"filters": [
[
"IsList",
"IsSmallList",
"HasIsSmallList"
],
[
"IsList",
"IsSmallList",
"HasIsSmallList"
]
],
"aka": [
"EQ_LIST_LIST_DEFAULT"
]
},
{
"rank": 10,
"comment": "=: for elements of a Rees 0-matrix semigroup",
"filters": [
[
"IsReesZeroMatrixSemigroupElement"
],
[
"IsReesZeroMatrixSemigroupElement"
]
]
},
{
"rank": 10,
"comment": "=: for elements of a Rees matrix semigroup",
"filters": [
[
"IsReesMatrixSemigroupElement"
],
[
"IsReesMatrixSemigroupElement"
]
]
},
{
"rank": 10,
"comment": "=: for two Knuth-Bendix rewriting systems",
"filters": [
[
"IsKnuthBendixRewritingSystem",
"IsKnuthBendixRewritingSystemRep"
],
[
"IsKnuthBendixRewritingSystem",
"IsKnuthBendixRewritingSystemRep"
]
]
},
{
"rank": 10,
"comment": "=: for two elements of a f.p. semigroup",
"filters": [
[
"IsElementOfFpSemigroup"
],
[
"IsElementOfFpSemigroup"
]
]
},
{
"rank": 10,
"comment": "=: for two domains",
"filters": [
[
"IsCollection",
"IsGeneralizedDomain"
],
[
"IsCollection",
"IsGeneralizedDomain"
]
]
},
{
"rank": 10,
"comment": "=: for a domain and a list",
"filters": [
[
"IsCollection",
"IsGeneralizedDomain"
],
[
"IsList",
"IsCollection"
]
]
},
{
"rank": 10,
"comment": "=: for a list and a domain",
"filters": [
[
"IsList",
"IsCollection"
],
[
"IsCollection",
"IsGeneralizedDomain"
]
]
},
{
"rank": 10,
"comment": "=: wrapped additive elements",
"filters": [
[
"IsAdditiveElementAsMultiplicativeElementRep"
],
[
"IsAdditiveElementAsMultiplicativeElementRep"
]
]
},
{
"rank": 9,
"comment": "=: for a list of elements and an infinite domain (ResClasses)",
"filters": [
[
"IsList",
"IsFinite",
"HasIsFinite"
],
[
"IsCollection",
"IsGeneralizedDomain"
]
]
},
{
"rank": 9,
"comment": "=: for an infinite domain and a list of elements (ResClasses)",
"filters": [
[
"IsCollection",
"IsGeneralizedDomain"
],
[
"IsList",
"IsFinite",
"HasIsFinite"
]
]
},
{
"rank": 8,
"comment": "=: for two words",
"filters": [
[
"IsWord"
],
[
"IsWord"
]
]
},
{
"rank": 8,
"comment": "=: for two finite lists (not necessarily small)",
"filters": [
[
"IsList",
"IsFinite",
"HasIsFinite"
],
[
"IsList",
"IsFinite",
"HasIsFinite"
]
]
},
{
"rank": 6,
"comment": "=: for omrec and omrec",
"filters": [
[
"MitM_OMRecRep"
],
[
"MitM_OMRecRep"
]
]
},
{
"rank": 6,
"comment": "=: for two lists with length - last resort",
"filters": [
[
"IsList",
"HasLENGTH"
],
[
"IsList",
"HasLENGTH"
]
]
},
{
"rank": 6,
"comment": "=: for two info classes",
"filters": [
[
"IsInfoClassListRep"
],
[
"IsInfoClassListRep"
]
]
},
{
"rank": 4,
"comment": "=: for classes",
"filters": [
[
"IsClass"
],
[
"IsClass"
]
]
},
{
"rank": 4,
"comment": "=: for two IO_Results",
"filters": [
[
"IO_Result"
],
[
"IO_Result"
]
]
},
{
"rank": 4,
"comment": "=: for two lists - last resort",
"filters": [
[
"IsList"
],
[
"IsList"
]
]
},
{
"rank": 2,
"comment": "=: for two IsFile objects",
"filters": [
[
"IsFile"
],
[
"IsFile"
]
]
},
{
"rank": 2,
"comment": "=: for another object and an IO_Result",
"filters": [
[],
[
"IO_Result"
]
]
},
{
"rank": 2,
"comment": "=: for an IO_Result and another object",
"filters": [
[
"IO_Result"
],
[]
]
},
{
"rank": 2,
"comment": "=: for two directories",
"filters": [
[
"IsDirectory"
],
[
"IsDirectory"
]
]
},
{
"rank": 2,
"comment": "=: for two families: delegate to `IsIdenticalObj'",
"filters": [
[
"IsFamily"
],
[
"IsFamily"
]
],
"aka": [
"IS_IDENTICAL_OBJ",
"IsIdenticalObj"
]
},
{
"rank": 0,
"comment": "=: fallback method to test conditions",
"filters": [
[
"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
],
[
"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 0,
"comment": "=: for two objects in different families",
"filters": [
[],
[]
]
}
],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"=",
"EQ"
]
},
{
"name": "<",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/object.gd",
"line": 150
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 222,
"comment": "<: for 32 bits pc word rep",
"filters": [
[
"IsMultiplicativeElementWithInverseByPolycyclicCollector",
"Is32BitsPcWordRep"
],
[
"IsMultiplicativeElementWithInverseByPolycyclicCollector",
"Is32BitsPcWordRep"
]
],
"aka": [
"32Bits_Less"
]
},
{
"rank": 222,
"comment": "<: for 16 bits pc word rep",
"filters": [
[
"IsMultiplicativeElementWithInverseByPolycyclicCollector",
"Is16BitsPcWordRep"
],
[
"IsMultiplicativeElementWithInverseByPolycyclicCollector",
"Is16BitsPcWordRep"
]
],
"aka": [
"16Bits_Less"
]
},
{
"rank": 222,
"comment": "<: method for 8 bits pc word rep",
"filters": [
[
"IsMultiplicativeElementWithInverseByPolycyclicCollector",
"Is8BitsPcWordRep"
],
[
"IsMultiplicativeElementWithInverseByPolycyclicCollector",
"Is8BitsPcWordRep"
]
],
"aka": [
"8Bits_Less"
]
},
{
"rank": 220,
"comment": "<: straight line program perms",
"filters": [
[
"IsPerm",
"IsStraightLineProgElm"
],
[
"IsPerm",
"IsStraightLineProgElm"
]
]
},
{
"rank": 214,
"comment": "<: two objects with memory",
"filters": [
[
"IsObjWithMemory"
],
[
"IsObjWithMemory"
]
]
},
{
"rank": 140,
"comment": "<: RightCosets of perm group",
"filters": [
[
"CategoryCollections(IsPerm)",
"IsRightCoset"
],
[
"CategoryCollections(IsPerm)",
"IsRightCoset"
]
]
},
{
"rank": 132,
"comment": "<: cgs comparison",
"filters": [
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
],
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"
]
]
},
{
"rank": 120,
"comment": "<: for two abelian number fields",
"filters": [
[
"IsAbelianNumberField",
"HasIsAbelianNumberField"
],
[
"IsAbelianNumberField",
"HasIsAbelianNumberField"
]
]
},
{
"rank": 116,
"comment": "<: for two inf. bits assoc. words",
"filters": [
[
"IsInfBitsAssocWord"
],
[
"IsInfBitsAssocWord"
]
],
"aka": [
"InfBits_Less"
]
},
{
"rank": 110,
"comment": "<: x with objects with memory",
"filters": [
[
"IsObjWithMemory"
],
[
"IsMultiplicativeElement"
]
]
},
{
"rank": 110,
"comment": "<: objects with memory with x",
"filters": [
[
"IsObjWithMemory"
],
[
"IsMultiplicativeElement"
]
]
},
{
"rank": 110,
"comment": "<: x with straight line program element",
"filters": [
[
"IsMultiplicativeElement"
],
[
"IsStraightLineProgElm"
]
]
},
{
"rank": 110,
"comment": "<: straight line program element with x",
"filters": [
[
"IsStraightLineProgElm"
],
[
"IsMultiplicativeElement"
]
]
},
{
"rank": 108,
"comment": "<: for two compressed 8 bit matrices",
"filters": [
[
"IsTable",
"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
"CategoryCollections(CategoryCollections(IsAdditiveElement))",
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
"CategoryCollections(CategoryCollections(IsFFE))",
"Is8BitMatrixRep"
],
[
"IsTable",
"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
"CategoryCollections(CategoryCollections(IsAdditiveElement))",
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
"CategoryCollections(CategoryCollections(IsFFE))",
"Is8BitMatrixRep"
]
],
"aka": [
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]
},
{
"rank": 90,
"comment": "<: for GF2 matrix and GF2 matrix",
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[
"IsTable",
"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
"CategoryCollections(CategoryCollections(IsAdditiveElement))",
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
"IsListDefault",
"IsGF2MatrixRep"
],
[
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"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
"CategoryCollections(CategoryCollections(IsAdditiveElement))",
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
"IsListDefault",
"IsGF2MatrixRep"
]
],
"aka": [
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]
},
{
"rank": 70,
"comment": "<: groups by smallest generating sets",
"filters": [
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
],
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 62,
"comment": "<: for two class functions",
"filters": [
[
"IsClassFunction"
],
[
"IsClassFunction"
]
]
},
{
"rank": 52,
"comment": "<: for two ANF automorphisms",
"filters": [
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
],
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
]
]
},
{
"rank": 52,
"comment": "<: for two Frobenius automorphisms",
"filters": [
[
"IsFrobeniusAutomorphism"
],
[
"IsFrobeniusAutomorphism"
]
]
},
{
"rank": 48,
"comment": "<: For 2 8 bit vectors",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
]
],
"aka": [
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]
},
{
"rank": 46,
"comment": "<: for two free left modules",
"filters": [
[
"IsFreeLeftModule"
],
[
"IsFreeLeftModule"
]
]
},
{
"rank": 44,
"comment": "<: for nilpotent Lie algebra automorphisms",
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[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsNilpotentLieAutomorphismRep"
],
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsNilpotentLieAutomorphismRep"
]
]
},
{
"rank": 43,
"comment": "<: for ANF automorphism and identity mapping",
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[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
],
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 43,
"comment": "<: for identity mapping and ANF automorphism",
"filters": [
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
],
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
]
]
},
{
"rank": 43,
"comment": "<: for a Frobenius automorphism, and an identity mapping",
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"IsFrobeniusAutomorphism"
],
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 43,
"comment": "<: for an identity mapping, and a Frobenius automorphism",
"filters": [
[
"IsOne",
"HasIsOne",
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
],
[
"IsFrobeniusAutomorphism"
]
]
},
{
"rank": 42,
"comment": "<: for GF2 vectors",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
]
],
"aka": [
"LT_GF2VEC_GF2VEC"
]
},
{
"rank": 42,
"comment": "<: for transformation semigroups",
"filters": [
[
"CategoryCollections(IsTransformation)",
"IsMagma",
"IsAssociative",
"HasIsAssociative"
],
[
"CategoryCollections(IsTransformation)",
"IsMagma",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 40,
"comment": "<: for two underlying relations of general mappings",
"filters": [
[
"IsCollection",
"IsGeneralizedDomain",
"CategoryCollections(IsDirectProductElement)",
"HasUnderlyingGeneralMapping"
],
[
"IsCollection",
"IsGeneralizedDomain",
"CategoryCollections(IsDirectProductElement)",
"HasUnderlyingGeneralMapping"
]
]
},
{
"rank": 38,
"comment": "<: for two elements in Z/pZ (ModulusRep, small)",
"filters": [
[
"IsFFE",
"IsLogOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
],
[
"IsFFE",
"IsLogOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
]
]
},
{
"rank": 38,
"comment": "<: for two elements in Z/pZ (ModulusRep, large)",
"filters": [
[
"IsFFE",
"IsLexOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
],
[
"IsFFE",
"IsLexOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
]
]
},
{
"rank": 38,
"comment": "<: for two direct product elements",
"filters": [
[
"IsDirectProductElement"
],
[
"IsDirectProductElement"
]
]
},
{
"rank": 36,
"comment": "<",
"filters": [
[
"IsLexOrderedFFE",
"IsCoeffsModConwayPolRep"
],
[
"IsLexOrderedFFE",
"IsCoeffsModConwayPolRep"
]
]
},
{
"rank": 36,
"comment": "<: for internal FFE and element in Z/pZ (ModulusRep)",
"filters": [
[
"IsFFE",
"IsInternalRep"
],
[
"IsFFE",
"IsLogOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
]
]
},
{
"rank": 36,
"comment": "<: for element in Z/pZ (ModulusRep) and internal FFE",
"filters": [
[
"IsFFE",
"IsLogOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
],
[
"IsFFE",
"IsInternalRep"
]
]
},
{
"rank": 36,
"comment": "<: for two unknowns in default representation",
"filters": [
[
"IsUnknown",
"IsUnknownDefaultRep"
],
[
"IsUnknown",
"IsUnknownDefaultRep"
]
]
},
{
"rank": 34,
"comment": "<: group homomorphisms: Images of smallest generators",
"filters": [
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
],
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
]
]
},
{
"rank": 34,
"comment": "<: for two elements in Z/nZ (ModulusRep, nonprime)",
"filters": [
[
"IsZmodnZObjNonprime",
"IsModulusRep"
],
[
"IsZmodnZObjNonprime",
"IsModulusRep"
]
]
},
{
"rank": 34,
"comment": "<: BFElm<BFElm",
"filters": [
[
"IsAlgBFRep"
],
[
"IsAlgBFRep"
]
]
},
{
"rank": 34,
"comment": "<: BFElm<AlgElm",
"filters": [
[
"IsAlgBFRep"
],
[
"IsKroneckerConstRep"
]
]
},
{
"rank": 34,
"comment": "<: AlgElm<BFElm",
"filters": [
[
"IsKroneckerConstRep"
],
[
"IsAlgBFRep"
]
]
},
{
"rank": 34,
"comment": "<: AlgElm<AlgElm",
"filters": [
[
"IsKroneckerConstRep"
],
[
"IsKroneckerConstRep"
]
]
},
{
"rank": 34,
"comment": "<: Univariate Polynomials",
"filters": [
[
"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
],
[
"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
]
]
},
{
"rank": 33,
"comment": "<: for a module and a residue class union (ResClasses)",
"filters": [
[
"IsRowModule",
"HasIsRowModule"
],
[
"IsResidueClassUnion"
]
],
"aka": [
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"IsShared",
"RETURN_TRUE",
"ReturnTrue"
]
},
{
"rank": 33,
"comment": "<: for a residue class union and a module (ResClasses)",
"filters": [
[
"IsResidueClassUnion"
],
[
"IsRowModule",
"HasIsRowModule"
]
]
},
{
"rank": 33,
"comment": "<: for a list and a class function",
"filters": [
[
"IsClassFunction"
],
[
"IsList"
]
]
},
{
"rank": 33,
"comment": "<: for a class function and a list",
"filters": [
[
"IsClassFunction"
],
[
"IsList"
]
]
},
{
"rank": 32,
"comment": "<: for a ring and a residue class union (ResClasses)",
"filters": [
[
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
],
[
"IsResidueClassUnion"
]
]
},
{
"rank": 32,
"comment": "<: for a residue class union and a ring (ResClasses)",
"filters": [
[
"IsResidueClassUnion"
],
[
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
]
]
},
{
"rank": 32,
"comment": "<: IsTransformationRepOfEndo, IsTransformationRepOfEndo",
"filters": [
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
],
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
]
]
},
{
"rank": 32,
"comment": "<: for cyclotomic and unknown",
"filters": [
[
"IsCyc"
],
[
"IsUnknown"
]
]
},
{
"rank": 32,
"comment": "<: for unknown and cyclotomic",
"filters": [
[
"IsUnknown"
],
[
"IsCyc"
]
]
},
{
"rank": 31,
"comment": "<: for `-infinity' and cyclotomic",
"filters": [
[
"IsNegInfinity"
],
[
"IsCyclotomic"
]
]
},
{
"rank": 31,
"comment": "<: for cyclotomic and `-infinity'",
"filters": [
[
"IsCyclotomic"
],
[
"IsNegInfinity"
]
]
},
{
"rank": 31,
"comment": "<: for `infinity' and cyclotomic",
"filters": [
[
"IsInfinity"
],
[
"IsCyclotomic"
]
]
},
{
"rank": 31,
"comment": "<: for cyclotomic and `infinity'",
"filters": [
[
"IsCyclotomic"
],
[
"IsInfinity"
]
]
},
{
"rank": 30,
"comment": "<: for two plist matrices",
"filters": [
[
"IsPlistMatrixRep"
],
[
"IsPlistMatrixRep"
]
]
},
{
"rank": 30,
"comment": "<: for two finite field elements in different characteristic",
"filters": [
[
"IsFFE"
],
[
"IsFFE"
]
]
},
{
"rank": 30,
"comment": "<: for a finite field element, and a cyclotomic",
"filters": [
[
"IsFFE"
],
[
"IsCyclotomic"
]
]
},
{
"rank": 30,
"comment": "<: for a cyclotomic, and a finite field element",
"filters": [
[
"IsCyclotomic"
],
[
"IsFFE"
]
]
},
{
"rank": 29,
"comment": "<: for a module and a list of elements (ResClasses)",
"filters": [
[
"IsRowModule",
"HasIsRowModule"
],
[
"IsList"
]
]
},
{
"rank": 29,
"comment": "<: for a list of elements and a module (ResClasses)",
"filters": [
[
"IsList"
],
[
"IsRowModule",
"HasIsRowModule"
]
]
},
{
"rank": 29,
"comment": "<: for float and rational",
"filters": [
[
"IsFloat"
],
[
"IsRat"
]
]
},
{
"rank": 29,
"comment": "<: for rational and float",
"filters": [
[
"IsRat"
],
[
"IsFloat"
]
]
},
{
"rank": 29,
"comment": "<: IsTransformationRepOfEndo, IsEndoMapping",
"filters": [
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
],
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 29,
"comment": "<: IsEndoMapping, IsTransformationRepOfEndo",
"filters": [
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
],
[
"IsGeneralMapping",
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsTransformationRepOfEndo"
]
]
},
{
"rank": 28,
"comment": "<: for a ring and a list of elements (ResClasses)",
"filters": [
[
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
],
[
"IsList"
]
]
},
{
"rank": 28,
"comment": "<: for a list of elements and a ring (ResClasses)",
"filters": [
[
"IsList"
],
[
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
]
]
},
{
"rank": 28,
"comment": "<",
"filters": [
[
"IsPadicExtensionNumber"
],
[
"IsPadicExtensionNumber"
]
]
},
{
"rank": 28,
"comment": "<",
"filters": [
[
"IsPurePadicNumber"
],
[
"IsPurePadicNumber"
]
]
},
{
"rank": 28,
"comment": "<: for two Lie objects in default representation",
"filters": [
[
"IsPackedElementDefaultRep",
"IsLieObject"
],
[
"IsPackedElementDefaultRep",
"IsLieObject"
]
]
},
{
"rank": 26,
"comment": "<: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
"filters": [
[
"IsZmodnZepsObj",
"IsZmodnZepsRep"
],
[
"IsZmodnZepsObj",
"IsZmodnZepsRep"
]
]
},
{
"rank": 26,
"comment": "<: for s. c. ring elements in dense vector rep.",
"filters": [
[
"IsSCRingObj",
"IsDenseCoeffVectorRep"
],
[
"IsSCRingObj",
"IsDenseCoeffVectorRep"
]
]
},
{
"rank": 26,
"comment": "<: for two UEALattice elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsUEALatticeElement"
],
[
"IsPackedElementDefaultRep",
"IsUEALatticeElement"
]
]
},
{
"rank": 26,
"comment": "<: for s. c. algebra elements in dense vector rep.",
"filters": [
[
"IsSCAlgebraObj",
"IsDenseCoeffVectorRep"
],
[
"IsSCAlgebraObj",
"IsDenseCoeffVectorRep"
]
]
},
{
"rank": 25,
"comment": "<: for floats",
"filters": [
[
"IsFloat"
],
[
"IsFloat"
]
]
},
{
"rank": 25,
"comment": "<: FElm<BFElm",
"filters": [
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
],
[
"IsAlgBFRep"
]
]
},
{
"rank": 25,
"comment": "<: BFElm<FElm",
"filters": [
[
"IsAlgBFRep"
],
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
]
]
},
{
"rank": 25,
"comment": "<: FElm<AlgElm",
"filters": [
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
],
[
"IsKroneckerConstRep"
]
]
},
{
"rank": 25,
"comment": "<: AlgElm<FElm",
"filters": [
[
"IsKroneckerConstRep"
],
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
]
]
},
{
"rank": 24,
"comment": "<: rational functions",
"filters": [
[
"IsPolynomialFunction"
],
[
"IsPolynomialFunction"
]
],
"aka": [
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]
},
{
"rank": 24,
"comment": "<: for binary rels over [1..n] with images list",
"filters": [
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
],
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
]
]
},
{
"rank": 23,
"comment": "<: for a permutation, and a finite field element",
"filters": [
[
"IsPerm"
],
[
"IsFFE"
]
]
},
{
"rank": 23,
"comment": "<: for a permutation, and a cyclotomic",
"filters": [
[
"IsPerm"
],
[
"IsCyclotomic"
]
]
},
{
"rank": 23,
"comment": "<: for a finite field element, and a permutation",
"filters": [
[
"IsFFE"
],
[
"IsPerm"
]
]
},
{
"rank": 23,
"comment": "<: for a cyclotomic, and a permutation",
"filters": [
[
"IsCyclotomic"
],
[
"IsPerm"
]
]
},
{
"rank": 22,
"comment": "<: for a transformation and finite field element",
"filters": [
[
"IsTransformation"
],
[
"IsFFE"
]
]
},
{
"rank": 22,
"comment": "<: for a finite field element and transformation",
"filters": [
[
"IsFFE"
],
[
"IsTransformation"
]
]
},
{
"rank": 22,
"comment": "<: for a cyclotomic and transformation",
"filters": [
[
"IsCyclotomic"
],
[
"IsTransformation"
]
]
},
{
"rank": 22,
"comment": "<: for a transformation and cyclotomic",
"filters": [
[
"IsTransformation"
],
[
"IsCyclotomic"
]
]
},
{
"rank": 22,
"comment": "<: for two plist vectors",
"filters": [
[
"IsPlistVectorRep"
],
[
"IsPlistVectorRep"
]
]
},
{
"rank": 22,
"comment": "<: for two weight rep elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsWeightRepElement"
],
[
"IsPackedElementDefaultRep",
"IsWeightRepElement"
]
]
},
{
"rank": 22,
"comment": "<: for two cochains",
"filters": [
[
"IsPackedElementDefaultRep",
"IsCochain"
],
[
"IsPackedElementDefaultRep",
"IsCochain"
]
]
},
{
"rank": 22,
"comment": "<: for direct sum elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsDirectSumElement"
],
[
"IsPackedElementDefaultRep",
"IsDirectSumElement"
]
]
},
{
"rank": 22,
"comment": "<: for sparse rowspace elements",
"filters": [
[
"IsPackedElementDefaultRep",
"IsSparseRowSpaceElement"
],
[
"IsPackedElementDefaultRep",
"IsSparseRowSpaceElement"
]
]
},
{
"rank": 22,
"comment": "<: for two algebra module elements in packed representation",
"filters": [
[
"IsPackedElementDefaultRep",
"IsAlgebraModuleElement"
],
[
"IsPackedElementDefaultRep",
"IsAlgebraModuleElement"
]
]
},
{
"rank": 22,
"comment": "<: for s. c. algebra elements",
"filters": [
[
"IsSCAlgebraObj"
],
[
"IsSCAlgebraObj"
]
]
},
{
"rank": 22,
"comment": "<: for two normalized f.p. algebra elements",
"filters": [
[
"IsElementOfFpAlgebra",
"IsNormalForm",
"HasIsNormalForm"
],
[
"IsElementOfFpAlgebra",
"IsNormalForm",
"HasIsNormalForm"
]
]
},
{
"rank": 22,
"comment": "<: for two free magma ring elements",
"filters": [
[
"IsElementOfMagmaRingModuloRelations"
],
[
"IsElementOfMagmaRingModuloRelations"
]
]
},
{
"rank": 20,
"comment": "<: xorbs, via AsSSortedList",
"filters": [
[
"IsExternalOrbit"
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]
]
},
{
"rank": 56,
"comment": "PrintObj: for a field with known generators",
"filters": [
[
"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",
"HasGeneratorsOfDivisionRing"
]
]
},
{
"rank": 55,
"comment": "PrintObj: for a field",
"filters": [
[
"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": 53,
"comment": "PrintObj: for a semigroup with known generators",
"filters": [
[
"CategoryCollections(IsPartialPerm)",
"IsMagma",
"IsMagmaWithInverses",
"HasGeneratorsOfMagma",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 50,
"comment": "PrintObj: for a pcp group",
"filters": [
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(IsPcpElement)"
]
]
},
{
"rank": 50,
"comment": "PrintObj: for a semigroup with known generators",
"filters": [
[
"CategoryCollections(IsTransformation)",
"IsMagma",
"IsMagmaWithInverses",
"HasGeneratorsOfMagma",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 48,
"comment": "PrintObj: for full matrix module",
"filters": [
[
"IsFreeLeftModule",
"IsFullMatrixModule",
"HasIsFullMatrixModule"
]
]
},
{
"rank": 48,
"comment": "PrintObj: for full row module",
"filters": [
[
"IsFreeLeftModule",
"IsFullRowModule",
"HasIsFullRowModule"
]
]
},
{
"rank": 45,
"comment": "PrintObj: for a matrix group",
"filters": [
[
"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 40,
"comment": "PrintObj: 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",
"HasGeneratorsOfLeftOperatorRing"
]
]
},
{
"rank": 39,
"comment": "PrintObj: 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": 38,
"comment": "PrintObj: for a FLMLOR-with-one with known generators",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsDistributiveLOpDSum",
"IsMagma",
"IsMagmaWithOne",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"IsFreeLeftModule",
"HasGeneratorsOfLeftOperatorRing"
]
]
},
{
"rank": 38,
"comment": "PrintObj: for an ordinary block matrix",
"filters": [
[
"IsOrdinaryMatrix",
"IsBlockMatrixRep"
]
]
},
{
"rank": 37,
"comment": "PrintObj: for an algebra with known generators",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsAssociativeLOpEProd",
"IsDistributiveLOpDSum",
"IsDistributiveLOpESum",
"IsTrivialLOpEOne",
"IsLeftActedOnByRing",
"IsLeftActedOnByDivisionRing",
"HasIsLeftActedOnByDivisionRing",
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"HasGeneratorsOfLeftOperatorRing"
]
]
},
{
"rank": 37,
"comment": "PrintObj: for a FLMLOR-with-one",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsDistributiveLOpDSum",
"IsMagma",
"IsMagmaWithOne",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"IsFreeLeftModule"
]
]
},
{
"rank": 36,
"comment": "PrintObj: for an algebra",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsAssociativeLOpEProd",
"IsDistributiveLOpDSum",
"IsDistributiveLOpESum",
"IsTrivialLOpEOne",
"IsLeftActedOnByRing",
"IsLeftActedOnByDivisionRing",
"HasIsLeftActedOnByDivisionRing",
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
]
]
},
{
"rank": 36,
"comment": "PrintObj: for a free magma ring",
"filters": [
[
"IsFreeMagmaRing"
]
]
},
{
"rank": 36,
"comment": "PrintObj: for a group with generators",
"filters": [
[
"IsMagmaWithInverses",
"HasGeneratorsOfMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 35,
"comment": "PrintObj: for a character",
"filters": [
[
"IsClassFunction",
"IsCharacter",
"HasIsCharacter"
]
]
},
{
"rank": 35,
"comment": "PrintObj: for a FLMLOR with known generators",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsDistributiveLOpDSum",
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"IsFreeLeftModule",
"HasGeneratorsOfLeftOperatorRing"
]
]
},
{
"rank": 35,
"comment": "PrintObj: for a group",
"filters": [
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 35,
"comment": "PrintObj: for null map matrix",
"filters": [
[
"IsNullMapMatrix"
]
]
},
{
"rank": 34,
"comment": "PrintObj: for a FLMLOR",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsDistributiveLOpDSum",
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"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": [
[
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]
]
},
{
"rank": 8,
"comment": "PrintObj: for a sparse rowspace element",
"filters": [
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]
]
},
{
"rank": 8,
"comment": "PrintObj: for a basis with basis vectors",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "PrintObj: for IsGroupClass and IsClassByPropertyRep",
"filters": [
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]
},
{
"rank": 7,
"comment": "PrintObj",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "PrintObj: for a Green's class",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "PrintObj: wreath elements",
"filters": [
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"IsWreathProductElement"
]
]
},
{
"rank": 7,
"comment": "PrintObj: for element of magma by mult. table",
"filters": [
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"IsMagmaByMultiplicationTableObj"
]
]
},
{
"rank": 7,
"comment": "PrintObj: for dense hash tables",
"filters": [
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"IsDenseHashRep"
]
]
},
{
"rank": 7,
"comment": "PrintObj: for a basis",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "PrintObj: for an element of a magma with zero adjoined",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "PrintObj: for a general mapping",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "PrintObj: method for a weak pointer object",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "PrintObj: for an enumerator that perhaps has its own `PrintObj' function",
"filters": [
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]
},
{
"rank": 6,
"comment": "PrintObj: for ioTCPstream",
"filters": [
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]
]
},
{
"rank": 6,
"comment": "PrintObj: for unions of residue classes with fixed rep's (ResClasses)",
"filters": [
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]
]
},
{
"rank": 6,
"comment": "PrintObj",
"filters": [
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]
]
},
{
"rank": 6,
"comment": "PrintObj: for pcp elements",
"filters": [
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]
},
{
"rank": 6,
"comment": "PrintObj",
"filters": [
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]
]
},
{
"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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]
},
{
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"comment": "PrintObj: assoc word in letter rep",
"filters": [
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]
},
{
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"comment": "PrintObj: for an eq. class",
"filters": [
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]
},
{
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"comment": "PrintObj: iostream",
"filters": [
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]
]
},
{
"rank": 5,
"comment": "PrintObj: for IsGroupClassByListRep",
"filters": [
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]
]
},
{
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"comment": "PrintObj: for IsClassByUnionRep",
"filters": [
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]
},
{
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"comment": "PrintObj: for IsClassByIntersectionRep",
"filters": [
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]
]
},
{
"rank": 5,
"comment": "PrintObj: for IsClassByComplementRep",
"filters": [
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]
]
},
{
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"comment": "PrintObj: for IsClassByPropertyRep",
"filters": [
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]
},
{
"rank": 5,
"comment": "PrintObj: for a Rees 0-matrix semigroup element",
"filters": [
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]
]
},
{
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]
},
{
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"comment": "PrintObj: for an f.p. semigroup element",
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]
},
{
"rank": 5,
"comment": "PrintObj: for a presentation in default representation",
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]
]
},
{
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"comment": "PrintObj: for an associative word",
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]
},
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"comment": "PrintObj: for a nonassociative word",
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]
},
{
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"comment": "PrintObj: wrapped additive elements",
"filters": [
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]
},
{
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]
},
{
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"comment": "PrintObj: for an infinite list of names",
"filters": [
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]
]
},
{
"rank": 4,
"comment": "PrintObj: for an enumerator",
"filters": [
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]
},
{
"rank": 3,
"comment": "PrintObj: lattice",
"filters": [
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]
]
},
{
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"comment": "PrintObj: for mutable basis with underlying mutable basis",
"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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"comment": "PrintObj",
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{
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"comment": "PrintObj: output text none",
"filters": [
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},
{
"rank": 2,
"comment": "PrintObj: output text file",
"filters": [
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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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"comment": "PrintObj: input text string",
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"comment": "PrintObj: default directory rep",
"filters": [
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},
{
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"comment": "PrintObj: for an operation",
"filters": [
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},
{
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"filters": [
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},
{
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"filters": [
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"comment": "PrintObj",
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"comment": "PrintObj: IsObjToBePrinted",
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"comment": "PrintObj",
"filters": [
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},
{
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"comment": "PrintObj: for a root system",
"filters": [
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},
{
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"comment": "PrintObj: closed stream",
"filters": [
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]
},
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]
},
{
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"comment": "PrintObj: for 'to be defined' objects",
"filters": [
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]
},
{
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"comment": "PRINT_OBJ: for a type",
"filters": [
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]
]
},
{
"rank": 1,
"comment": "PRINT_OBJ: for a family",
"filters": [
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]
},
{
"rank": 0,
"comment": "PrintObj: default method delegating to PrintString",
"filters": [
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}
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"3args": [],
"4args": [],
"5args": [],
"6args": []
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{
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"type": "Operation",
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{
"file": "/home/mtorpey/gap/lib/object.gd",
"line": 513
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{
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"line": 514
}
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"methods": {
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{
"rank": 36,
"comment": "PrintString: for a group with generators",
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]
},
{
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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",
"filters": [
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]
},
{
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"filters": [
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]
]
},
{
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"filters": [
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]
},
{
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"filters": [
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]
},
{
"rank": 19,
"comment": "PrintString: for a direct product element",
"filters": [
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]
},
{
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"comment": "PrintString: for a magma-with-inverses with generators",
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]
},
{
"rank": 16,
"comment": "PrintString: RightCoset",
"filters": [
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]
]
},
{
"rank": 16,
"comment": "PrintString: for a semigroup with known generators",
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},
{
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]
},
{
"rank": 12,
"comment": "PrintString: for a magma with generators",
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},
{
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"comment": "PrintString: for a magma",
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{
"rank": 9,
"comment": "PrintString: for right transversal",
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},
{
"rank": 8,
"comment": "PrintString: for a partial perm",
"filters": [
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]
},
{
"rank": 7,
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{
"rank": 7,
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{
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"comment": "PrintString: default method delegating to String",
"filters": [
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}
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},
{
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},
{
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{
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"comment": "Display: for partitions of Z^2 into residue class unions (ResClasses)",
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]
]
},
{
"rank": 54,
"comment": "Display: for matrix of FFEs (for larger fields)",
"filters": [
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},
{
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"comment": "Display: for matrix of FFEs",
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]
},
{
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"comment": "Display: for matrix over Integers mod n",
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]
},
{
"rank": 38,
"comment": "Display: for finitely presented groups",
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{
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"comment": "Display: for a matrix",
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{
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{
"rank": 20,
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"filters": [
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{
"rank": 15,
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{
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]
},
{
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{
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{
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"comment": "Display: for a straight line decision",
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"comment": "Display: for a black box program",
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"comment": "Display: for a straight line program",
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"comment": "Display: for a table of marks (add empty options record)",
"filters": [
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{
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"comment": "Display: generic: use DisplayString or otherwise PrintObj",
"filters": [
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}
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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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{
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},
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"comment": "Display: for a table of marks and an options record",
"filters": [
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"4args": [],
"5args": [],
"6args": []
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"line": 600
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"methods": {
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{
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"comment": "DisplayString: For large finite field elements",
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{
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"comment": "DisplayString: for an internal FFE via String",
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{
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"comment": "DisplayString: for floats",
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{
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{
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{
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"comment": "DisplayString: for a type",
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},
{
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},
{
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]
},
{
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]
},
{
"rank": 12,
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]
},
{
"rank": 11,
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]
},
{
"rank": 11,
"comment": "Size: for a conjugacy class",
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]
},
{
"rank": 11,
"comment": "Size: method for an ext. orbit by stabilizer",
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]
},
{
"rank": 10,
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"filters": [
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]
},
{
"rank": 8,
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]
]
},
{
"rank": 8,
"comment": "Size: for sparse hash tables",
"filters": [
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]
]
},
{
"rank": 7,
"comment": "Size: for Green's classes",
"filters": [
[
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]
]
},
{
"rank": 7,
"comment": "Size: for dense hash tables",
"filters": [
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]
},
{
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"comment": "Size: for a list that is a collection",
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],
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"Length"
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},
{
"rank": 5,
"comment": "Size",
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]
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{
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]
},
{
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}
],
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"3args": [],
"4args": [],
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"6args": []
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},
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{
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"line": 1199
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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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"line": 1527
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{
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"rank": 20004,
"comment": "Representative: system getter",
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]
},
{
"rank": 10018,
"comment": "Representative: for additive-magma-with-zero with known zero",
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"IsNearAdditiveMagma",
"IsNearAdditiveMagmaWithZero",
"IsAdditivelyCommutative",
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],
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"ZeroAttr",
"ZeroImmutable"
]
},
{
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[
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"IsMagmaWithOne"
]
],
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"One",
"OneAttr",
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},
{
"rank": 10014,
"comment": "Representative: for additive coset in default repres.",
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[
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"IsAdditiveCosetDefaultRep"
]
]
},
{
"rank": 62,
"comment": "Representative",
"filters": [
[
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"HasIsCyclotomicField"
]
]
},
{
"rank": 54,
"comment": "Representative: for a division ring with known generators",
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[
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"HasIsNonTrivial",
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsAssociativeLOpEProd",
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"IsDistributiveLOpESum",
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"IsLeftActedOnByRing",
"IsLeftActedOnByDivisionRing",
"HasIsLeftActedOnByDivisionRing",
"IsMagma",
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"IsAssociative",
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"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
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"IsLDistributive",
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"IsRDistributive",
"HasIsRDistributive",
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"HasGeneratorsOfDivisionRing"
]
]
},
{
"rank": 48,
"comment": "Representative: for full matrix module",
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[
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"IsFullMatrixModule",
"HasIsFullMatrixModule"
]
]
},
{
"rank": 48,
"comment": "Representative: for full row module",
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[
"IsFreeLeftModule",
"IsFullRowModule",
"HasIsFullRowModule"
]
]
},
{
"rank": 43,
"comment": "Representative: LAGUNA: for a Lie algebra coming from an associative algebra",
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[
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"IsAssociativeLOpEProd",
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"HasIsLeftActedOnByDivisionRing",
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"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"IsJacobianRing",
"HasIsJacobianRing",
"IsZeroSquaredRing",
"HasIsZeroSquaredRing",
"IsLieAlgebraByAssociativeAlgebra"
]
]
},
{
"rank": 36,
"comment": "Representative: for full hom space of linear mappings",
"filters": [
[
"CategoryCollections(IsGeneralMapping)",
"IsFreeLeftModule",
"IsFullHomModule",
"HasIsFullHomModule"
]
]
},
{
"rank": 33,
"comment": "Representative: for left operator ring-with-one with known generators",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsDistributiveLOpDSum",
"IsMagma",
"IsMagmaWithOne",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"HasGeneratorsOfLeftOperatorRingWithOne"
]
]
},
{
"rank": 30,
"comment": "Representative: for left operator ring with known generators",
"filters": [
[
"IsExtLSet",
"IsAssociativeLOpDProd",
"IsDistributiveLOpDSum",
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"HasGeneratorsOfLeftOperatorRing"
]
]
},
{
"rank": 30,
"comment": "Representative: for a ring-with-one with generators",
"filters": [
[
"IsMagma",
"IsMagmaWithOne",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"HasGeneratorsOfRingWithOne"
]
]
},
{
"rank": 27,
"comment": "Representative: for a ring with generators",
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[
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"HasGeneratorsOfRing"
]
]
},
{
"rank": 20,
"comment": "Representative: for a subsemigroup of Rees 0-matrix semigroup with generators",
"filters": [
[
"IsMagma",
"HasGeneratorsOfMagma",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(IsReesZeroMatrixSemigroupElement)"
]
]
},
{
"rank": 20,
"comment": "Representative: for a subsemigroup of Rees matrix semigroup with generators",
"filters": [
[
"IsMagma",
"HasGeneratorsOfMagma",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(IsReesMatrixSemigroupElement)"
]
]
},
{
"rank": 19,
"comment": "Representative: for right operator additive group with known generators",
"filters": [
[
"IsExtRSet",
"IsDistributiveROpDSum",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"HasGeneratorsOfRightOperatorAdditiveGroup"
]
]
},
{
"rank": 19,
"comment": "Representative: for left operator additive group with known generators",
"filters": [
[
"IsExtLSet",
"IsDistributiveLOpDSum",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"HasGeneratorsOfLeftOperatorAdditiveGroup"
]
]
},
{
"rank": 18,
"comment": "Representative: for magma-with-inverses with generators",
"filters": [
[
"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",
"filters": [
[
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"HasGeneratorsOfNearAdditiveGroup"
]
]
},
{
"rank": 15,
"comment": "Representative: for additive-magma-with-zero with stored parent",
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[
"HasParentAttr",
"IsNearAdditiveMagma",
"IsNearAdditiveMagmaWithZero",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
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]
},
{
"rank": 15,
"comment": "Representative: for additive-magma-with-zero with known generators",
"filters": [
[
"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",
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[
"IsList"
]
]
}
],
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"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
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},
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"1args": [],
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"rank": 2,
"comment": "SetRepresentative: system setter",
"filters": [
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[]
]
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{
"rank": 0,
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[]
]
}
],
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"4args": [],
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"file": "/home/mtorpey/gap/lib/coll.gd",
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"2args": [],
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{
"name": "RepresentativeSmallest",
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"file": "/home/mtorpey/gap/lib/coll.gd",
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"1args": [
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{
"rank": 20,
"comment": "RepresentativeSmallest: for an empty list",
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]
},
{
"rank": 8,
"comment": "RepresentativeSmallest: for a strictly sorted list",
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]
},
{
"rank": 5,
"comment": "RepresentativeSmallest",
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{
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},
{
"rank": 2,
"comment": "RepresentativeSmallest: for a list",
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},
{
"rank": 2,
"comment": "RepresentativeSmallest: for a collection",
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]
}
],
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"3args": [],
"4args": [],
"5args": [],
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"aka": [
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},
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"file": "/home/mtorpey/gap/lib/coll.gd",
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{
"rank": 0,
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[]
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"file": "/home/mtorpey/gap/lib/coll.gd",
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{
"name": "Random",
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"file": "/home/mtorpey/gap/lib/coll.gd",
"line": 1658
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{
"file": "/home/mtorpey/gap/lib/coll.gd",
"line": 1659
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{
"file": "/home/mtorpey/gap/lib/random.gd",
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{
"file": "/home/mtorpey/gap/lib/random.gd",
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],
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"methods": {
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{
"rank": 403,
"comment": "Random: for natural SL",
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},
{
"rank": 401,
"comment": "Random: for natural GL",
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"comment": "Random: for a group handled by nice monomorphism",
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{
"rank": 116,
"comment": "Random: for an internal list",
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{
"rank": 108,
"comment": "Random: for sparse hash tables",
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{
"rank": 107,
"comment": "Random: for dense hash tables",
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]
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{
"rank": 75,
"comment": "Random: for a natural alternating group: floyd's algorithm",
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"HasIsNaturalAlternatingGroup"
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]
},
{
"rank": 75,
"comment": "Random: for a natural symmetric group: floyd's algorithm",
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},
{
"rank": 71,
"comment": "Random: for a permutation group",
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"HasIsAssociative"
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]
},
{
"rank": 70,
"comment": "Random: for Rationals",
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"HasIsNonTrivial",
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"IsMagma",
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"HasIsAssociative",
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"IsNearAdditiveGroup",
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"HasIsLDistributive",
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"HasIsRDistributive",
"IsEuclideanRing",
"IsPrimeField",
"HasIsPrimeField"
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]
},
{
"rank": 66,
"comment": "Random: for a large non-prime finite field",
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"HasIsFinite",
"CategoryCollections(IsFFE)",
"IsExtLSet",
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"IsMagma",
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"IsAssociative",
"HasIsAssociative",
"IsCommutative",
"HasIsCommutative",
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"IsAdditivelyCommutative",
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"HasIsLDistributive",
"IsRDistributive",
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"IsEuclideanRing"
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]
},
{
"rank": 61,
"comment": "Random: for a finite prime field",
"filters": [
[
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"HasIsFinite",
"IsExtLSet",
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"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"
]
]
},
{
"rank": 56,
"comment": "Random: for an algebraic extension",
"filters": [
[
"IsAlgebraicExtension"
]
]
},
{
"rank": 55,
"comment": "Random: for a pcgs computable groups",
"filters": [
[
"IsFinite",
"HasIsFinite",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"CanEasilyComputePcgs"
]
]
},
{
"rank": 50,
"comment": "Random: for a pcp group",
"filters": [
[
"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"
]
]
},
{
"rank": 36,
"comment": "Random: for full hom space of linear mappings",
"filters": [
[
"CategoryCollections(IsGeneralMapping)",
"IsFreeLeftModule",
"IsFullHomModule",
"HasIsFullHomModule"
]
]
},
{
"rank": 24,
"comment": "Random: for a free monoid",
"filters": [
[
"IsMagmaWithOne",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
]
]
},
{
"rank": 23,
"comment": "Random: for a free left module",
"filters": [
[
"IsFreeLeftModule"
]
]
},
{
"rank": 18,
"comment": "Random: for a free semigroup",
"filters": [
[
"IsMagma",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections((IsWord and IsAssociativeElement))"
]
]
},
{
"rank": 18,
"comment": "Random: for the full collection Z/nZ(m)",
"filters": [
[
"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"
]
},
{
"rank": 5,
"comment": "Random: for p-adic extension family",
"filters": [
[
"CategoryFamily(IsPadicExtensionNumber)"
]
]
},
{
"rank": 5,
"comment": "Random: for a pure p-adic family",
"filters": [
[
"CategoryFamily(IsPurePadicNumber)"
]
]
},
{
"rank": 4,
"comment": "Random: for an infinite list of generators",
"filters": [
[
"IsList",
"IsInfiniteListOfGeneratorsRep"
]
]
},
{
"rank": 3,
"comment": "Random: for a dense (small) list",
"filters": [
[
"IsList",
"IsDenseList"
]
]
},
{
"rank": 0,
"comment": "Random: for a (finite) collection",
"filters": [
[
"IsCollection",
"IsFinite",
"HasIsFinite"
]
]
},
{
"rank": 0,
"comment": "Random: fallback method to test conditions",
"filters": [
[
"IsCollection"
]
]
}
],
"2args": [
{
"rank": 405,
"comment": "Random: for a random source and natural SL",
"filters": [
[
"IsRandomSource"
],
[
"IsFinite",
"HasIsFinite",
"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"IsNaturalSL",
"HasIsNaturalSL"
]
]
},
{
"rank": 403,
"comment": "Random: for a random source and natural GL",
"filters": [
[
"IsRandomSource"
],
[
"IsFinite",
"HasIsFinite",
"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))",
"CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"IsNaturalGL",
"HasIsNaturalGL"
]
]
},
{
"rank": 374,
"comment": "Random: for a random source and a group handled by nice monomorphism",
"filters": [
[
"IsRandomSource"
],
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"IsHandledByNiceMonomorphism",
"HasIsHandledByNiceMonomorphism"
]
]
},
{
"rank": 77,
"comment": "Random: for a random source and a natural alternating group: floyd's algorithm",
"filters": [
[
"IsRandomSource"
],
[
"IsNaturalAlternatingGroup",
"HasIsNaturalAlternatingGroup"
]
]
},
{
"rank": 77,
"comment": "Random: for a random source and a natural symmetric group: floyd's algorithm",
"filters": [
[
"IsRandomSource"
],
[
"IsNaturalSymmetricGroup",
"HasIsNaturalSymmetricGroup"
]
]
},
{
"rank": 73,
"comment": "Random: for a random source and a permutation group",
"filters": [
[
"IsRandomSource"
],
[
"CategoryCollections(IsPerm)",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 72,
"comment": "Random: for a random source and Rationals",
"filters": [
[
"IsRandomSource"
],
[
"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": 68,
"comment": "Random: for a random source and a large non-prime finite field",
"filters": [
[
"IsRandomSource"
],
[
"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": 63,
"comment": "Random: for a random source and a finite prime field",
"filters": [
[
"IsRandomSource"
],
[
"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": 62,
"comment": "Random: for a random source and a finite field with known primitive root",
"filters": [
[
"IsRandomSource"
],
[
"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"
]
]
},
{
"rank": 58,
"comment": "Random: for a random source and an algebraic extension",
"filters": [
[
"IsRandomSource"
],
[
"IsAlgebraicExtension"
]
]
},
{
"rank": 57,
"comment": "Random: for a random source and a pcgs computable groups",
"filters": [
[
"IsRandomSource"
],
[
"IsFinite",
"HasIsFinite",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"CanEasilyComputePcgs"
]
]
},
{
"rank": 51,
"comment": "Random: for a random source and full ring Z/nZ",
"filters": [
[
"IsRandomSource"
],
[
"IsWholeFamily",
"HasIsWholeFamily",
"CategoryCollections(IsZmodnZObjNonprime)"
]
]
},
{
"rank": 51,
"comment": "Random: for a random source and an fp group",
"filters": [
[
"IsRandomSource"
],
[
"IsFinite",
"HasIsFinite",
"IsSubgroupFpGroup"
]
]
},
{
"rank": 50,
"comment": "Random: for a random source and a full matrix module",
"filters": [
[
"IsRandomSource"
],
[
"IsFreeLeftModule",
"IsFullMatrixModule",
"HasIsFullMatrixModule"
]
]
},
{
"rank": 50,
"comment": "Random: for a random source and a full row module",
"filters": [
[
"IsRandomSource"
],
[
"IsFreeLeftModule",
"IsFullRowModule",
"HasIsFullRowModule"
]
]
},
{
"rank": 50,
"comment": "Random: for a random source and a free group",
"filters": [
[
"IsRandomSource"
],
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"
]
]
},
{
"rank": 42,
"comment": "Random: for a random source and `Integers'",
"filters": [
[
"IsRandomSource"
],
[
"IsIntegers"
]
]
},
{
"rank": 38,
"comment": "Random: for a random source and full hom space of linear mappings",
"filters": [
[
"IsRandomSource"
],
[
"CategoryCollections(IsGeneralMapping)",
"IsFreeLeftModule",
"IsFullHomModule",
"HasIsFullHomModule"
]
]
},
{
"rank": 36,
"comment": "Random: for two integers",
"filters": [
[
"IsInt"
],
[
"IsInt"
]
]
},
{
"rank": 26,
"comment": "Random: for a random source and a free monoid",
"filters": [
[
"IsRandomSource"
],
[
"IsMagmaWithOne",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"
]
]
},
{
"rank": 25,
"comment": "Random: for a random source and a free left module",
"filters": [
[
"IsRandomSource"
],
[
"IsFreeLeftModule"
]
]
},
{
"rank": 20,
"comment": "Random: for a random source and a free semigroup",
"filters": [
[
"IsRandomSource"
],
[
"IsMagma",
"IsAssociative",
"HasIsAssociative",
"CategoryCollections((IsWord and IsAssociativeElement))"
]
]
},
{
"rank": 20,
"comment": "Random: for a random source and the full collection Z/nZ(m)",
"filters": [
[
"IsRandomSource"
],
[
"IsWholeFamily",
"HasIsWholeFamily",
"CategoryCollections(IsZmodnZepsObj)"
]
]
},
{
"rank": 18,
"comment": "Random: for a random source and a RightCoset",
"filters": [
[
"IsRandomSource"
],
[
"IsRightCoset"
]
]
},
{
"rank": 15,
"comment": "Random: for a random source and a free magma",
"filters": [
[
"IsRandomSource"
],
[
"IsMagma",
"CategoryCollections(IsNonassocWord)"
]
]
},
{
"rank": 14,
"comment": "Random: for a random source and an additive coset",
"filters": [
[
"IsRandomSource"
],
[
"IsAdditiveCoset"
]
]
},
{
"rank": 12,
"comment": "Random: for a random source and for an external orbit: via acting domain",
"filters": [
[
"IsRandomSource"
],
[
"IsExternalOrbit"
]
]
},
{
"rank": 10,
"comment": "Random: for a random source and a double coset",
"filters": [
[
"IsRandomSource"
],
[
"IsDoubleCoset"
]
]
},
{
"rank": 7,
"comment": "Random: for a random source and p-adic extension family",
"filters": [
[
"IsRandomSource"
],
[
"CategoryFamily(IsPadicExtensionNumber)"
]
]
},
{
"rank": 7,
"comment": "Random: for a random source and a pure p-adic family",
"filters": [
[
"IsRandomSource"
],
[
"CategoryFamily(IsPurePadicNumber)"
]
]
},
{
"rank": 6,
"comment": "Random: for a random source and an infinite list of generators",
"filters": [
[
"IsRandomSource"
],
[
"IsList",
"IsInfiniteListOfGeneratorsRep"
]
]
},
{
"rank": 5,
"comment": "Random: for a real random source and a list",
"filters": [
[
"IsRealRandomSource"
],
[
"IsList"
]
]
},
{
"rank": 5,
"comment": "Random",
"filters": [
[
"IsMersenneTwister"
],
[
"IsList"
]
]
},
{
"rank": 5,
"comment": "Random",
"filters": [
[
"IsGAPRandomSource"
],
[
"IsList"
]
]
},
{
"rank": 5,
"comment": "Random",
"filters": [
[
"IsGlobalRandomSource"
],
[
"IsList"
]
]
},
{
"rank": 4,
"comment": "Random",
"filters": [
[
"IsRandomSource"
],
[
"IsList"
]
]
},
{
"rank": 2,
"comment": "Random: for a random source and a (finite) collection",
"filters": [
[
"IsRandomSource"
],
[
"IsCollection",
"IsFinite",
"HasIsFinite"
]
]
},
{
"rank": 0,
"comment": "Random: fallback method to test conditions",
"filters": [
[
"IsRandomSource"
],
[
"IsCollection"
]
]
}
],
"3args": [
{
"rank": 39,
"comment": "Random: for a real random source and two integers",
"filters": [
[
"IsRealRandomSource"
],
[
"IsInt"
],
[
"IsInt"
]
]
},
{
"rank": 39,
"comment": "Random",
"filters": [
[
"IsMersenneTwister"
],
[
"IsInt"
],
[
"IsInt"
]
]
},
{
"rank": 38,
"comment": "Random",
"filters": [
[
"IsRandomSource"
],
[
"IsInt"
],
[
"IsInt"
]
]
}
],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"Random"
]
},
{
"name": "PseudoRandom",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/coll.gd",
"line": 1737
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [
{
"rank": 116,
"comment": "PseudoRandom: for an internal list",
"filters": [
[
"IsList",
"IsInternalRep"
]
]
},
{
"rank": 37,
"comment": "PseudoRandom: subgroups fp group: force generators",
"filters": [
[
"IsSubgroupFpGroup"
]
]
},
{
"rank": 36,
"comment": "PseudoRandom: product replacement",
"filters": [
[
"IsMagmaWithInverses",
"HasGeneratorsOfMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
],
"aka": [
"Group_PseudoRandom"
]
},
{
"rank": 27,
"comment": "PseudoRandom: polynomial ring",
"filters": [
[
"IsPolynomialRing"
]
]
},
{
"rank": 16,
"comment": "PseudoRandom: RightCoset",
"filters": [
[
"IsRightCoset"
]
]
},
{
"rank": 8,
"comment": "PseudoRandom: double coset",
"filters": [
[
"IsDoubleCoset"
]
]
},
{
"rank": 1,
"comment": "PseudoRandom: for a list or collection (delegate to `Random')",
"filters": [
[
"IsListOrCollection"
]
]
}
],
"2args": [],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"PseudoRandom"
]
},
{
"name": "PseudoRandomSeed",
"type": "Attribute",
"locations": [
{
"file": "/home/mtorpey/gap/lib/coll.gd",
"line": 1751
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [
{
"rank": 20004,
"comment": "PseudoRandomSeed: system getter",
"filters": [
[
"IsAttributeStoringRep",
"HasPseudoRandomSeed"
]
]
}
],
"2args": [],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"PseudoRandomSeed"
]
},
{
"name": "SetPseudoRandomSeed",
"type": "Operation",
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],
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]
]
},
{
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"comment": "IsSubset: subgroups of fp group: test generators",
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],
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]
},
{
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"comment": "IsSubset: subgp fp group: via quotient rep",
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],
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]
]
},
{
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"comment": "IsSubset: for two FLMLORs-with-one",
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"IsMagmaWithOne",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
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"IsFreeLeftModule"
],
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"IsAdditivelyCommutative",
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]
},
{
"rank": 73,
"comment": "IsSubset: for Z_(pi) and Integers (ResClasses)",
"filters": [
[
"IsZ_pi",
"HasIsZ_pi"
],
[
"IsIntegers"
]
]
},
{
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"comment": "IsSubset: generic method for two groups",
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"IsAssociative",
"HasIsAssociative"
],
[
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"IsAssociative",
"HasIsAssociative"
]
]
},
{
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"comment": "IsSubset: for two FLMLORs",
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"IsDistributiveLOpDSum",
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"IsNearAdditiveMagma",
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"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
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"IsRDistributive",
"HasIsRDistributive",
"IsFreeLeftModule"
],
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"IsAdditivelyCommutative",
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"IsLDistributive",
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"IsRDistributive",
"HasIsRDistributive",
"IsFreeLeftModule"
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]
},
{
"rank": 66,
"comment": "IsSubset: for Z_(pi)'s (ResClasses)",
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"IsZ_pi",
"HasIsZ_pi"
],
[
"IsZ_pi",
"HasIsZ_pi"
]
]
},
{
"rank": 56,
"comment": "IsSubset: for two rings-with-one",
"filters": [
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"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
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"IsRDistributive",
"HasIsRDistributive"
],
[
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"IsNearAdditiveMagma",
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"IsAdditivelyCommutative",
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"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"HasGeneratorsOfRingWithOne"
]
]
},
{
"rank": 53,
"comment": "IsSubset: for two rings",
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"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
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"IsRDistributive",
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],
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"HasGeneratorsOfRing"
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]
},
{
"rank": 46,
"comment": "IsSubset: for two free left modules",
"filters": [
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"IsFreeLeftModule"
],
[
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]
]
},
{
"rank": 38,
"comment": "IsSubset: for two collections that are internal lists",
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"IsCollection"
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"IsCollection"
]
],
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{
"rank": 34,
"comment": "IsSubset: for two magmas with inverses",
"filters": [
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],
[
"IsMagmaWithInverses"
]
]
},
{
"rank": 32,
"comment": "IsSubset: for two additive magmas with inverses",
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"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
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"IsAdditivelyCommutative",
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]
]
},
{
"rank": 32,
"comment": "IsSubset: for two internal lists",
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"IsInternalRep"
],
[
"IsList",
"IsInternalRep"
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]
},
{
"rank": 28,
"comment": "IsSubset: for two additive magmas with zero",
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"IsNearAdditiveMagmaWithZero",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
],
[
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"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
]
]
},
{
"rank": 28,
"comment": "IsSubset: for two magmas with one",
"filters": [
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"IsMagmaWithOne"
],
[
"IsMagmaWithOne"
]
]
},
{
"rank": 24,
"comment": "IsSubset: for two additive magmas",
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"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
],
[
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"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative"
]
]
},
{
"rank": 22,
"comment": "IsSubset: for two magmas",
"filters": [
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"IsMagma"
],
[
"IsMagma"
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]
},
{
"rank": 22,
"comment": "IsSubset: for collection and empty list",
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],
[
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"IsEmpty",
"HasIsEmpty"
]
]
},
{
"rank": 22,
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"HasIsEmpty"
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]
},
{
"rank": 18,
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[
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"IsResidueClassUnionResidueListRep"
]
]
},
{
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"comment": "IsSubset: for two residue class unions in different rep. (ResClasses)",
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"IsResidueClassUnionResidueListRep"
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[
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]
},
{
"rank": 18,
"comment": "IsSubset: for two residue class unions in sparse rep. (ResClasses)",
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"IsResidueClassUnionClassListRep"
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[
"IsResidueClassUnion",
"IsResidueClassUnionClassListRep"
]
]
},
{
"rank": 18,
"comment": "IsSubset: for two residue class unions in standard rep. (ResClasses)",
"filters": [
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"IsResidueClassUnionResidueListRep"
],
[
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"IsResidueClassUnionResidueListRep"
]
]
},
{
"rank": 12,
"comment": "IsSubset: for two unions of residue classes with fixed rep's (ResClasses)",
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],
[
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]
]
},
{
"rank": 11,
"comment": "IsSubset: for a residue class union and the base ring (ResClasses)",
"filters": [
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[
"IsCollection",
"IsGeneralizedDomain"
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]
},
{
"rank": 11,
"comment": "IsSubset: for the base ring and a residue class union (ResClasses)",
"filters": [
[
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"IsGeneralizedDomain"
],
[
"IsResidueClassUnion"
]
]
},
{
"rank": 8,
"comment": "IsSubset: for residue class union and element list (ResClasses)",
"filters": [
[
"IsResidueClassUnion"
],
[
"IsList"
]
]
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{
"rank": 6,
"comment": "IsSubset: for two collections with known `AsSSortedList'",
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[
"IsCollection",
"HasAsSSortedList"
],
[
"IsCollection",
"HasAsSSortedList"
]
]
},
{
"rank": 4,
"comment": "IsSubset: for two collections (loop over the elements of the second)",
"filters": [
[
"IsCollection"
],
[
"IsCollection"
]
]
},
{
"rank": 4,
"comment": "IsSubset: for two collections in different families",
"filters": [
[
"IsCollection"
],
[
"IsCollection"
]
]
}
],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
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},
{
"name": "Intersection2",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/coll.gd",
"line": 3075
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 10009,
"comment": "Intersection2: domain and whole family",
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[
"IsCollection",
"IsGeneralizedDomain"
],
[
"IsCollection",
"IsWholeFamily",
"HasIsWholeFamily"
]
]
},
{
"rank": 10009,
"comment": "Intersection2: whole family and domain",
"filters": [
[
"IsCollection",
"IsWholeFamily",
"HasIsWholeFamily"
],
[
"IsCollection",
"IsGeneralizedDomain"
]
]
},
{
"rank": 10002,
"comment": "Intersection2: for two times the same ring (ResClasses)",
"filters": [
[
"IsListOrCollection"
],
[
"IsListOrCollection"
]
]
},
{
"rank": 744,
"comment": "Intersection2: handled by nice monomorphism:group CollColl",
"filters": [
[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative",
"IsHandledByNiceMonomorphism",
"HasIsHandledByNiceMonomorphism"
],
[
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"IsAssociative",
"HasIsAssociative",
"IsHandledByNiceMonomorphism",
"HasIsHandledByNiceMonomorphism"
]
]
},
{
"rank": 136,
"comment": "Intersection2: for two cyclotomic fields of cyclotomics",
"filters": [
[
"CategoryCollections(IsCyclotomic)",
"IsCyclotomicField",
"HasIsCyclotomicField"
],
[
"CategoryCollections(IsCyclotomic)",
"IsCyclotomicField",
"HasIsCyclotomicField"
]
]
},
{
"rank": 134,
"comment": "Intersection2: for abelian number field and cyclotomic field",
"filters": [
[
"CategoryCollections(IsCyclotomic)",
"IsAbelianNumberField",
"HasIsAbelianNumberField"
],
[
"CategoryCollections(IsCyclotomic)",
"IsCyclotomicField",
"HasIsCyclotomicField"
]
]
},
{
"rank": 134,
"comment": "Intersection2: for cyclotomic field and abelian number field",
"filters": [
[
"CategoryCollections(IsCyclotomic)",
"IsCyclotomicField",
"HasIsCyclotomicField"
],
[
"CategoryCollections(IsCyclotomic)",
"IsAbelianNumberField",
"HasIsAbelianNumberField"
]
]
},
{
"rank": 132,
"comment": "Intersection2: for two abelian number fields",
"filters": [
[
"CategoryCollections(IsCyclotomic)",
"IsAbelianNumberField",
"HasIsAbelianNumberField"
],
[
"CategoryCollections(IsCyclotomic)",
"IsAbelianNumberField",
"HasIsAbelianNumberField"
]
]
},
{
"rank": 130,
"comment": "Intersection2",
"filters": [
[
"IsNaturalAlternatingGroup",
"HasIsNaturalAlternatingGroup"
],
[
"IsNaturalAlternatingGroup",
"HasIsNaturalAlternatingGroup"
]
]
},
{
"rank": 130,
"comment": "Intersection2",
"filters": [
[
"IsNaturalAlternatingGroup",
"HasIsNaturalAlternatingGroup"
],
[
"IsNaturalSymmetricGroup",
"HasIsNaturalSymmetricGroup"
]
]
},
{
"rank": 130,
"comment": "Intersection2",
"filters": [
[
"IsNaturalSymmetricGroup",
"HasIsNaturalSymmetricGroup"
],
[
"IsNaturalAlternatingGroup",
"HasIsNaturalAlternatingGroup"
]
]
},
{
"rank": 130,
"comment": "Intersection2",
"filters": [
[
"IsNaturalSymmetricGroup",
"HasIsNaturalSymmetricGroup"
],
[
"IsNaturalSymmetricGroup",
"HasIsNaturalSymmetricGroup"
]
]
},
{
"rank": 126,
"comment": "Intersection2",
"filters": [
[
"CategoryCollections(IsPerm)",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
],
[
"IsNaturalAlternatingGroup",
"HasIsNaturalAlternatingGroup"
]
]
},
{
"rank": 126,
"comment": "Intersection2",
"filters": [
[
"IsNaturalAlternatingGroup",
"HasIsNaturalAlternatingGroup"
],
[
"CategoryCollections(IsPerm)",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 126,
"comment": "Intersection2",
"filters": [
[
"CategoryCollections(IsPerm)",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
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[
"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",
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"IsRDistributive",
"HasIsRDistributive",
"IsEuclideanRing"
],
[
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"IsAssociativeLOpEProd",
"IsDistributiveLOpDSum",
"IsDistributiveLOpESum",
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"IsLeftActedOnByDivisionRing",
"HasIsLeftActedOnByDivisionRing",
"IsMagma",
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"IsAssociative",
"HasIsAssociative",
"IsCommutative",
"HasIsCommutative",
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"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
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"HasIsRDistributive",
"IsEuclideanRing"
]
]
},
{
"rank": 122,
"comment": "Intersection2: perm groups",
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[
"CategoryCollections(IsPerm)",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
],
[
"CategoryCollections(IsPerm)",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"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": [
[
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"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"
],
[
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"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)))"
],
[
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"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)",
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"IsNearAdditiveMagma",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
],
[
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"IsMagmaWithOne",
"IsNearAdditiveMagma",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
]
]
},
{
"rank": 76,
"comment": "Intersection2: subgroups of fp group by quotient",
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[
"IsSubgroupFpGroup",
"IsSubgroupOfWholeGroupByQuotientRep"
],
[
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"IsSubgroupOfWholeGroupByQuotientRep"
]
]
},
{
"rank": 74,
"comment": "Intersection2: subgroups of fp group",
"filters": [
[
"IsSubgroupFpGroup"
],
[
"IsSubgroupFpGroup"
]
]
},
{
"rank": 74,
"comment": "Intersection2: generic method for two FLMLORs-with-one",
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[
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"IsMagmaWithOne",
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"IsAdditivelyCommutative",
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"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"IsFreeLeftModule"
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"IsDistributiveLOpDSum",
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"HasIsLDistributive",
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]
]
},
{
"rank": 72,
"comment": "Intersection2: groups with pcgs",
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"IsAssociative",
"HasIsAssociative",
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],
[
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"HasIsAssociative",
"HasHomePcgs"
]
]
},
{
"rank": 70,
"comment": "Intersection2: for two spaces in a common s.c. algebra",
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[
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"IsAssociativeLOpEProd",
"IsDistributiveLOpDSum",
"IsDistributiveLOpESum",
"IsTrivialLOpEOne",
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"HasIsLeftActedOnByDivisionRing",
"IsNearAdditiveMagma",
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"HasIsAdditivelyCommutative",
"CategoryCollections(IsSCAlgebraObj)"
],
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"IsTrivialLOpEOne",
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]
]
},
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"rank": 54,
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]
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]
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"rank": 48,
"comment": "+: For two 8 bit vectors in same characteristic",
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"rank": 48,
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"IsGeneralizedRowVector"
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"IsOrdinaryMatrix",
"IsBlockMatrixRep"
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"rank": 46,
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[
"IsOrdinaryMatrix",
"IsBlockMatrixRep"
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[
"IsGeneralizedRowVector"
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]
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"rank": 45,
"comment": "+: For an 8 bit vector of char 2 and a GF2 vector",
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"IsExtRElement",
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"IsGF2VectorRep"
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]
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{
"rank": 45,
"comment": "+: For a GF2 vector and an 8 bit vector of char 2",
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"rank": 44,
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"rank": 38,
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"IsRingGeneralMappingByImagesDefaultRep"
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]
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"rank": 38,
"comment": "+: for ring g.m.b.i. and ring general mapping",
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"HasRespectsAdditiveInverses"
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]
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{
"rank": 38,
"comment": "+: for mapping and linear m.b.m.",
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"IsTotal",
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"HasIsSingleValued"
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[
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"IsSingleValued",
"HasIsSingleValued",
"IsLinearMappingByMatrixDefaultRep"
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]
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{
"rank": 38,
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"IsTotal",
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"IsTotal",
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"IsSingleValued",
"HasIsSingleValued"
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{
"rank": 38,
"comment": "+: for mapping and linear m.b.i.",
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"IsGeneralMapping",
"IsTotal",
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[
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"IsSingleValued",
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"IsLinearGeneralMappingByImagesDefaultRep"
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]
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{
"rank": 38,
"comment": "+: for linear m.b.i. and mapping",
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"IsTotal",
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"HasIsSingleValued",
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[
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"IsTotal",
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"IsSingleValued",
"HasIsSingleValued"
]
]
},
{
"rank": 38,
"comment": "+: for two direct product elements",
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[
"IsDirectProductElement"
],
[
"IsDirectProductElement"
]
]
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"rank": 36,
"comment": "+: for internal FFE and element in Z/pZ (ModulusRep)",
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[
"IsFFE",
"IsInternalRep"
],
[
"IsFFE",
"IsLogOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
]
]
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{
"rank": 36,
"comment": "+: for element in Z/pZ (ModulusRep) and internal FFE",
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"IsFFE",
"IsLogOrderedFFE",
"IsZmodnZObj",
"IsModulusRep"
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[
"IsFFE",
"IsInternalRep"
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]
},
{
"rank": 34,
"comment": "+",
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[
"IsFFE",
"IsCoeffsModConwayPolRep"
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[
"IsFFE",
"IsCoeffsModConwayPolRep"
]
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"rank": 34,
"comment": "+: for integer and element in Z/nZ (ModulusRep)",
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[
"IsInt"
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[
"IsZmodnZObj",
"IsModulusRep"
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"rank": 34,
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[
"IsZmodnZObj",
"IsModulusRep"
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[
"IsInt"
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]
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{
"rank": 34,
"comment": "+: BFElm+BFElm",
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[
"IsAlgBFRep"
],
[
"IsAlgBFRep"
]
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"rank": 34,
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"IsAlgBFRep"
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[
"IsKroneckerConstRep"
]
]
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{
"rank": 34,
"comment": "+: AlgElm+BFElm",
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"IsKroneckerConstRep"
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[
"IsAlgBFRep"
]
]
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{
"rank": 34,
"comment": "+: AlgElm+AlgElm",
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[
"IsKroneckerConstRep"
],
[
"IsKroneckerConstRep"
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]
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{
"rank": 34,
"comment": "+: laurent + laurent",
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[
"IsPolynomialFunction",
"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
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[
"IsPolynomialFunction",
"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
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]
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{
"rank": 33,
"comment": "+: for rational and element in Z/nZ (ModulusRep)",
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[
"IsRat"
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[
"IsZmodnZObj",
"IsModulusRep"
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{
"rank": 33,
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[
"IsZmodnZObj",
"IsModulusRep"
],
[
"IsRat"
]
]
},
{
"rank": 32,
"comment": "+",
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[
"IsFFE"
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[
"IsFFE",
"IsCoeffsModConwayPolRep"
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]
},
{
"rank": 32,
"comment": "+",
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[
"IsFFE",
"IsCoeffsModConwayPolRep"
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[
"IsFFE"
]
]
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{
"rank": 32,
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[
"IsRat"
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[
"IsFFE"
]
]
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{
"rank": 32,
"comment": "+: for a FFE and a rational",
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[
"IsFFE"
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[
"IsRat"
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]
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{
"rank": 32,
"comment": "+: for two elements in Z/nZ (ModulusRep)",
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[
"IsZmodnZObj",
"IsModulusRep"
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[
"IsZmodnZObj",
"IsModulusRep"
]
]
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{
"rank": 32,
"comment": "+: for two unknowns",
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[
"IsUnknown"
],
[
"IsUnknown"
]
]
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{
"rank": 32,
"comment": "+: for cyclotomic and unknown",
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[
"IsCyc"
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[
"IsUnknown"
]
]
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{
"rank": 32,
"comment": "+: for unknown and cyclotomic",
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[
"IsUnknown"
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[
"IsCyc"
]
]
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{
"rank": 32,
"comment": "+: for general mapping and algebra g.m.b.i.",
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[
"IsGeneralMapping"
],
[
"IsGeneralMapping",
"IsAlgebraGeneralMappingByImagesDefaultRep"
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]
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{
"rank": 32,
"comment": "+: for an algebra g.m.b.i. and general mapping",
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[
"IsGeneralMapping",
"IsAlgebraGeneralMappingByImagesDefaultRep"
],
[
"IsGeneralMapping"
]
]
},
{
"rank": 32,
"comment": "+: for `-infinity' and `-infinity'",
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[
"IsNegInfinity"
],
[
"IsNegInfinity"
]
]
},
{
"rank": 32,
"comment": "+: for cyclotomic and `-infinity'",
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[
"IsCyc"
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[
"IsNegInfinity"
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]
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{
"rank": 32,
"comment": "+: for `-infinity' and cyclotomic",
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[
"IsNegInfinity"
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[
"IsCyc"
]
]
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{
"rank": 32,
"comment": "+: for `infinity' and `infinity'",
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[
"IsInfinity"
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[
"IsInfinity"
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{
"rank": 32,
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"IsCyc"
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[
"IsInfinity"
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]
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{
"rank": 32,
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[
"IsInfinity"
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[
"IsCyc"
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]
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{
"rank": 31,
"comment": "+: for object, and class function",
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[],
[
"IsClassFunction"
]
]
},
{
"rank": 31,
"comment": "+: for class function, and object",
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[
"IsClassFunction"
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[]
]
},
{
"rank": 30,
"comment": "+: for two plist matrices",
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[
"IsPlistMatrixRep"
],
[
"IsPlistMatrixRep"
]
]
},
{
"rank": 30,
"comment": "+",
"filters": [
[
"IsFFE"
],
[
"IsFFE"
]
]
},
{
"rank": 30,
"comment": "+: univariate + univariate",
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"IsPolynomialFunction",
"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction"
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"IsPolynomialFunction",
"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction"
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"aka": [
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{
"rank": 30,
"comment": "+: for general mapping and linear g.m.b.i.",
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[
"IsGeneralMapping"
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[
"IsGeneralMapping",
"IsLinearGeneralMappingByImagesDefaultRep"
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]
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{
"rank": 30,
"comment": "+: for linear g.m.b.i. and general mapping",
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[
"IsGeneralMapping",
"IsLinearGeneralMappingByImagesDefaultRep"
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[
"IsGeneralMapping"
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]
},
{
"rank": 29,
"comment": "+: for float and rational",
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[
"IsFloat"
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[
"IsRat"
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]
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{
"rank": 29,
"comment": "+: for rational and float",
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[
"IsRat"
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[
"IsFloat"
]
]
},
{
"rank": 29,
"comment": "+: for a default list, and a direct product element",
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"IsListDefault"
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[
"IsDirectProductElement"
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"aka": [
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{
"rank": 29,
"comment": "+: for a direct product element, and a default list",
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[
"IsDirectProductElement"
],
[
"IsListDefault"
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"aka": [
"SUM_SCL_LIST_DEFAULT"
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{
"rank": 28,
"comment": "+",
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[
"IsPadicExtensionNumber"
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[
"IsPadicExtensionNumber"
]
]
},
{
"rank": 28,
"comment": "+",
"filters": [
[
"IsPurePadicNumber"
],
[
"IsPurePadicNumber"
]
]
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{
"rank": 28,
"comment": "+: zmodnze : for cyclotomic and element in Z/nZ(m) (ZmodnZepsRep)",
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[
"IsCyclotomic"
],
[
"IsZmodnZepsObj",
"IsZmodnZepsRep"
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]
},
{
"rank": 28,
"comment": "+: zmodnze : for element in Z/nZ(m) (ZmodnZepsRep) and cyclotomic",
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[
"IsZmodnZepsObj",
"IsZmodnZepsRep"
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[
"IsCyclotomic"
]
]
},
{
"rank": 28,
"comment": "+: polynomial + polynomial",
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[
"IsPolynomial",
"HasIsPolynomial"
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[
"IsPolynomial",
"HasIsPolynomial"
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]
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{
"rank": 28,
"comment": "+: for two Lie objects in default representation",
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[
"IsPackedElementDefaultRep",
"IsLieObject"
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[
"IsPackedElementDefaultRep",
"IsLieObject"
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]
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{
"rank": 28,
"comment": "+",
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[
"IsSmallList",
"HasIsSmallList",
"IsListDefault"
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[
"IsSmallList",
"HasIsSmallList",
"IsListDefault"
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{
"rank": 26,
"comment": "+: zmodnze : for two elements in Z/nZ(m) (ZmodnZepsRep)",
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"IsZmodnZepsObj",
"IsZmodnZepsRep"
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[
"IsZmodnZepsObj",
"IsZmodnZepsRep"
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]
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{
"rank": 26,
"comment": "+: rat-fun + rat-fun",
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[
"IsRationalFunction"
],
[
"IsRationalFunction"
]
]
},
{
"rank": 26,
"comment": "+: for s. c. ring elements in dense vector rep.",
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[
"IsSCRingObj",
"IsDenseCoeffVectorRep"
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[
"IsSCRingObj",
"IsDenseCoeffVectorRep"
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]
},
{
"rank": 26,
"comment": "+: for two UEALattice elements",
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[
"IsPackedElementDefaultRep",
"IsUEALatticeElement"
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[
"IsPackedElementDefaultRep",
"IsUEALatticeElement"
]
]
},
{
"rank": 26,
"comment": "+: for s. c. algebra elements in dense vector rep.",
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[
"IsSCAlgebraObj",
"IsDenseCoeffVectorRep"
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[
"IsSCAlgebraObj",
"IsDenseCoeffVectorRep"
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]
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{
"rank": 25,
"comment": "+: for floats",
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[
"IsFloat"
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[
"IsFloat"
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]
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{
"rank": 25,
"comment": "+: FElm+BFElm",
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"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
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[
"IsAlgBFRep"
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{
"rank": 25,
"comment": "+: BFElm+FElm",
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[
"IsAlgBFRep"
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[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
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]
},
{
"rank": 25,
"comment": "+: FElm+AlgElm",
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"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
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[
"IsKroneckerConstRep"
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{
"rank": 25,
"comment": "+: AlgElm+FElm",
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"IsKroneckerConstRep"
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[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
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{
"rank": 25,
"comment": "+: laurent + coeff",
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"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction",
"IsLaurentPolynomial",
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[
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"IsMultiplicativeElement"
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]
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{
"rank": 25,
"comment": "+: coeff + laurent",
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"IsAdditiveElement",
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"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
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{
"rank": 25,
"comment": "+: laurent + coeff(embed)",
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"HasIsUnivariateRationalFunction",
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[
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"IsAdditiveElement",
"IsMultiplicativeElement"
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]
},
{
"rank": 25,
"comment": "+: coeff(embed) + laurent",
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"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
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"HasIsUnivariateRationalFunction",
"IsLaurentPolynomial",
"HasIsLaurentPolynomial"
]
]
},
{
"rank": 24,
"comment": "+: for two 0-cochains",
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[
"IsCochain",
"IsZeroCochainRep"
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[
"IsCochain",
"IsZeroCochainRep"
]
]
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{
"rank": 24,
"comment": "+: fp algebra elements",
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[
"IsPackedElementDefaultRep",
"IsElementOfFpAlgebra"
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[
"IsPackedElementDefaultRep",
"IsElementOfFpAlgebra"
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]
},
{
"rank": 24,
"comment": "+: for binary relations on points",
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[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
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[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
]
]
},
{
"rank": 24,
"comment": "+: for zero mapping and general mapping",
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[
"IsZero",
"HasIsZero",
"IsGeneralMapping"
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[
"IsGeneralMapping"
]
]
},
{
"rank": 24,
"comment": "+: for general mapping and zero mapping",
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[
"IsGeneralMapping"
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[
"IsZero",
"HasIsZero",
"IsGeneralMapping"
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]
},
{
"rank": 23,
"comment": "+: univariate + coeff",
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"IsPolynomialFunction",
"IsUnivariateRationalFunction",
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"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"
]
]
},
{
"rank": 17,
"comment": "*: Alg*List",
"filters": [
[
"IsAlgebraicElement"
],
[
"IsList"
]
]
},
{
"rank": 16,
"comment": "*: for two 32 bits assoc. words",
"filters": [
[
"Is32BitsAssocWord"
],
[
"Is32BitsAssocWord"
]
],
"aka": [
"32Bits_Product"
]
},
{
"rank": 16,
"comment": "*: for two 16 bits assoc. words",
"filters": [
[
"Is16BitsAssocWord"
],
[
"Is16BitsAssocWord"
]
],
"aka": [
"16Bits_Product"
]
},
{
"rank": 16,
"comment": "*: for two 8 bits assoc. words",
"filters": [
[
"Is8BitsAssocWord"
],
[
"Is8BitsAssocWord"
]
],
"aka": [
"8Bits_Product"
]
},
{
"rank": 15,
"comment": "*: univariate * rat",
"filters": [
[
"IsPolynomialFunction",
"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction"
],
[
"IsRat"
]
]
},
{
"rank": 15,
"comment": "*: rat * univariate",
"filters": [
[
"IsRat"
],
[
"IsPolynomialFunction",
"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction"
]
]
},
{
"rank": 14,
"comment": "*: for a ring element and a union of res.-cl. with fixed rep's (ResClasses)",
"filters": [
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
],
[
"IsUnionOfResidueClassesWithFixedRepresentatives"
]
]
},
{
"rank": 14,
"comment": "*: for a union of res.-cl. with fixed rep's and a ring element (ResClasses)",
"filters": [
[
"IsUnionOfResidueClassesWithFixedRepresentatives"
],
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
]
]
},
{
"rank": 14,
"comment": "*: for ring element and residue class union (ResClasses)",
"filters": [
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElement"
],
[
"IsResidueClassUnion"
]
]
},
{
"rank": 14,
"comment": "*: for two f.p. group elements",
"filters": [
[
"IsElementOfFpGroup"
],
[
"IsElementOfFpGroup"
]
]
},
{
"rank": 14,
"comment": "*: wreath elements",
"filters": [
[
"IsWreathProductElement"
],
[
"IsWreathProductElement"
]
]
},
{
"rank": 14,
"comment": "*: for two elements of magma by mult. table",
"filters": [
[
"IsMagmaByMultiplicationTableObj"
],
[
"IsMagmaByMultiplicationTableObj"
]
]
},
{
"rank": 14,
"comment": "*: assoc words in B letter rep",
"filters": [
[
"IsAssociativeElement",
"IsWord",
"IsBLetterAssocWordRep"
],
[
"IsAssociativeElement",
"IsWord",
"IsBLetterAssocWordRep"
]
]
},
{
"rank": 14,
"comment": "*: assoc words in W letter rep",
"filters": [
[
"IsAssociativeElement",
"IsWord",
"IsWLetterAssocWordRep"
],
[
"IsAssociativeElement",
"IsWord",
"IsWLetterAssocWordRep"
]
]
},
{
"rank": 14,
"comment": "*: for magma ring element and magma element",
"filters": [
[
"IsElementOfMagmaRingModuloRelations"
],
[
"IsMultiplicativeElement"
]
]
},
{
"rank": 14,
"comment": "*: for magma element and magma ring element",
"filters": [
[
"IsMultiplicativeElement"
],
[
"IsElementOfMagmaRingModuloRelations"
]
]
},
{
"rank": 14,
"comment": "*: for two elements of a magma with zero adjoined",
"filters": [
[
"IsMagmaWithZeroAdjoinedElementRep"
],
[
"IsMagmaWithZeroAdjoinedElementRep"
]
]
},
{
"rank": 14,
"comment": "*: for two general mappings",
"filters": [
[
"IsGeneralMapping"
],
[
"IsGeneralMapping"
]
]
},
{
"rank": 14,
"comment": "*",
"filters": [
[],
[
"IsSmallList",
"HasIsSmallList",
"IsListDefault"
]
]
},
{
"rank": 14,
"comment": "*",
"filters": [
[
"IsSmallList",
"HasIsSmallList",
"IsListDefault"
],
[]
]
},
{
"rank": 13,
"comment": "*: for list and binary relation on points",
"filters": [
[
"IsListOrCollection"
],
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
]
]
},
{
"rank": 13,
"comment": "*: for binary relation on points and list",
"filters": [
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
],
[
"IsListOrCollection"
]
]
},
{
"rank": 12,
"comment": "*",
"filters": [
[
"IsMonoidByAdjoiningIdentityElt"
],
[
"IsMonoidByAdjoiningIdentityElt"
]
]
},
{
"rank": 12,
"comment": "*: for two elements of a fp monoid",
"filters": [
[
"IsElementOfFpMonoid"
],
[
"IsElementOfFpMonoid"
]
]
},
{
"rank": 12,
"comment": "*: rws-element * rws-element",
"filters": [
[
"IsMultiplicativeElementWithInverseByRws"
],
[
"IsMultiplicativeElementWithInverseByRws"
]
]
},
{
"rank": 12,
"comment": "*: for two assoc. words in syllable rep",
"filters": [
[
"IsAssociativeElement",
"IsWord",
"IsSyllableAssocWordRep"
],
[
"IsAssociativeElement",
"IsWord",
"IsSyllableAssocWordRep"
]
],
"aka": [
"AssocWord_Product"
]
},
{
"rank": 12,
"comment": "*: rat * ratfun ",
"filters": [
[
"IsRat"
],
[
"IsPolynomialFunction"
]
]
},
{
"rank": 12,
"comment": "*: ratfun * rat",
"filters": [
[
"IsPolynomialFunction"
],
[
"IsRat"
]
]
},
{
"rank": 10,
"comment": "*: for elements of a Rees 0-matrix semigroup",
"filters": [
[
"IsReesZeroMatrixSemigroupElement"
],
[
"IsReesZeroMatrixSemigroupElement"
]
]
},
{
"rank": 10,
"comment": "*: for elements of a Rees matrix semigroup",
"filters": [
[
"IsReesMatrixSemigroupElement"
],
[
"IsReesMatrixSemigroupElement"
]
]
},
{
"rank": 10,
"comment": "*: for two elements of a f.p. semigroup",
"filters": [
[
"IsElementOfFpSemigroup"
],
[
"IsElementOfFpSemigroup"
]
]
},
{
"rank": 10,
"comment": "*: for two assoc. words: force syllable rep",
"filters": [
[
"IsAssociativeElement",
"IsWord"
],
[
"IsAssociativeElement",
"IsWord"
]
]
},
{
"rank": 10,
"comment": "*: for two nonassoc. words",
"filters": [
[
"IsNonassocWord"
],
[
"IsNonassocWord"
]
]
},
{
"rank": 10,
"comment": "*: wrapped additive elements",
"filters": [
[
"IsAdditiveElementAsMultiplicativeElementRep"
],
[
"IsAdditiveElementAsMultiplicativeElementRep"
]
]
}
],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"*",
"PROD"
]
},
{
"name": "OneImmutable",
"type": "Attribute",
"locations": [
{
"file": "/home/mtorpey/gap/lib/arith.gd",
"line": 1644
},
{
"file": "/home/mtorpey/gap/lib/arith.gd",
"line": 1645
},
{
"file": "/home/mtorpey/gap/lib/magma.gd",
"line": 147
},
{
"file": "/home/mtorpey/gap/lib/pperm.gd",
"line": 86
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [
{
"rank": 20007,
"comment": "OneImmutable: system getter",
"filters": [
[
"IsAttributeStoringRep",
"HasOneImmutable"
]
]
},
{
"rank": 10015,
"comment": "OneImmutable: for a magma-with-one that has a parent",
"filters": [
[
"HasParentAttr",
"IsMagmaWithOne"
]
]
},
{
"rank": 136,
"comment": "OneImmutable: partial method for a group (beats to ask family)",
"filters": [
[
"IsMagmaWithOne",
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 114,
"comment": "OneImmutable: partial method for a magma-with-one (ask family)",
"filters": [
[
"IsMagmaWithOne"
]
]
},
{
"rank": 107,
"comment": "OneImmutable: objects with memory",
"filters": [
[
"IsObjWithMemory"
]
]
},
{
"rank": 56,
"comment": "OneImmutable: 8 bit matrix",
"filters": [
[
"IsTable",
"IsSmallList",
"HasIsSmallList",
"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
"CategoryCollections(CategoryCollections(IsAdditiveElement))",
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))",
"IsMultiplicativeElementWithInverse",
"IsOrdinaryMatrix",
"CategoryCollections(CategoryCollections(IsCommutativeElement))",
"CategoryCollections(CategoryCollections(IsFFE))",
"Is8BitMatrixRep"
]
]
},
{
"rank": 44,
"comment": "OneImmutable: for GF2 Matrix",
"filters": [
[
"IsMultiplicativeElementWithOne",
"IsOrdinaryMatrix",
"IsGF2MatrixRep"
]
]
},
{
"rank": 28,
"comment": "OneImmutable: for a partial perm monoid",
"filters": [
[
"CategoryCollections(IsPartialPerm)",
"IsMagmaWithOne",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 26,
"comment": "OneImmutable: for SC Rings -- try generators",
"filters": [
[
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
]
]
},
{
"rank": 26,
"comment": "OneImmutable: for finite SC Rings",
"filters": [
[
"IsMagma",
"IsNearAdditiveMagma",
"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
"HasIsAdditivelyCommutative",
"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive"
]
]
},
{
"rank": 24,
"comment": "OneImmutable: for a partial perm semigroup",
"filters": [
[
"CategoryCollections(IsPartialPerm)",
"IsMagma",
"IsAssociative",
"HasIsAssociative"
]
]
},
{
"rank": 17,
"comment": "OneImmutable",
"filters": [
[
"IsFFE",
"IsCoeffsModConwayPolRep"
]
]
},
{
"rank": 16,
"comment": "OneImmutable: for macfloats",
"filters": [
[
"IsIEEE754FloatRep"
]
]
},
{
"rank": 16,
"comment": "OneImmutable: for a partial perm coll",
"filters": [
[
"CategoryCollections(IsPartialPerm)"
]
]
},
{
"rank": 15,
"comment": "OneImmutable: for a plist matrix",
"filters": [
[
"IsPlistMatrixRep"
]
]
},
{
"rank": 15,
"comment": "OneImmutable: univariate",
"filters": [
[
"IsPolynomialFunction",
"IsUnivariateRationalFunction",
"HasIsUnivariateRationalFunction"
]
],
"aka": [
"ONE",
"OneMutable",
"OneOp"
]
},
{
"rank": 14,
"comment": "OneImmutable: for a magma-with-one",
"filters": [
[
"IsMagmaWithOne"
]
]
},
{
"rank": 12,
"comment": "OneImmutable: for floats",
"filters": [
[
"IsFloat"
]
]
},
{
"rank": 12,
"comment": "OneImmutable: for binary relation on points and a set of integers",
"filters": [
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
]
]
},
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],
[
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],
[
"IsInt",
"IsPosRat"
],
[
"IsInt",
"IsPosRat"
]
]
},
{
"rank": 40,
"comment": "AddRowVector: error if immutable",
"filters": [
[
"IsList"
],
[],
[],
[
"IsInt",
"IsPosRat"
],
[
"IsInt",
"IsPosRat"
]
]
}
],
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},
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]
},
{
"name": "AddCoeffs",
"type": "Operation",
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{
"file": "/home/mtorpey/gap/lib/listcoef.gd",
"line": 94
}
],
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"1args": [],
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{
"rank": 48,
"comment": "AddCoeffs: two 8 bit vectors",
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[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
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"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
]
],
"aka": [
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},
{
"rank": 45,
"comment": "AddCoeffs: GF2 vector and 8 bit vector",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
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"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
]
]
},
{
"rank": 45,
"comment": "AddCoeffs: 8 bit vector and GF2 vector",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
]
]
},
{
"rank": 43,
"comment": "AddCoeffs: for empty list, GF2 vector",
"filters": [
[
"IsMutable",
"IsList",
"IsEmpty",
"HasIsEmpty"
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[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
]
]
},
{
"rank": 43,
"comment": "AddCoeffs: for GF2 vectors",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
]
]
},
{
"rank": 25,
"comment": "AddCoeffs: generic method (2nd arg empty)",
"filters": [
[
"IsMutable",
"IsDenseList"
],
[
"IsList",
"IsEmpty",
"HasIsEmpty"
]
]
},
{
"rank": 8,
"comment": "AddCoeffs: generic method (2 args)",
"filters": [
[
"IsMutable",
"IsDenseList"
],
[
"IsDenseList"
]
]
},
{
"rank": 2,
"comment": "AddCoeffs: error if immutable",
"filters": [
[
"IsList"
],
[]
]
}
],
"3args": [
{
"rank": 63,
"comment": "AddCoeffs: two 8 bit vectors",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsFFE"
]
],
"aka": [
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]
},
{
"rank": 60,
"comment": "AddCoeffs: GF2 vector and 8 bit vector",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsFFE"
]
]
},
{
"rank": 60,
"comment": "AddCoeffs: 8 bit vector and GF2 vector",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsFFE"
]
]
},
{
"rank": 58,
"comment": "AddCoeffs: for empty list, GF2 vector and FFE",
"filters": [
[
"IsMutable",
"IsList",
"IsEmpty",
"HasIsEmpty"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsFFE"
]
]
},
{
"rank": 58,
"comment": "AddCoeffs: for GF2 vectors and FFE",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsFFE"
]
]
},
{
"rank": 11,
"comment": "AddCoeffs: generic method 3args",
"filters": [
[
"IsMutable",
"IsDenseList"
],
[
"IsDenseList"
],
[
"IsMultiplicativeElement"
]
],
"aka": [
"ADDCOEFFS_GENERIC_3"
]
},
{
"rank": 2,
"comment": "AddCoeffs: error if immutable",
"filters": [
[
"IsList"
],
[],
[]
]
}
],
"4args": [],
"5args": [
{
"rank": 17,
"comment": "AddCoeffs: generic method (5 args)",
"filters": [
[
"IsMutable",
"IsDenseList"
],
[
"IsDenseList"
],
[
"IsDenseList"
],
[
"IsDenseList"
],
[
"IsMultiplicativeElement"
]
]
},
{
"rank": 2,
"comment": "AddCoeffs: error if immutable",
"filters": [
[
"IsList"
],
[],
[],
[],
[]
]
}
],
"6args": []
},
"aka": [
"AddCoeffs"
]
},
{
"name": "MultVectorLeft",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/listcoef.gd",
"line": 119
},
{
"file": "/home/mtorpey/gap/lib/matobj2.gd",
"line": 420
},
{
"file": "/home/mtorpey/gap/lib/matobj2.gd",
"line": 424
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 59,
"comment": "MultVectorLeft: kernel method for a mutable row vector of ffes in plain list rep, and an ffe",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsPlistRep",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"CategoryCollections(IsFFE)"
],
[
"IsFFE"
]
],
"aka": [
"MULT_VECTOR_VECFFES"
]
},
{
"rank": 57,
"comment": "MultVectorLeft: kernel method for a mutable dense plain list of cyclotomics, and a cyclotomic",
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[
"IsMutable",
"IsDenseList",
"IsPlistRep",
"CategoryCollections(IsCyclotomic)"
],
[
"IsCyclotomic"
]
],
"aka": [
"MULT_VECTOR_2_FAST"
]
},
{
"rank": 41,
"comment": "MultVectorLeft: For an 8 bit vector and an ffe",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsFFE",
"IsInternalRep"
]
],
"aka": [
"MULT_VECTOR_VEC8BITS"
]
},
{
"rank": 37,
"comment": "MultVectorLeft: for GF(2) vector and char 2 scalar",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsFFE"
]
],
"aka": [
"MULT_VECTOR_GF2VECS_2"
]
},
{
"rank": 15,
"comment": "MultVectorLeft: for an integer vector, and a small integer",
"filters": [
[
"IsMutable",
"IsPlistVectorRep",
"IsIntVector"
],
[
"IsSmallIntRep"
]
]
},
{
"rank": 12,
"comment": "MultVectorLeft: for a plist vector, and an object",
"filters": [
[
"IsMutable",
"IsPlistVectorRep"
],
[]
]
},
{
"rank": 10,
"comment": "MultVectorLeft: generic method for a mutable vector, and an object",
"filters": [
[
"IsMutable",
"IsVectorObj"
],
[]
]
},
{
"rank": 9,
"comment": "MultVectorLeft: kernel method for a mutable dense small list, and an object",
"filters": [
[
"IsMutable",
"IsDenseList",
"IsSmallList",
"HasIsSmallList"
],
[]
],
"aka": [
"MULT_VECTOR_LEFT_2"
]
},
{
"rank": 5,
"comment": "MultVectorLeft: for a mutable dense list, and an object",
"filters": [
[
"IsMutable",
"IsDenseList"
],
[]
]
},
{
"rank": 2,
"comment": "MultVectorLeft: error if immutable",
"filters": [
[
"IsList"
],
[]
]
}
],
"3args": [],
"4args": [
{
"rank": 46,
"comment": "MultVectorLeft: generic method for a mutable vector, an object, an int, and an int",
"filters": [
[
"IsMutable",
"IsVectorObj"
],
[],
[
"IsInt"
],
[
"IsInt"
]
]
}
],
"5args": [
{
"rank": 14,
"comment": "MultVectorLeft: obsolete five argument method",
"filters": [
[
"IsMutable",
"IsDenseList"
],
[
"IsDenseList"
],
[
"IsDenseList"
],
[
"IsDenseList"
],
[]
]
},
{
"rank": 2,
"comment": "MultVectorLeft: error if immutable",
"filters": [
[
"IsList"
],
[],
[],
[],
[]
]
}
],
"6args": []
},
"aka": [
"MultVector",
"MultVectorLeft"
]
},
{
"name": "CoeffsMod",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/listcoef.gd",
"line": 148
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 21,
"comment": "CoeffsMod",
"filters": [
[
"IsDenseList"
],
[
"IsInt"
]
]
}
],
"3args": [
{
"rank": 39,
"comment": "CoeffsMod: call `ReduceCoeffsMod'",
"filters": [
[
"IsDenseList"
],
[
"IsInt"
],
[
"IsInt"
]
]
}
],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"CoeffsMod"
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},
{
"name": "MultCoeffs",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/listcoef.gd",
"line": 192
}
],
"filters": [],
"methods": {
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"1args": [],
"2args": [],
"3args": [],
"4args": [],
"5args": [
{
"rank": 46,
"comment": "MultCoeffs: generic method",
"filters": [
[
"IsMutable",
"IsList"
],
[
"IsDenseList"
],
[
"IsInt"
],
[
"IsDenseList"
],
[
"IsInt"
]
]
},
{
"rank": 38,
"comment": "MultCoeffs: error if immutable",
"filters": [
[
"IsList"
],
[],
[
"IsInt"
],
[],
[
"IsInt"
]
]
}
],
"6args": []
},
"aka": [
"MultCoeffs"
]
},
{
"name": "PowerModCoeffs",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/listcoef.gd",
"line": 224
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [],
"3args": [
{
"rank": 24,
"comment": "PowerModCoeffs: default, 3 argt",
"filters": [
[
"IsDenseList"
],
[
"IsInt"
],
[
"IsDenseList"
]
]
}
],
"4args": [],
"5args": [
{
"rank": 103,
"comment": "PowerModCoeffs: for 8 bit vectors",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsInt"
],
[
"IsInt",
"IsPosRat"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsInt"
]
]
},
{
"rank": 97,
"comment": "PowerModCoeffs: for gf2vectors",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsInt"
],
[
"IsInt",
"IsPosRat"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsInt"
]
]
},
{
"rank": 60,
"comment": "PowerModCoeffs: default five argt method",
"filters": [
[
"IsDenseList"
],
[
"IsInt"
],
[
"IsInt"
],
[
"IsDenseList"
],
[
"IsInt"
]
]
}
],
"6args": []
},
"aka": [
"PowerModCoeffs"
]
},
{
"name": "ProductCoeffs",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/listcoef.gd",
"line": 253
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 48,
"comment": "ProductCoeffs: 8 bit vectors, kernel method (2 arg)",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
]
]
},
{
"rank": 42,
"comment": "ProductCoeffs: Gf2 vectors, kernel method (2 arg)",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
]
]
},
{
"rank": 6,
"comment": "ProductCoeffs: call PRODUCT_COEFFS_GENERIC_LISTS with lengths",
"filters": [
[
"IsDenseList"
],
[
"IsDenseList"
]
]
}
],
"3args": [],
"4args": [
{
"rank": 84,
"comment": "ProductCoeffs: 8 bit vectors, kernel method",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsInt"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsInt"
]
],
"aka": [
"PROD_COEFFS_VEC8BIT"
]
},
{
"rank": 78,
"comment": "ProductCoeffs: GF2 vectors, kernel method",
"filters": [
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsInt"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsInt"
]
],
"aka": [
"PROD_COEFFS_GF2VEC"
]
},
{
"rank": 42,
"comment": "ProductCoeffs: call PRODUCT_COEFFS_GENERIC_LISTS",
"filters": [
[
"IsDenseList"
],
[
"IsInt"
],
[
"IsDenseList"
],
[
"IsInt"
]
],
"aka": [
"PRODUCT_COEFFS_GENERIC_LISTS"
]
}
],
"5args": [],
"6args": []
},
"aka": [
"ProductCoeffs"
]
},
{
"name": "ReduceCoeffs",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/listcoef.gd",
"line": 288
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 49,
"comment": "ReduceCoeffs: 8 bit vectors, kernel method (2 arg)",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
]
]
},
{
"rank": 43,
"comment": "ReduceCoeffs: Gf2 vectors, kernel method (2 arg)",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
]
]
},
{
"rank": 8,
"comment": "ReduceCoeffs",
"filters": [
[
"IsMutable",
"IsDenseList"
],
[
"IsDenseList"
]
]
},
{
"rank": 2,
"comment": "ReduceCoeffs: error if immutable",
"filters": [
[
"IsList"
],
[]
]
}
],
"3args": [],
"4args": [
{
"rank": 85,
"comment": "ReduceCoeffs: 8 bit vectors, kernel method",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsInt"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"Is8BitVectorRep"
],
[
"IsInt"
]
]
},
{
"rank": 79,
"comment": "ReduceCoeffs: GF2 vectors, kernel method",
"filters": [
[
"IsMutable",
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsInt"
],
[
"IsHomogeneousList",
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsExtLElement",
"IsExtRElement",
"IsOddAdditiveNestingDepthObject",
"IsGF2VectorRep"
],
[
"IsInt"
]
],
"aka": [
"REDUCE_COEFFS_GF2VEC"
]
},
{
"rank": 72,
"comment": "ReduceCoeffs: for float vectors",
"filters": [
[
"CategoryCollections(IsFloat)"
],
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"rank": 23,
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"rank": 17,
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{
"rank": 13,
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{
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"rank": 2,
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{
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[]
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"name": "IsSurjective",
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"file": "/home/mtorpey/gap/lib/mapping.gd",
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"rank": 20010,
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{
"rank": 10013,
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},
{
"rank": 23,
"comment": "IsSurjective: for a field homomorphism",
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[
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},
{
"rank": 18,
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{
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"rank": 10,
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[
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{
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"IsGeneralMapping"
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}
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"rank": 2,
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{
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[]
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"name": "Range",
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"file": "/home/mtorpey/gap/lib/mapping.gd",
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{
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"rank": 29,
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{
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},
{
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},
{
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{
"rank": 23,
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"rank": 23,
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},
{
"rank": 22,
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]
}
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},
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"rank": 2,
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[]
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},
{
"rank": 0,
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[]
]
}
],
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},
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},
{
"name": "Source",
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"aka": [
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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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"aka": [
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},
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[]
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"rank": 18,
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{
"rank": 13,
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"RespectsInverses",
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}
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[]
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{
"rank": 23,
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{
"rank": 23,
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{
"rank": 23,
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{
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{
"rank": 23,
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{
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{
"rank": 17,
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[]
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]
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]
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{
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{
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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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"comment": "ImagesRepresentative: for embedding of ring into magma ring, and ring element",
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]
},
{
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"comment": "ImagesRepresentative: using `RepresentativeAction'",
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},
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"rank": 28,
"comment": "ImagesRepresentative: for isom by matrix groups (Polenta)",
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"rank": 28,
"comment": "ImagesRepresentative: for group by field elems isom",
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]
},
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"rank": 28,
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"rank": 28,
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{
"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: 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/mtorpey/gap/lib/mapping.gd",
"line": 832
}
],
"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"
]
]
},
{
"rank": 11,
"comment": "ImagesSet: for an inverse mapping and a collection",
"filters": [
[
"IsGeneralMapping",
"IsInverseGeneralMappingRep"
],
[
"IsCollection"
]
]
},
{
"rank": 9,
"comment": "ImagesSet: for general mapping, and finite collection",
"filters": [
[
"IsGeneralMapping"
],
[
"IsCollection"
]
]
}
],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"ImagesSet"
]
},
{
"name": "ImageElm",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/mapping.gd",
"line": 855
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 10017,
"comment": "ImageElm: for zero mapping and object",
"filters": [
[
"IsZero",
"HasIsZero",
"IsGeneralMapping"
],
[]
]
},
{
"rank": 10017,
"comment": "ImageElm: for identity mapping and object",
"filters": [
[
"IsOne",
"HasIsOne",
"IsGeneralMapping"
],
[]
]
},
{
"rank": 42,
"comment": "ImageElm: for ANF automorphism and scalar",
"filters": [
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
],
[
"IsCyc"
]
]
},
{
"rank": 31,
"comment": "ImageElm: for Fp to SCA mapping, and element",
"filters": [
[
"IsFptoSCAMorphism"
],
[
"IsElementOfFpAlgebra"
]
]
},
{
"rank": 26,
"comment": "ImageElm: for Frobenius automorphism and source element",
"filters": [
[
"IsFrobeniusAutomorphism"
],
[]
]
},
{
"rank": 14,
"comment": "ImageElm: for mapping by function",
"filters": [
[
"IsMappingByFunctionRep"
],
[]
]
},
{
"rank": 13,
"comment": "ImageElm: for an inverse mapping and an element",
"filters": [
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsInverseGeneralMappingRep"
],
[]
]
},
{
"rank": 11,
"comment": "ImageElm: for mapping, and element",
"filters": [
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued"
],
[]
]
},
{
"rank": 7,
"comment": "ImageElm: for general mapping, and element",
"filters": [
[
"IsGeneralMapping"
],
[]
]
}
],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"ImageElm"
]
},
{
"name": "PreImagesElm",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/mapping.gd",
"line": 982
}
],
"filters": [],
"methods": {
"0args": [],
"1args": [],
"2args": [
{
"rank": 10017,
"comment": "PreImagesElm: for zero mapping and object",
"filters": [
[
"IsZero",
"HasIsZero",
"IsGeneralMapping"
],
[]
]
},
{
"rank": 10017,
"comment": "PreImagesElm: for identity mapping and object",
"filters": [
[
"IsOne",
"HasIsOne",
"IsGeneralMapping"
],
[]
]
},
{
"rank": 37,
"comment": "PreImagesElm: for embedding of ring into magma ring, and free magma ring element",
"filters": [
[
"IsEmbeddingRingMagmaRing"
],
[
"IsElementOfFreeMagmaRing"
]
]
},
{
"rank": 36,
"comment": "PreImagesElm: for ANF automorphism and scalar",
"filters": [
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
],
[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 31,
"comment": "PreImagesElm: for embedding of magma into magma ring, and free magma ring element",
"filters": [
[
"IsEmbeddingMagmaMagmaRing"
],
[
"IsElementOfFreeMagmaRing"
]
]
},
{
"rank": 31,
"comment": "PreImagesElm: for binary rels over [1..n] with images list",
"filters": [
[
"IsEndoGeneralMapping",
"HasIsEndoGeneralMapping",
"IsBinaryRelationOnPointsRep"
],
[
"IsInt",
"IsPosRat"
]
]
},
{
"rank": 24,
"comment": "PreImagesElm: for Lie embedding and Lie object in default representation",
"filters": [
[
"IsGeneralMapping",
"IsLieEmbeddingRep"
],
[
"IsPackedElementDefaultRep",
"IsLieObject"
]
]
},
{
"rank": 23,
"comment": "PreImagesElm: for field homomorphism and element",
"filters": [
[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism"
],
[]
]
},
{
"rank": 22,
"comment": "PreImagesElm: equivalence relations with parition and element",
"filters": [
[
"IsEquivalenceRelation",
"HasIsEquivalenceRelation",
"HasEquivalenceRelationPartition"
],
[]
]
},
{
"rank": 19,
"comment": "PreImagesElm: for mapping by function",
"filters": [
[
"IsMappingByFunctionWithInverseRep"
],
[]
]
},
{
"rank": 14,
"comment": "PreImagesElm: method for s.p. gen. mapping respecting add. & add.inv., and element",
"filters": [
[
"IsSPGeneralMapping",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
"HasRespectsAdditiveInverses"
],
[]
]
},
{
"rank": 14,
"comment": "PreImagesElm: method for s.p. general mapping respecting mult. & inv., and element",
"filters": [
[
"IsSPGeneralMapping",
"RespectsMultiplication",
"HasRespectsMultiplication",
"RespectsInverses",
"HasRespectsInverses"
],
[]
]
},
{
"rank": 10,
"comment": "PreImagesElm: for a restricted mapping, and an element",
"filters": [
[
"IsGeneralRestrictedMappingRep"
],
[]
]
},
{
"rank": 10,
"comment": "PreImagesElm: for a composition mapping, and an element",
"filters": [
[
"IsCompositionMappingRep"
],
[]
]
},
{
"rank": 9,
"comment": "PreImagesElm: for an inverse mapping and an element",
"filters": [
[
"IsGeneralMapping",
"IsInverseGeneralMappingRep"
],
[]
]
},
{
"rank": 9,
"comment": "PreImagesElm: for constant time access general mapping, and element",
"filters": [
[
"IsGeneralMapping",
"IsConstantTimeAccessGeneralMapping",
"HasIsConstantTimeAccessGeneralMapping"
],
[]
]
},
{
"rank": 7,
"comment": "PreImagesElm: for general mapping with finite source, and element",
"filters": [
[
"IsGeneralMapping"
],
[]
]
}
],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"PreImagesElm"
]
},
{
"name": "PreImageElm",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/mapping.gd",
"line": 1005
}
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{
"rank": 10017,
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[
"IsOne",
"HasIsOne",
"IsGeneralMapping"
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[]
]
},
{
"rank": 40,
"comment": "PreImageElm: for ANF automorphism and scalar",
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[
"IsTotal",
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"IsSingleValued",
"HasIsSingleValued",
"IsInjective",
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"IsSurjective",
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[
"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
"IsMultiplicativeElementWithInverse"
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]
},
{
"rank": 19,
"comment": "PreImageElm: for mapping by function",
"filters": [
[
"IsMappingByFunctionWithInverseRep"
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[]
]
},
{
"rank": 13,
"comment": "PreImageElm: for an inj. & surj. inverse mapping, and an element",
"filters": [
[
"IsGeneralMapping",
"IsInjective",
"HasIsInjective",
"IsSurjective",
"HasIsSurjective",
"IsInverseGeneralMappingRep"
],
[]
]
},
{
"rank": 11,
"comment": "PreImageElm: for inj. & surj. general mapping, and element",
"filters": [
[
"IsGeneralMapping",
"IsInjective",
"HasIsInjective",
"IsSurjective",
"HasIsSurjective"
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[]
],
"aka": [
"PreImagesRepresentative"
]
},
{
"rank": 7,
"comment": "PreImageElm: for general mapping, and element",
"filters": [
[
"IsGeneralMapping"
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[]
]
}
],
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"4args": [],
"5args": [],
"6args": []
},
"aka": [
"PreImageElm"
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},
{
"name": "PreImagesRepresentative",
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{
"file": "/home/mtorpey/gap/lib/mapping.gd",
"line": 1031
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],
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"comment": "PreImagesRepresentative: for zero mapping and object",
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[
"IsZero",
"HasIsZero",
"IsGeneralMapping"
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[]
]
},
{
"rank": 10017,
"comment": "PreImagesRepresentative: for identity mapping and object",
"filters": [
[
"IsOne",
"HasIsOne",
"IsGeneralMapping"
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[]
]
},
{
"rank": 63,
"comment": "PreImagesRepresentative: for an alg. hom. from f. p. algebra, and an element",
"filters": [
[
"IsAlgebraHomomorphismFromFpRep"
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[
"IsTable",
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"CategoryCollections(CategoryCollections(IsAdditiveElement))",
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
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],
"aka": [
"PreImagesRepresentativeOperationAlgebraHomomorphism"
]
},
{
"rank": 63,
"comment": "PreImagesRepresentative: for an operation algebra homomorphism, and an element",
"filters": [
[
"IsOperationAlgebraHomomorphismDefaultRep"
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[
"IsTable",
"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))",
"CategoryCollections(CategoryCollections(IsAdditiveElement))",
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))"
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]
},
{
"rank": 51,
"comment": "PreImagesRepresentative: for a blow up isomorphism, and a matrix in the range",
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[
"IsBlowUpIsomorphism"
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[
"IsTable",
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]
},
{
"rank": 37,
"comment": "PreImagesRepresentative: for embedding of ring into magma ring, and free magma ring element",
"filters": [
[
"IsEmbeddingRingMagmaRing"
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[
"IsElementOfFreeMagmaRing"
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]
},
{
"rank": 36,
"comment": "PreImagesRepresentative: for ANF automorphism and scalar",
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[
"IsFieldHomomorphism",
"HasIsFieldHomomorphism",
"IsANFAutomorphismRep"
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"IsNearAdditiveElementWithInverse",
"IsAdditiveElement",
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]
},
{
"rank": 35,
"comment": "PreImagesRepresentative: for ToPcpGHBI",
"filters": [
[
"IsToPcpGHBI"
],
[
"IsPcpElement"
]
]
},
{
"rank": 33,
"comment": "PreImagesRepresentative: for Fp to SCA mapping, and element",
"filters": [
[
"IsFptoSCAMorphism"
],
[
"IsSCAlgebraObj"
]
]
},
{
"rank": 32,
"comment": "PreImagesRepresentative: AutomGroup Niceomorphism",
"filters": [
[
"IsActionHomomorphismAutomGroup"
],
[
"IsPerm"
]
]
},
{
"rank": 31,
"comment": "PreImagesRepresentative: IsProjectiveActionHomomorphism",
"filters": [
[
"IsProjectiveActionHomomorphism"
],
[
"IsPerm"
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]
},
{
"rank": 31,
"comment": "PreImagesRepresentative: IsLinearActionHomomorphism",
"filters": [
[
"IsLinearActionHomomorphism"
],
[
"IsPerm"
]
]
},
{
"rank": 31,
"comment": "PreImagesRepresentative: constituent homomorphism",
"filters": [
[
"IsConstituentHomomorphism"
],
[
"IsPerm"
]
]
},
{
"rank": 31,
"comment": "PreImagesRepresentative: for embedding of magma into magma ring, and free magma ring element",
"filters": [
[
"IsEmbeddingMagmaMagmaRing"
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[
"IsElementOfFreeMagmaRing"
]
]
},
{
"rank": 30,
"comment": "PreImagesRepresentative",
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[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsPcgsToPcgsGeneralMappingByImages"
],
[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 29,
"comment": "PreImagesRepresentative: imprim perm wreath product embedding",
"filters": [
[
"IsEmbeddingImprimitiveWreathProductPermGroup"
],
[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: hom. to standard generators of fp group, using 'MappedWord'",
"filters": [
[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsToFpGroupGeneralMappingByImages"
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[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: imprim matrix wreath product embedding",
"filters": [
[
"IsEmbeddingImprimitiveWreathProductMatrixGroup"
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[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: matrix direct product projection",
"filters": [
[
"IsProjectionDirectProductMatrixGroup"
],
[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: matrix direct product embedding",
"filters": [
[
"IsEmbeddingDirectProductMatrixGroup"
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[
"IsMultiplicativeElementWithInverse"
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]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: perm subdirect product projection",
"filters": [
[
"IsProjectionSubdirectProductPermGroup"
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[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: perm direct product projection",
"filters": [
[
"IsProjectionDirectProductPermGroup"
],
[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: perm direct product embedding",
"filters": [
[
"IsEmbeddingDirectProductPermGroup"
],
[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: blocks homomorphism",
"filters": [
[
"IsBlocksHomomorphism"
],
[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 28,
"comment": "PreImagesRepresentative: for conjugator isomorphism",
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[
"IsConjugatorIsomorphism",
"HasIsConjugatorIsomorphism"
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[
"IsMultiplicativeElementWithInverse"
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]
},
{
"rank": 27,
"comment": "PreImagesRepresentative: method for pcgs hom",
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[
"IsGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"IsToPcGroupGeneralMappingByImages"
],
[
"IsMultiplicativeElementWithInverse"
]
]
},
{
"rank": 26,
"comment": "PreImagesRepresentative: for algebra g.m.b.i. knowing inverse, and element",
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[
"IsGeneralMapping",
"HasInverseGeneralMapping",
"IsAlgebraGeneralMappingByImagesDefaultRep"
],
[]
]
},
{
"rank": 25,
"comment": "PreImagesRepresentative: for homomorphisms of free groups",
"filters": [
[
"IsToFpGroupGeneralMappingByImages"
],
[
"IsMultiplicativeElementWithInverse",
"IsAssociativeElement",
"IsWord"
]
]
},
{
"rank": 25,
"comment": "PreImagesRepresentative: for algebra g.m.b.i., and element",
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[
"IsGeneralMapping",
"IsAlgebraGeneralMappingByImagesDefaultRep"
],
[]
]
},
{
"rank": 23,
"comment": "PreImagesRepresentative: for PBG-Niceo",
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[
"IsPreimagesByAsGroupGeneralMappingByImages",
"IsNiceMonomorphism"
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[
"IsMultiplicativeElementWithInverse"
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]
},
{
"rank": 23,
"comment": "PreImagesRepresentative",
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[
"IsToPermGroupGeneralMappingByImages"
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[
"IsMultiplicativeElementWithInverse"
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]
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{
"rank": 23,
"comment": "PreImagesRepresentative: for ring g.m.b.i., and element",
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[
"IsGeneralMapping",
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"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
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"HasRespectsAdditiveInverses",
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],
[]
]
},
{
"rank": 23,
"comment": "PreImagesRepresentative: for left module m.b.m., and element",
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"IsGeneralMapping",
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]
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{
"rank": 23,
"comment": "PreImagesRepresentative: for left module g.m.b.i., and element",
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"IsGeneralMapping",
"IsLinearGeneralMappingByImagesDefaultRep"
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[]
]
},
{
"rank": 22,
"comment": "PreImagesRepresentative: for GHBI and mult.-elm.-with-inverse",
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[
"IsGroupGeneralMappingByImages"
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[
"IsMultiplicativeElementWithInverse"
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]
},
{
"rank": 22,
"comment": "PreImagesRepresentative: for PBG-Hom",
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[
"IsPreimagesByAsGroupGeneralMappingByImages"
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[
"IsMultiplicativeElementWithInverse"
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]
},
{
"rank": 21,
"comment": "PreImagesRepresentative: equivalence relations",
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[
"IsEquivalenceRelation",
"HasIsEquivalenceRelation"
],
[]
]
},
{
"rank": 20,
"comment": "PreImagesRepresentative: for semigroup homomorphism by images",
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"IsGeneralMapping",
"IsSPGeneralMapping",
"IsTotal",
"HasIsTotal",
"IsSingleValued",
"HasIsSingleValued",
"RespectsMultiplication",
"HasRespectsMultiplication",
"IsSemigroupHomomorphismByImagesRep"
],
[
"IsMultiplicativeElement"
]
]
},
{
"rank": 19,
"comment": "PreImagesRepresentative: for mapping by function with inverse",
"filters": [
[
"IsMappingByFunctionWithInverseRep"
],
[]
]
},
{
"rank": 14,
"comment": "PreImagesRepresentative: for mapping by function",
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[
"IsMappingByFunctionRep"
],
[]
]
},
{
"rank": 10,
"comment": "PreImagesRepresentative: for a restricted mapping, and an element",
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"IsGeneralRestrictedMappingRep"
],
[]
]
},
{
"rank": 10,
"comment": "PreImagesRepresentative: for a composition mapping, and an element",
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[
"IsCompositionMappingRep"
],
[]
]
},
{
"rank": 9,
"comment": "PreImagesRepresentative: for an inverse mapping and an element",
"filters": [
[
"IsInverseGeneralMappingRep"
],
[]
]
},
{
"rank": 8,
"comment": "PreImagesRepresentative: for total non-s.p. general mapping, and element",
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[
"IsNonSPGeneralMapping"
],
[]
]
},
{
"rank": 8,
"comment": "PreImagesRepresentative: for s.p. general mapping, and element",
"filters": [
[
"IsSPGeneralMapping"
],
[]
]
}
],
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"4args": [],
"5args": [],
"6args": []
}
},
{
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"line": 1054
}
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"rank": 10019,
"comment": "PreImagesSet: for zero mapping and collection",
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"IsZero",
"HasIsZero",
"IsGeneralMapping"
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"IsCollection"
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]
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{
"rank": 10019,
"comment": "PreImagesSet: for identity mapping and collection",
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"IsOne",
"HasIsOne",
"IsGeneralMapping"
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"IsCollection"
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]
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{
"rank": 91,
"comment": "PreImagesSet: for PcpGHBI",
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"IsFromPcpGHBI",
"IsToPcpGHBI"
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"IsAssociative",
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]
},
{
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"comment": "PreImagesSet",
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]
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{
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"comment": "PreImagesSet: constituent homomorphism",
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"IsConstituentHomomorphism"
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"CategoryCollections(IsPerm)",
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"IsAssociative",
"HasIsAssociative"
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]
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{
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"comment": "PreImagesSet: for ANF automorphism and scalar",
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"IsFieldHomomorphism",
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"IsANFAutomorphismRep"
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"IsAssociativeLOpDProd",
"IsAssociativeLOpEProd",
"IsDistributiveLOpDSum",
"IsDistributiveLOpESum",
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"IsLeftActedOnByRing",
"IsLeftActedOnByDivisionRing",
"HasIsLeftActedOnByDivisionRing",
"IsMagma",
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"IsNearAdditiveGroup",
"IsAdditivelyCommutative",
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"IsLDistributive",
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"IsRDistributive",
"HasIsRDistributive",
"IsEuclideanRing"
]
]
},
{
"rank": 78,
"comment": "PreImagesSet: for field homomorphism and field",
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"IsFieldHomomorphism",
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],
[
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"IsExtLSet",
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"IsAssociativeLOpEProd",
"IsDistributiveLOpDSum",
"IsDistributiveLOpESum",
"IsTrivialLOpEOne",
"IsLeftActedOnByRing",
"IsLeftActedOnByDivisionRing",
"HasIsLeftActedOnByDivisionRing",
"IsMagma",
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"IsAssociative",
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"HasIsAdditivelyCommutative",
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"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
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]
]
},
{
"rank": 63,
"comment": "PreImagesSet: map from (sub)group of fp group",
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"IsTotal",
"HasIsTotal",
"IsSingleValued",
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"IsAssociative",
"HasIsAssociative"
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]
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{
"rank": 58,
"comment": "PreImagesSet: for conjugator isomorphism, and group",
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"IsConjugatorIsomorphism",
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[
"IsMagmaWithInverses",
"IsAssociative",
"HasIsAssociative"
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]
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{
"rank": 57,
"comment": "PreImagesSet: method for algebra-with-one hom. and FLMLOR-with-one",
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"RespectsAddition",
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"RespectsAdditiveInverses",
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"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
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[
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"IsLDistributive",
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"IsRDistributive",
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"IsFreeLeftModule"
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]
},
{
"rank": 55,
"comment": "PreImagesSet: method for injective s.p. mapping respecting mult. & inv., and group",
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"IsGeneralMapping",
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"IsTotal",
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"HasRespectsMultiplication",
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"HasRespectsInverses"
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"IsAssociative",
"HasIsAssociative"
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{
"rank": 53,
"comment": "PreImagesSet: method for permgroup homs",
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"IsGeneralMapping",
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"HasIsSingleValued",
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]
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{
"rank": 52,
"comment": "PreImagesSet: method for algebra hom. and FLMLOR",
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"HasRespectsMultiplication",
"RespectsAddition",
"HasRespectsAddition",
"RespectsAdditiveInverses",
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"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
],
[
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"IsDistributiveLOpDSum",
"IsMagma",
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"IsAdditivelyCommutative",
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"IsLDistributive",
"HasIsLDistributive",
"IsRDistributive",
"HasIsRDistributive",
"IsFreeLeftModule"
]
]
},
{
"rank": 49,
"comment": "PreImagesSet: method for s.p. general mapping respecting mult. & inv., and group",
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"IsSPGeneralMapping",
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"HasRespectsMultiplication",
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"IsAssociative",
"HasIsAssociative"
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{
"rank": 38,
"comment": "PreImagesSet: method for linear mapping and left module",
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"IsSPGeneralMapping",
"RespectsAddition",
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"RespectsAdditiveInverses",
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"RespectsScalarMultiplication",
"HasRespectsScalarMultiplication"
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[
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"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"
],
[
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"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": [
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"IsGeneralMapping"
],
[
"IsCollection"
]
]
}
],
"3args": [],
"4args": [],
"5args": [],
"6args": []
},
"aka": [
"PreImagesSet"
]
},
{
"name": "CompositionMapping2",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/mapping.gd",
"line": 1189
}
],
"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"
],
[
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{
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},
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[]
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},
{
"rank": 52,
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}
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},
{
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"line": 196
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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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"line": 196
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},
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{
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"line": 196
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{
"rank": 52,
"comment": "IsRightIdeal: try to exploit the in-parent attribute IsRightIdealInParent",
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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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{
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{
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}
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{
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{
"file": "/home/mtorpey/.gap/pkg/laguna-3.9.2/lib/laguna.gd",
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{
"file": "/home/mtorpey/.gap/pkg/laguna-3.9.2/lib/laguna.gd",
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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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{
"file": "/home/mtorpey/gap/lib/ctbl.gd",
"line": 743
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{
"file": "/home/mtorpey/gap/lib/ctbl.gd",
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"file": "/home/mtorpey/gap/lib/ctbl.gd",
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{
"file": "/home/mtorpey/gap/lib/ctbl.gd",
"line": 877
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{
"file": "/home/mtorpey/gap/lib/ctbl.gd",
"line": 878
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{
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"comment": "CharacterDegrees: handled by nice monomorphism: Attribute",
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"HasIsAssociative",
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{
"rank": 21,
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{
"rank": 1,
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}
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{
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{
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"IsAssociative",
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}
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},
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"line": 876
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"line": 878
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[]
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}
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"line": 876
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{
"name": "Irr",
"type": "Attribute",
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"file": "/home/mtorpey/gap/lib/ctbl.gd",
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{
"file": "/home/mtorpey/gap/lib/ctbl.gd",
"line": 971
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{
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{
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]
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{
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{
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{
"rank": 86,
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{
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{
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{
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{
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{
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"filters": [
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"HasIsAssociative"
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]
},
{
"rank": 54,
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"filters": [
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[
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"aka": [
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},
{
"name": "SetIrr",
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{
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"line": 972
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"name": "IndicatorOp",
"type": "Operation",
"locations": [
{
"file": "/home/mtorpey/gap/lib/ctbl.gd",
"line": 2765
}
],
"filters": [],
"methods": {
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"1args": [],
"2args": [],
"3args": [
{
"rank": 45,
"comment": "IndicatorOp: for a Brauer character table and <n>