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    {"IsEmpty" : {"type" : "GAP_Property","implied" : ["IsEmpty","Tester(IsEmpty)"]},"IsTrivial" : {"type" : "GAP_Property","implied" : ["IsTrivial","Tester(IsTrivial)","IsFinite","Tester(IsFinite)","CanComputeSize"]},"IsNonTrivial" : {"type" : "GAP_Property","implied" : ["IsNonTrivial","Tester(IsNonTrivial)"]},"IsFinite" : {"type" : "GAP_Property","implied" : ["IsFinite","Tester(IsFinite)"]},"IsWholeFamily" : {"type" : "GAP_Property","implied" : ["IsWholeFamily","Tester(IsWholeFamily)"]},"CanEasilyCompareElements" : {"type" : "GAP_Property","implied" : ["CanEasilyCompareElements","Tester(CanEasilyCompareElements)"]},"CanEasilySortElements" : {"type" : "GAP_Property","implied" : ["CanEasilyCompareElements","Tester(CanEasilyCompareElements)","CanEasilySortElements","Tester(CanEasilySortElements)"]},"IsSmallList" : {"type" : "GAP_Property","implied" : ["IsSmallList","Tester(IsSmallList)"]},"IsSortedList" : {"type" : "GAP_Property","implied" : ["IsSortedList","Tester(IsSortedList)"]},"IsSSortedList" : {"type" : "GAP_Property","implied" : ["IsSSortedList","Tester(IS_SSORT_LIST)","IsSortedList","Tester(IsSortedList)"]},"IsDuplicateFree" : {"type" : "GAP_Property","implied" : ["IsDuplicateFree","Tester(IsDuplicateFree)"]},"IsPositionsList" : {"type" : "GAP_Property","implied" : ["IsPositionsList","Tester(IS_POSS_LIST)"]},"IsZero" : {"type" : "GAP_Property","implied" : ["IsZero","Tester(IsZero)"]},"IsOne" : {"type" : "GAP_Property","implied" : ["IsOne","Tester(IsOne)"]},"IsCommutativeFamily" : {"type" : "GAP_Property","implied" : ["IsCommutativeFamily","Tester(IsCommutativeFamily)"]},"IsSkewFieldFamily" : {"type" : "GAP_Property","implied" : ["IsSkewFieldFamily","Tester(IsSkewFieldFamily)"]},"IsUFDFamily" : {"type" : "GAP_Property","implied" : ["IsUFDFamily","Tester(IsUFDFamily)"]},"IsIdempotent" : {"type" : "GAP_Property","implied" : ["IsIdempotent","Tester(IsIdempotent)"]},"IsIntegralCyclotomic" : {"type" : "GAP_Property","implied" : ["IsIntegralCyclotomic","Tester(IsIntegralCyclotomic)"]},"IsRectangularTable" : {"type" : "GAP_Property","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsRectangularTable","Tester(IsRectangularTable)"]},"IsPInfinity" : {"type" : "GAP_Property","implied" : ["IsPInfinity","Tester(IsPInfinity)"]},"IsNInfinity" : {"type" : "GAP_Property","implied" : ["IsNInfinity","Tester(IsNInfinity)"]},"IsXInfinity" : {"type" : "GAP_Property","implied" : ["IsXInfinity","Tester(IsXInfinity)"]},"IsNaN" : {"type" : "GAP_Property","implied" : ["IsNaN","Tester(IsNaN)"]},"IsLeftActedOnByDivisionRing" : {"type" : "GAP_Property","implied" : ["IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)"]},"IsConstantTimeAccessGeneralMapping" : {"type" : "GAP_Property","implied" : ["IsConstantTimeAccessGeneralMapping","Tester(IsConstantTimeAccessGeneralMapping)"]},"IsEndoGeneralMapping" : {"type" : "GAP_Property","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]},"IsTotal" : {"type" : "GAP_Property","implied" : ["IsTotal","Tester(IsTotal)"]},"IsSingleValued" : {"type" : "GAP_Property","implied" : ["IsSingleValued","Tester(IsSingleValued)"]},"IsInjective" : {"type" : "GAP_Property","implied" : ["IsInjective","Tester(IsInjective)"]},"IsSurjective" : {"type" : "GAP_Property","implied" : ["IsSurjective","Tester(IsSurjective)"]},"RespectsMultiplication" : {"type" : "GAP_Property","implied" : ["RespectsMultiplication","Tester(RespectsMultiplication)"]},"RespectsOne" : {"type" : "GAP_Property","implied" : ["RespectsOne","Tester(RespectsOne)"]},"RespectsInverses" : {"type" : "GAP_Property","implied" : ["RespectsInverses","Tester(RespectsInverses)"]},"RespectsAddition" : {"type" : "GAP_Property","implied" : ["RespectsAddition","Tester(RespectsAddition)"]},"RespectsZero" : {"type" : "GAP_Property","implied" : ["RespectsZero","Tester(RespectsZero)"]},"RespectsAdditiveInverses" : {"type" : "GAP_Property","implied" : ["RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)"]},"RespectsScalarMultiplication" : {"type" : "GAP_Property","implied" : ["RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]},"IsFieldHomomorphism" : {"type" : "GAP_Property","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]},"TransformsMultiplicationIntoAddition" : {"type" : "GAP_Property","implied" : ["TransformsMultiplicationIntoAddition","Tester(TransformsMultiplicationIntoAddition)"]},"TranformsOneIntoZero" : {"type" : "GAP_Property","implied" : ["TranformsOneIntoZero","Tester(TranformsOneIntoZero)"]},"TransformsInversesIntoAdditiveInverses" : {"type" : "GAP_Property","implied" : ["TransformsInversesIntoAdditiveInverses","Tester(TransformsInversesIntoAdditiveInverses)"]},"TransformsAdditionIntoMultiplication" : {"type" : "GAP_Property","implied" : ["TransformsAdditionIntoMultiplication","Tester(TransformsAdditionIntoMultiplication)"]},"TransformsZeroIntoOne" : {"type" : "GAP_Property","implied" : ["TransformsZeroIntoOne","Tester(TransformsZeroIntoOne)"]},"TransformsAdditiveInversesIntoInverses" : {"type" : "GAP_Property","implied" : ["TransformsAdditiveInversesIntoInverses","Tester(TransformsAdditiveInversesIntoInverses)"]},"IsReflexiveBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)"]},"IsSymmetricBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)"]},"IsTransitiveBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)"]},"IsAntisymmetricBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsAntisymmetricBinaryRelation","Tester(IsAntisymmetricBinaryRelation)"]},"IsPreOrderBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)"]},"IsPartialOrderBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsPartialOrderBinaryRelation","Tester(IsPartialOrderBinaryRelation)"]},"IsLatticeOrderBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsPartialOrderBinaryRelation","Tester(IsPartialOrderBinaryRelation)","IsLatticeOrderBinaryRelation","Tester(IsLatticeOrderBinaryRelation)"]},"IsEquivalenceRelation" : {"type" : "GAP_Property","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]},"IsHasseDiagram" : {"type" : "GAP_Property","implied" : ["IsHasseDiagram","Tester(IsHasseDiagram)"]},"IsGeneratorsOfMagmaWithInverses" : {"type" : "GAP_Property","implied" : ["IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)"]},"IsAssociative" : {"type" : "GAP_Property","implied" : ["IsAssociative","Tester(IsAssociative)"]},"IsCommutative" : {"type" : "GAP_Property","implied" : ["IsCommutative","Tester(IsCommutative)"]},"IsLeftSemigroupCongruence" : {"type" : "GAP_Property","implied" : ["IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)"]},"IsRightSemigroupCongruence" : {"type" : "GAP_Property","implied" : ["IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)"]},"IsSemigroupCongruence" : {"type" : "GAP_Property","implied" : ["IsLeftSemigroupCongruence","Tester(IsLeftSemigroupCongruence)","IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)","IsSemigroupCongruence","Tester(IsSemigroupCongruence)"]},"IsReesCongruence" : {"type" : "GAP_Property","implied" : ["IsReesCongruence","Tester(IsReesCongruence)"]},"IsGeneratorsOfSemigroup" : {"type" : "GAP_Property","implied" : ["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsZeroGroup" : {"type" : "GAP_Property","implied" : ["IsZeroGroup","Tester(IsZeroGroup)","IsZeroSimpleSemigroup","Tester(IsZeroSimpleSemigroup)"]},"IsSimpleSemigroup" : {"type" : "GAP_Property","implied" : ["IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)"]},"IsZeroSimpleSemigroup" : {"type" : "GAP_Property","implied" : ["IsZeroSimpleSemigroup","Tester(IsZeroSimpleSemigroup)"]},"IsReesCongruenceSemigroup" : {"type" : "GAP_Property","implied" : ["IsReesCongruenceSemigroup","Tester(IsReesCongruenceSemigroup)"]},"IsRegularSemigroup" : {"type" : "GAP_Property","implied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)"]},"IsInverseSemigroup" : {"type" : "GAP_Property","implied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},"IsBand" : {"type" : "GAP_Property","implied" : ["IsBand","Tester(IsBand)"]},"IsBrandtSemigroup" : {"type" : "GAP_Property","implied" : ["IsBrandtSemigroup","Tester(IsBrandtSemigroup)"]},"IsCliffordSemigroup" : {"type" : "GAP_Property","implied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCliffordSemigroup","Tester(IsCliffordSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},"IsCommutativeSemigroup" : {"type" : "GAP_Property","implied" : ["IsCommutativeSemigroup","Tester(IsCommutativeSemigroup)"]},"IsCompletelyRegularSemigroup" : {"type" : "GAP_Property","implied" : ["IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)"]},"IsCompletelySimpleSemigroup" : {"type" : "GAP_Property","implied" : ["IsCompletelySimpleSemigroup","Tester(IsCompletelySimpleSemigroup)"]},"IsGroupAsSemigroup" : {"type" : "GAP_Property","implied" : ["IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},"IsIdempotentGenerated" : {"type" : "GAP_Property","implied" : ["IsIdempotentGenerated","Tester(IsIdempotentGenerated)","IsSemiband","Tester(IsSemiband)"]},"IsLeftZeroSemigroup" : {"type" : "GAP_Property","implied" : ["IsLeftZeroSemigroup","Tester(IsLeftZeroSemigroup)"]},"IsMonogenicSemigroup" : {"type" : "GAP_Property","implied" : ["IsMonogenicSemigroup","Tester(IsMonogenicSemigroup)"]},"IsMonoidAsSemigroup" : {"type" : "GAP_Property","implied" : ["IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)"]},"IsNilpotentSemigroup" : {"type" : "GAP_Property","implied" : ["IsNilpotentSemigroup","Tester(IsNilpotentSemigroup)"]},"IsOrthodoxSemigroup" : {"type" : "GAP_Property","implied" : ["IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},"IsRectangularBand" : {"type" : "GAP_Property","implied" : ["IsRectangularBand","Tester(IsRectangularBand)"]},"IsRightZeroSemigroup" : {"type" : "GAP_Property","implied" : ["IsRightZeroSemigroup","Tester(IsRightZeroSemigroup)"]},"IsSemiband" : {"type" : "GAP_Property","implied" : ["IsSemiband","Tester(IsSemiband)"]},"IsSemilattice" : {"type" : "GAP_Property","implied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsBand","Tester(IsBand)","IsCliffordSemigroup","Tester(IsCliffordSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsIdempotentGenerated","Tester(IsIdempotentGenerated)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSemiband","Tester(IsSemiband)","IsSemilattice","Tester(IsSemilattice)"]},"IsZeroSemigroup" : {"type" : "GAP_Property","implied" : ["IsZeroSemigroup","Tester(IsZeroSemigroup)"]},"IsLeftSemigroupIdeal" : {"type" : "GAP_Property","implied" : ["IsLeftSemigroupIdeal","Tester(IsLeftSemigroupIdeal)"]},"IsRightSemigroupIdeal" : {"type" : "GAP_Property","implied" : ["IsRightSemigroupIdeal","Tester(IsRightSemigroupIdeal)"]},"IsSemigroupIdeal" : {"type" : "GAP_Property","implied" : ["IsSemigroupIdeal","Tester(IsSemigroupIdeal)"]},"IsCyclic" : {"type" : "GAP_Property","implied" : ["IsCyclic","Tester(IsCyclic)"]},"IsElementaryAbelian" : {"type" : "GAP_Property","implied" : ["IsElementaryAbelian","Tester(IsElementaryAbelian)"]},"IsFinitelyGeneratedGroup" : {"type" : "GAP_Property","implied" : ["IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)"]},"IsSubsetLocallyFiniteGroup" : {"type" : "GAP_Property","implied" : ["IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)"]},"KnowsHowToDecompose" : {"type" : "GAP_Property","implied" : ["KnowsHowToDecompose","Tester(KnowsHowToDecompose)"]},"IsPGroup" : {"type" : "GAP_Property","implied" : ["IsPGroup","Tester(IsPGroup)"]},"IsNilpotentGroup" : {"type" : "GAP_Property","implied" : ["IsNilpotentGroup","Tester(IsNilpotentGroup)","IsSupersolvableGroup","Tester(IsSupersolvableGroup)","IsSolvableGroup","Tester(IsSolvableGroup)","IsNilpotentByFinite","Tester(IsNilpotentByFinite)"]},"IsPerfectGroup" : {"type" : "GAP_Property","implied" : ["IsPerfectGroup","Tester(IsPerfectGroup)"]},"IsSporadicSimpleGroup" : {"type" : "GAP_Property","implied" : ["IsSporadicSimpleGroup","Tester(IsSporadicSimpleGroup)"]},"IsSimpleGroup" : {"type" : "GAP_Property","implied" : ["IsSimpleGroup","Tester(IsSimpleGroup)"]},"IsAlmostSimpleGroup" : {"type" : "GAP_Property","implied" : ["IsAlmostSimpleGroup","Tester(IsAlmostSimpleGroup)"]},"IsSupersolvableGroup" : {"type" : "GAP_Property","implied" : ["IsSupersolvableGroup","Tester(IsSupersolvableGroup)","IsSolvableGroup","Tester(IsSolvableGroup)"]},"IsMonomialGroup" : {"type" : "GAP_Property","implied" : ["IsMonomialGroup","Tester(IsMonomialGroup)","IsSolvableGroup","Tester(IsSolvableGroup)"]},"IsSolvableGroup" : {"type" : "GAP_Property","implied" : ["IsSolvableGroup","Tester(IsSolvableGroup)"]},"IsPolycyclicGroup" : {"type" : "GAP_Property","implied" : ["IsSolvableGroup","Tester(IsSolvableGroup)","IsPolycyclicGroup","Tester(IsPolycyclicGroup)"]},"IsNormalInParent" : {"type" : "GAP_Property","implied" : ["IsNormalInParent","Tester(IsNormalInParent)"]},"IsGeneratorsOfInverseSemigroup" : {"type" : "GAP_Property","implied" : ["IsGeneratorsOfInverseSemigroup","Tester(IsGeneratorsOfInverseSemigroup)"]},"IsAdditivelyCommutative" : {"type" : "GAP_Property","implied" : ["IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]},"IsLDistributive" : {"type" : "GAP_Property","implied" : ["IsLDistributive","Tester(IsLDistributive)"]},"IsRDistributive" : {"type" : "GAP_Property","implied" : ["IsRDistributive","Tester(IsRDistributive)"]},"IsAnticommutative" : {"type" : "GAP_Property","implied" : ["IsAnticommutative","Tester(IsAnticommutative)"]},"IsIntegralRing" : {"type" : "GAP_Property","implied" : ["IsIntegralRing","Tester(IsIntegralRing)"]},"IsJacobianRing" : {"type" : "GAP_Property","implied" : ["IsJacobianRing","Tester(IsJacobianRing)"]},"IsZeroSquaredRing" : {"type" : "GAP_Property","implied" : ["IsZeroSquaredRing","Tester(IsZeroSquaredRing)"]},"IsZeroMultiplicationRing" : {"type" : "GAP_Property","implied" : ["IsZeroMultiplicationRing","Tester(IsZeroMultiplicationRing)"]},"IsGeneralizedCartanMatrix" : {"type" : "GAP_Property","implied" : ["IsGeneralizedCartanMatrix","Tester(IsGeneralizedCartanMatrix)"]},"IsMonomialMatrix" : {"type" : "GAP_Property","implied" : ["IsMonomialMatrix","Tester(IsMonomialMatrix)"]},"IsTwoSidedIdealInParent" : {"type" : "GAP_Property","implied" : ["IsTwoSidedIdealInParent","Tester(IsTwoSidedIdealInParent)","IsLeftIdealInParent","Tester(IsLeftIdealInParent)","IsRightIdealInParent","Tester(IsRightIdealInParent)"]},"IsLeftIdealInParent" : {"type" : "GAP_Property","implied" : ["IsLeftIdealInParent","Tester(IsLeftIdealInParent)"]},"IsRightIdealInParent" : {"type" : "GAP_Property","implied" : ["IsRightIdealInParent","Tester(IsRightIdealInParent)"]},"IsFiniteDimensional" : {"type" : "GAP_Property","implied" : ["IsFiniteDimensional","Tester(IsFiniteDimensional)"]},"IsFullRowModule" : {"type" : "GAP_Property","implied" : ["IsFullRowModule","Tester(IsFullRowModule)","IsRowModule","Tester(IsRowModule)"]},"IsFullMatrixModule" : {"type" : "GAP_Property","implied" : ["IsFullMatrixModule","Tester(IsFullMatrixModule)","IsMatrixModule","Tester(IsMatrixModule)"]},"IsRowModule" : {"type" : "GAP_Property","implied" : ["IsRowModule","Tester(IsRowModule)"]},"IsMatrixModule" : {"type" : "GAP_Property","implied" : ["IsMatrixModule","Tester(IsMatrixModule)"]},"IsCanonicalBasis" : {"type" : "GAP_Property","implied" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)"]},"IsCanonicalBasisFullRowModule" : {"type" : "GAP_Property","implied" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullRowModule","Tester(IsCanonicalBasisFullRowModule)"]},"IsCanonicalBasisFullMatrixModule" : {"type" : "GAP_Property","implied" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullMatrixModule","Tester(IsCanonicalBasisFullMatrixModule)"]},"IsIntegralBasis" : {"type" : "GAP_Property","implied" : ["IsIntegralBasis","Tester(IsIntegralBasis)"]},"IsNormalBasis" : {"type" : "GAP_Property","implied" : ["IsNormalBasis","Tester(IsNormalBasis)"]},"IsSemiEchelonized" : {"type" : "GAP_Property","implied" : ["IsSemiEchelonized","Tester(IsSemiEchelonized)"]},"IsVectorSpaceHomomorphism" : {"type" : "GAP_Property","implied" : ["IsVectorSpaceHomomorphism","Tester(IsVectorSpaceHomomorphism)"]},"IsFullHomModule" : {"type" : "GAP_Property","implied" : ["IsFullHomModule","Tester(IsFullHomModule)"]},"IsPseudoCanonicalBasisFullHomModule" : {"type" : "GAP_Property","implied" : ["IsPseudoCanonicalBasisFullHomModule","Tester(IsPseudoCanonicalBasisFullHomModule)"]},"IsSimpleAlgebra" : {"type" : "GAP_Property","implied" : ["IsSimpleAlgebra","Tester(IsSimpleAlgebra)"]},"IsGroupRing" : {"type" : "GAP_Property","implied" : ["IsGroupRing","Tester(IsGroupRing)"]},"IsFullFpAlgebra" : {"type" : "GAP_Property","implied" : ["IsFullFpAlgebra","Tester(IsFullFpAlgebra)"]},"IsNormalForm" : {"type" : "GAP_Property","implied" : ["IsNormalForm","Tester(IsNormalForm)"]},"IsLieAbelian" : {"type" : "GAP_Property","implied" : ["IsLieAbelian","Tester(IsLieAbelian)","IsLieNilpotent","Tester(IsLieNilpotent)","IsLieSolvable","Tester(IsLieSolvable)"]},"IsLieNilpotent" : {"type" : "GAP_Property","implied" : ["IsLieNilpotent","Tester(IsLieNilpotent)","IsLieSolvable","Tester(IsLieSolvable)"]},"IsRestrictedLieAlgebra" : {"type" : "GAP_Property","implied" : ["IsRestrictedLieAlgebra","Tester(IsRestrictedLieAlgebra)"]},"IsLieSolvable" : {"type" : "GAP_Property","implied" : ["IsLieSolvable","Tester(IsLieSolvable)"]},"IsFullSCAlgebra" : {"type" : "GAP_Property","implied" : ["IsFullSCAlgebra","Tester(IsFullSCAlgebra)"]},"IsCanonicalBasisFullSCAlgebra" : {"type" : "GAP_Property","implied" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullSCAlgebra","Tester(IsCanonicalBasisFullSCAlgebra)"]},"IsAlgebraModule" : {"type" : "GAP_Property","implied" : ["IsAlgebraModule","Tester(IsAlgebraModule)"]},"IsLeftAlgebraModule" : {"type" : "GAP_Property","implied" : ["IsLeftAlgebraModule","Tester(IsLeftAlgebraModule)"]},"IsRightAlgebraModule" : {"type" : "GAP_Property","implied" : ["IsRightAlgebraModule","Tester(IsRightAlgebraModule)"]},"IsWeylGroup" : {"type" : "GAP_Property","implied" : ["IsWeylGroup","Tester(IsWeylGroup)"]},"IsPolynomial" : {"type" : "GAP_Property","implied" : ["IsPolynomial","Tester(IsPolynomial)"]},"IsUnivariateRationalFunction" : {"type" : "GAP_Property","implied" : ["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]},"IsLaurentPolynomial" : {"type" : "GAP_Property","implied" : ["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]},"IsConstantRationalFunction" : {"type" : "GAP_Property","implied" : ["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsConstantRationalFunction","Tester(IsConstantRationalFunction)"]},"IsPrimeField" : {"type" : "GAP_Property","implied" : ["IsPrimeField","Tester(IsPrimeField)"]},"IsNumberField" : {"type" : "GAP_Property","implied" : ["IsNumberField","Tester(IsNumberField)"]},"IsAbelianNumberField" : {"type" : "GAP_Property","implied" : ["IsNumberField","Tester(IsNumberField)","IsAbelianNumberField","Tester(IsAbelianNumberField)"]},"IsCyclotomicField" : {"type" : "GAP_Property","implied" : ["IsNumberField","Tester(IsNumberField)","IsAbelianNumberField","Tester(IsAbelianNumberField)","IsCyclotomicField","Tester(IsCyclotomicField)"]},"IsFreeSemigroup" : {"type" : "GAP_Property","implied" : ["IsFreeSemigroup","Tester(IsFreeSemigroup)"]},"IsFreeMonoid" : {"type" : "GAP_Property","implied" : ["IsFreeMonoid","Tester(IsFreeMonoid)"]},"IsBuiltFromAdditiveMagmaWithInverses" : {"type" : "GAP_Property","implied" : ["IsBuiltFromAdditiveMagmaWithInverses","Tester(IsBuiltFromAdditiveMagmaWithInverses)"]},"IsBuiltFromMagma" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)"]},"IsBuiltFromMagmaWithOne" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)"]},"IsBuiltFromMagmaWithInverses" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)"]},"IsBuiltFromGroup" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]},"IsBuiltFromSemigroup" : {"type" : "GAP_Property","implied" : ["IsBuiltFromSemigroup","Tester(IsBuiltFromSemigroup)"]},"IsBuiltFromMonoid" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMonoid","Tester(IsBuiltFromMonoid)"]},"IsConfluent" : {"type" : "GAP_Property","implied" : ["IsConfluent","Tester(IsConfluent)"]},"IsReduced" : {"type" : "GAP_Property","implied" : ["IsReduced","Tester(IsReduced)"]},"IsPcgsElementaryAbelianSeries" : {"type" : "GAP_Property","implied" : ["IsPcgsElementaryAbelianSeries","Tester(IsPcgsElementaryAbelianSeries)"]},"IsPcgsCentralSeries" : {"type" : "GAP_Property","implied" : ["IsPcgsCentralSeries","Tester(IsPcgsCentralSeries)"]},"IsPcgsPCentralSeriesPGroup" : {"type" : "GAP_Property","implied" : ["IsPcgsPCentralSeriesPGroup","Tester(IsPcgsPCentralSeriesPGroup)"]},"IsPcgsChiefSeries" : {"type" : "GAP_Property","implied" : ["IsPcgsChiefSeries","Tester(IsPcgsChiefSeries)"]},"IsPrimeOrdersPcgs" : {"type" : "GAP_Property","implied" : ["IsPrimeOrdersPcgs","Tester(IsPrimeOrdersPcgs)","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)"]},"IsFiniteOrdersPcgs" : {"type" : "GAP_Property","implied" : ["IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)"]},"IsCanonicalPcgs" : {"type" : "GAP_Property","implied" : ["IsCanonicalPcgs","Tester(IsCanonicalPcgs)"]},"IsParentPcgsFamilyPcgs" : {"type" : "GAP_Property","implied" : ["IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)"]},"IsFamilyPcgs" : {"type" : "GAP_Property","implied" : ["IsCanonicalPcgs","Tester(IsCanonicalPcgs)","IsParentPcgsFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsFamilyPcgs","Tester(IsFamilyPcgs)"]},"IsNumeratorParentPcgsFamilyPcgs" : {"type" : "GAP_Property","implied" : ["IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)"]},"IsSpecialPcgs" : {"type" : "GAP_Property","implied" : ["IsPcgsElementaryAbelianSeries","Tester(IsPcgsElementaryAbelianSeries)","IsSpecialPcgs","Tester(IsSpecialPcgs)"]},"IsInducedPcgsWrtSpecialPcgs" : {"type" : "GAP_Property","implied" : ["IsInducedPcgsWrtSpecialPcgs","Tester(IsInducedPcgsWrtSpecialPcgs)"]},"IsCanonicalPcgsWrtSpecialPcgs" : {"type" : "GAP_Property","implied" : ["IsCanonicalPcgsWrtSpecialPcgs","Tester(IsCanonicalPcgsWrtSpecialPcgs)"]},"IsConjugatorIsomorphism" : {"type" : "GAP_Property","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]},"IsInnerAutomorphism" : {"type" : "GAP_Property","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)","IsInnerAutomorphism","Tester(IsInnerAutomorphism)"]},"IsNaturalSymmetricGroup" : {"type" : "GAP_Property","implied" : ["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)","IsSymmetricGroup","Tester(IsSymmetricGroup)"]},"IsNaturalAlternatingGroup" : {"type" : "GAP_Property","implied" : ["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGroup)","IsAlternatingGroup","Tester(IsAlternatingGroup)"]},"IsAlternatingGroup" : {"type" : "GAP_Property","implied" : ["IsAlternatingGroup","Tester(IsAlternatingGroup)"]},"IsSymmetricGroup" : {"type" : "GAP_Property","implied" : ["IsSymmetricGroup","Tester(IsSymmetricGroup)"]},"IsDihedralGroup" : {"type" : "GAP_Property","implied" : ["IsDihedralGroup","Tester(IsDihedralGroup)"]},"IsQuaternionGroup" : {"type" : "GAP_Property","implied" : ["IsQuaternionGroup","Tester(IsQuaternionGroup)"]},"IsQuasiDihedralGroup" : {"type" : "GAP_Property","implied" : ["IsQuasiDihedralGroup","Tester(IsQuasiDihedralGroup)"]},"IsPSL" : {"type" : "GAP_Property","implied" : ["IsPSL","Tester(IsPSL)"]},"IsPQuotientSystem" : {"type" : "GAP_Property","implied" : ["IsPQuotientSystem","Tester(IsPQuotientSystem)"]},"IsNilpQuotientSystem" : {"type" : "GAP_Property","implied" : ["IsNilpQuotientSystem","Tester(IsNilpQuotientSystem)"]},"IsTransitive" : {"type" : "GAP_Property","implied" : ["IsTransitive","Tester(IsTransitive)"]},"IsPrimitive" : {"type" : "GAP_Property","implied" : ["IsPrimitive","Tester(IsPrimitive)"]},"IsPrimitiveAffine" : {"type" : "GAP_Property","implied" : ["IsPrimitiveAffine","Tester(IsPrimitiveAffine)"]},"IsSemiRegular" : {"type" : "GAP_Property","implied" : ["IsSemiRegular","Tester(IsSemiRegular)"]},"IsRegular" : {"type" : "GAP_Property","implied" : ["IsRegular","Tester(IsRegular)"]},"IsCentralFactor" : {"type" : "GAP_Property","implied" : ["IsCentralFactor","Tester(IsCentralFactor)"]},"IsFrattiniFree" : {"type" : "GAP_Property","implied" : ["IsFrattiniFree","Tester(IsFrattiniFree)"]},"IsWordDecompHomomorphism" : {"type" : "GAP_Property","implied" : ["IsWordDecompHomomorphism","Tester(IsWordDecompHomomorphism)"]},"IsCanonicalNiceMonomorphism" : {"type" : "GAP_Property","implied" : ["IsCanonicalNiceMonomorphism","Tester(IsCanonicalNiceMonomorphism)"]},"IsHandledByNiceMonomorphism" : {"type" : "GAP_Property","implied" : ["CanEasilyTestMembership","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)"]},"IsGroupOfAutomorphisms" : {"type" : "GAP_Property","implied" : ["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)"]},"IsGroupOfAutomorphismsFiniteGroup" : {"type" : "GAP_Property","implied" : ["IsFinite","Tester(IsFinite)","CanEasilyTestMembership","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)","IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)","IsGroupOfAutomorphismsFiniteGroup","Tester(IsGroupOfAutomorphismsFiniteGroup)"]},"IsAutomorphismGroup" : {"type" : "GAP_Property","implied" : ["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)","IsAutomorphismGroup","Tester(IsAutomorphismGroup)"]},"IsGeneralLinearGroup" : {"type" : "GAP_Property","implied" : ["IsGeneralLinearGroup","Tester(IsGeneralLinearGroup)"]},"IsNaturalGL" : {"type" : "GAP_Property","implied" : ["IsGeneralLinearGroup","Tester(IsGeneralLinearGroup)","IsNaturalGL","Tester(IsNaturalGL)"]},"IsSpecialLinearGroup" : {"type" : "GAP_Property","implied" : ["IsSpecialLinearGroup","Tester(IsSpecialLinearGroup)"]},"IsNaturalSL" : {"type" : "GAP_Property","implied" : ["IsSpecialLinearGroup","Tester(IsSpecialLinearGroup)","IsNaturalSL","Tester(IsNaturalSL)","IsSubgroupSL","Tester(IsSubgroupSL)"]},"IsSubgroupSL" : {"type" : "GAP_Property","implied" : ["IsSubgroupSL","Tester(IsSubgroupSL)"]},"IsFullSubgroupGLorSLRespectingBilinearForm" : {"type" : "GAP_Property","implied" : ["IsFullSubgroupGLorSLRespectingBilinearForm","Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"]},"IsFullSubgroupGLorSLRespectingSesquilinearForm" : {"type" : "GAP_Property","implied" : ["IsFullSubgroupGLorSLRespectingSesquilinearForm","Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]},"IsFullSubgroupGLorSLRespectingQuadraticForm" : {"type" : "GAP_Property","implied" : ["IsFullSubgroupGLorSLRespectingQuadraticForm","Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"]},"IsRationalMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)"]},"IsIntegerMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsRationalMatrixGroup","Tester(IsRationalMatrixGroup)","IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"]},"IsBravaisGroup" : {"type" : "GAP_Property","implied" : ["IsBravaisGroup","Tester(IsBravaisGroup)"]},"IsWellFoundedOrdering" : {"type" : "GAP_Property","implied" : ["IsWellFoundedOrdering","Tester(IsWellFoundedOrdering)"]},"IsTotalOrdering" : {"type" : "GAP_Property","implied" : ["IsTotalOrdering","Tester(IsTotalOrdering)"]},"IsOrderingOnFamilyOfAssocWords" : {"type" : "GAP_Property","implied" : ["IsOrderingOnFamilyOfAssocWords","Tester(IsOrderingOnFamilyOfAssocWords)"]},"IsTranslationInvariantOrdering" : {"type" : "GAP_Property","implied" : ["IsTranslationInvariantOrdering","Tester(IsTranslationInvariantOrdering)"]},"IsShortLexOrdering" : {"type" : "GAP_Property","implied" : ["IsShortLexOrdering","Tester(IsShortLexOrdering)"]},"IsWeightLexOrdering" : {"type" : "GAP_Property","implied" : ["IsWeightLexOrdering","Tester(IsWeightLexOrdering)"]},"IsBasicWreathProductOrdering" : {"type" : "GAP_Property","implied" : ["IsBasicWreathProductOrdering","Tester(IsBasicWreathProductOrdering)"]},"IsWreathProductOrdering" : {"type" : "GAP_Property","implied" : ["IsWreathProductOrdering","Tester(IsWreathProductOrdering)"]},"IsFiniteSemigroupGreensRelation" : {"type" : "GAP_Property","implied" : ["IsFiniteSemigroupGreensRelation","Tester(IsFiniteSemigroupGreensRelation)"]},"IsRegularDClass" : {"type" : "GAP_Property","implied" : ["IsRegularDClass","Tester(IsRegularDClass)"]},"IsGroupHClass" : {"type" : "GAP_Property","implied" : ["IsGroupHClass","Tester(IsGroupHClass)"]},"IsFpSemigpReducedElt" : {"type" : "GAP_Property","implied" : ["IsFpSemigpReducedElt","Tester(IsFpSemigpReducedElt)"]},"IsFpMonoidReducedElt" : {"type" : "GAP_Property","implied" : ["IsFpMonoidReducedElt","Tester(IsFpMonoidReducedElt)"]},"IsFullTransformationSemigroup" : {"type" : "GAP_Property","implied" : ["IsFullTransformationSemigroup","Tester(IsFullTransformationSemigroup)"]},"IsReesMatrixSemigroup" : {"type" : "GAP_Property","implied" : ["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]},"IsReesZeroMatrixSemigroup" : {"type" : "GAP_Property","implied" : ["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]},"IsSymmetricInverseSemigroup" : {"type" : "GAP_Property","implied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSymmetricInverseSemigroup","Tester(IsSymmetricInverseSemigroup)"]},"IsAlmostSimpleCharacterTable" : {"type" : "GAP_Property","implied" : ["IsAlmostSimpleCharacterTable","Tester(IsAlmostSimpleCharacterTable)"]},"IsMonomialCharacterTable" : {"type" : "GAP_Property","implied" : ["IsMonomialCharacterTable","Tester(IsMonomialCharacterTable)"]},"IsNilpotentCharacterTable" : {"type" : "GAP_Property","implied" : ["IsNilpotentCharacterTable","Tester(IsNilpotentCharacterTable)"]},"IsPerfectCharacterTable" : {"type" : "GAP_Property","implied" : ["IsPerfectCharacterTable","Tester(IsPerfectCharacterTable)"]},"IsSimpleCharacterTable" : {"type" : "GAP_Property","implied" : ["IsSimpleCharacterTable","Tester(IsSimpleCharacterTable)"]},"IsSolvableCharacterTable" : {"type" : "GAP_Property","implied" : ["IsSolvableCharacterTable","Tester(IsSolvableCharacterTable)"]},"IsSporadicSimpleCharacterTable" : {"type" : "GAP_Property","implied" : ["IsSporadicSimpleCharacterTable","Tester(IsSporadicSimpleCharacterTable)"]},"IsSupersolvableCharacterTable" : {"type" : "GAP_Property","implied" : ["IsSupersolvableCharacterTable","Tester(IsSupersolvableCharacterTable)"]},"IsCharacter" : {"type" : "GAP_Property","implied" : ["IsCharacter","Tester(IsCharacter)"]},"IsVirtualCharacter" : {"type" : "GAP_Property","implied" : ["IsVirtualCharacter","Tester(IsVirtualCharacter)"]},"IsIrreducibleCharacter" : {"type" : "GAP_Property","implied" : ["IsIrreducibleCharacter","Tester(IsIrreducibleCharacter)"]},"IsBergerCondition" : {"type" : "GAP_Property","implied" : ["IsBergerCondition","Tester(IsBergerCondition)"]},"IsPrimitiveCharacter" : {"type" : "GAP_Property","implied" : ["IsPrimitiveCharacter","Tester(IsPrimitiveCharacter)"]},"IsQuasiPrimitive" : {"type" : "GAP_Property","implied" : ["IsQuasiPrimitive","Tester(IsQuasiPrimitive)"]},"IsInducedFromNormalSubgroup" : {"type" : "GAP_Property","implied" : ["IsInducedFromNormalSubgroup","Tester(IsInducedFromNormalSubgroup)"]},"IsMonomialCharacter" : {"type" : "GAP_Property","implied" : ["IsMonomialCharacter","Tester(IsMonomialCharacter)"]},"IsMonomialNumber" : {"type" : "GAP_Property","implied" : ["IsMonomialNumber","Tester(IsMonomialNumber)"]},"IsSubnormallyMonomial" : {"type" : "GAP_Property","implied" : ["IsSubnormallyMonomial","Tester(IsSubnormallyMonomial)"]},"IsRelativelySM" : {"type" : "GAP_Property","implied" : ["IsRelativelySM","Tester(IsRelativelySM)"]},"IsMinimalNonmonomial" : {"type" : "GAP_Property","implied" : ["IsMinimalNonmonomial","Tester(IsMinimalNonmonomial)"]},"IsAbelianTom" : {"type" : "GAP_Property","implied" : ["IsAbelianTom","Tester(IsAbelianTom)"]},"IsCyclicTom" : {"type" : "GAP_Property","implied" : ["IsCyclicTom","Tester(IsCyclicTom)"]},"IsNilpotentTom" : {"type" : "GAP_Property","implied" : ["IsNilpotentTom","Tester(IsNilpotentTom)"]},"IsPerfectTom" : {"type" : "GAP_Property","implied" : ["IsPerfectTom","Tester(IsPerfectTom)"]},"IsSolvableTom" : {"type" : "GAP_Property","implied" : ["IsSolvableTom","Tester(IsSolvableTom)"]},"IsPrimitiveMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsPrimitiveMatrixGroup","Tester(IsPrimitiveMatrixGroup)"]},"IsUnitGroup" : {"type" : "GAP_Property","implied" : ["IsUnitGroup","Tester(IsUnitGroup)"]},"IsUnitGroupIsomorphism" : {"type" : "GAP_Property","implied" : ["IsUnitGroupIsomorphism","Tester(IsUnitGroupIsomorphism)"]},"IsNumberFieldByMatrices" : {"type" : "GAP_Property","implied" : ["IsNumberFieldByMatrices","Tester(IsNumberFieldByMatrices)"]},"IsMultGroupByFieldElemsIsomorphism" : {"type" : "GAP_Property","implied" : ["IsMultGroupByFieldElemsIsomorphism","Tester(IsMultGroupByFieldElemsIsomorphism)"]},"IsWeightedCollector" : {"type" : "GAP_Property","implied" : ["IsWeightedCollector","Tester(IsWeightedCollector)"]},"IsPolynomialCollector" : {"type" : "GAP_Property","implied" : ["IsPolynomialCollector","Tester(IsPolynomialCollector)"]},"UseLibraryCollector" : {"type" : "GAP_Property","implied" : ["UseLibraryCollector","Tester(UseLibraryCollector)"]},"IsPolycyclicPresentation" : {"type" : "GAP_Property","implied" : ["IsPolycyclicPresentation","Tester(IsPolycyclicPresentation)"]},"IsHomomorphismIntoMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsHomomorphismIntoMatrixGroup","Tester(IsHomomorphismIntoMatrixGroup)"]},"IsNilpotentByFinite" : {"type" : "GAP_Property","implied" : ["IsNilpotentByFinite","Tester(IsNilpotentByFinite)"]},"IsTorsionFree" : {"type" : "GAP_Property","implied" : ["IsTorsionFree","Tester(IsTorsionFree)"]},"IsFreeAbelian" : {"type" : "GAP_Property","implied" : ["IsFreeAbelian","Tester(IsFreeAbelian)"]},"IsGroupClass" : {"type" : "GAP_Property","implied" : ["IsGroupClass","Tester(IsGroupClass)"]},"ContainsTrivialGroup" : {"type" : "GAP_Property","implied" : ["ContainsTrivialGroup","Tester(ContainsTrivialGroup)"]},"IsSubgroupClosed" : {"type" : "GAP_Property","implied" : ["IsSubgroupClosed","Tester(IsSubgroupClosed)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)"]},"IsNormalSubgroupClosed" : {"type" : "GAP_Property","implied" : ["IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)"]},"IsQuotientClosed" : {"type" : "GAP_Property","implied" : ["IsQuotientClosed","Tester(IsQuotientClosed)"]},"IsResiduallyClosed" : {"type" : "GAP_Property","implied" : ["IsResiduallyClosed","Tester(IsResiduallyClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)"]},"IsNormalProductClosed" : {"type" : "GAP_Property","implied" : ["IsNormalProductClosed","Tester(IsNormalProductClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)"]},"IsDirectProductClosed" : {"type" : "GAP_Property","implied" : ["IsDirectProductClosed","Tester(IsDirectProductClosed)"]},"IsSchunckClass" : {"type" : "GAP_Property","implied" : ["ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsSchunckClass","Tester(IsSchunckClass)","IsSaturated","Tester(IsSaturated)"]},"IsSaturated" : {"type" : "GAP_Property","implied" : ["IsSaturated","Tester(IsSaturated)"]},"IsPrimitiveSolvableGroup" : {"type" : "GAP_Property","implied" : ["IsPrimitiveSolvableGroup","Tester(IsPrimitiveSolvableGroup)"]},"KnowsSomeGroupInfo" : {"type" : "GAP_Property","implied" : ["KnowsSomeGroupInfo","Tester(KnowsSomeGroupInfo)"]},"IsNontrivialDirectProduct" : {"type" : "GAP_Property","implied" : ["IsNontrivialDirectProduct","Tester(IsNontrivialDirectProduct)"]},"KnowsDeligneLusztigNames" : {"type" : "GAP_Property","implied" : ["KnowsDeligneLusztigNames","Tester(KnowsDeligneLusztigNames)"]},"IsDuplicateTable" : {"type" : "GAP_Property","implied" : ["IsDuplicateTable","Tester(IsDuplicateTable)"]},"IsIrreducibleMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsIrreducibleMatrixGroup","Tester(IsIrreducibleMatrixGroup)"]},"IsAbsolutelyIrreducibleMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsAbsolutelyIrreducibleMatrixGroup","Tester(IsAbsolutelyIrreducibleMatrixGroup)"]},"IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup","Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"]},"IsLieNilpotentOverFp" : {"type" : "GAP_Property","implied" : ["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]},"IsLieCover" : {"type" : "GAP_Property","implied" : ["IsLieCover","Tester(IsLieCover)"]},"IsLieAlgebraWithNB" : {"type" : "GAP_Property","implied" : ["IsLieAlgebraWithNB","Tester(IsLieAlgebraWithNB)"]},"IsNilpotentBasis" : {"type" : "GAP_Property","implied" : ["IsNilpotentBasis","Tester(IsNilpotentBasis)"]},"IsGroupAlgebra" : {"type" : "GAP_Property","implied" : ["IsGroupAlgebra","Tester(IsGroupAlgebra)"]},"IsFModularGroupAlgebra" : {"type" : "GAP_Property","implied" : ["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"]},"IsPModularGroupAlgebra" : {"type" : "GAP_Property","implied" : ["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]},"IsGroupOfUnitsOfMagmaRing" : {"type" : "GAP_Property","implied" : ["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]},"IsUnitGroupOfGroupRing" : {"type" : "GAP_Property","implied" : ["IsUnitGroupOfGroupRing","Tester(IsUnitGroupOfGroupRing)"]},"IsNormalizedUnitGroupOfGroupRing" : {"type" : "GAP_Property","implied" : ["IsListOrCollection","IsCollection","CanComputeSize","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","CanComputeSizeAnySubgroup","IsSolvableGroup","Tester(IsSolvableGroup)","CanEasilyComputePcgs","IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]},"IsLieAlgebraOfGroupRing" : {"type" : "GAP_Property","implied" : ["IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]},"IsBasisOfLieAlgebraOfGroupRing" : {"type" : "GAP_Property","implied" : ["IsBasisOfLieAlgebraOfGroupRing","Tester(IsBasisOfLieAlgebraOfGroupRing)"]},"IsLieMetabelian" : {"type" : "GAP_Property","implied" : ["IsLieMetabelian","Tester(IsLieMetabelian)"]},"IsLieCentreByMetabelian" : {"type" : "GAP_Property","implied" : ["IsLieCentreByMetabelian","Tester(IsLieCentreByMetabelian)"]},"IsSolvablePolynomial" : {"type" : "GAP_Property","implied" : ["IsSolvablePolynomial","Tester(IsSolvablePolynomial)"]},"IsSeparablePolynomial" : {"type" : "GAP_Property","implied" : ["IsSeparablePolynomial","Tester(IsSeparablePolynomial)"]},"IsAffineCrystGroupOnRight" : {"type" : "GAP_Property","implied" : ["CanComputeSize","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)","IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]},"IsAffineCrystGroupOnLeft" : {"type" : "GAP_Property","implied" : ["CanComputeSize","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)","IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]},"IsAffineCrystGroupOnLeftOrRight" : {"type" : "GAP_Property","implied" : ["CanComputeSize","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]},"IsSpaceGroup" : {"type" : "GAP_Property","implied" : ["IsSpaceGroup","Tester(IsSpaceGroup)"]},"IsStandardAffineCrystGroup" : {"type" : "GAP_Property","implied" : ["IsStandardAffineCrystGroup","Tester(IsStandardAffineCrystGroup)"]},"IsSymmorphicSpaceGroup" : {"type" : "GAP_Property","implied" : ["IsSymmorphicSpaceGroup","Tester(IsSymmorphicSpaceGroup)"]},"IsPointGroup" : {"type" : "GAP_Property","implied" : ["IsPointGroup","Tester(IsPointGroup)"]},"IsPointHomomorphism" : {"type" : "GAP_Property","implied" : ["IsPointHomomorphism","Tester(IsPointHomomorphism)"]},"IsFromAffineCrystGroupToFpGroup" : {"type" : "GAP_Property","implied" : ["IsFromAffineCrystGroupToFpGroup","Tester(IsFromAffineCrystGroupToFpGroup)"]},"IsFromAffineCrystGroupToPcpGroup" : {"type" : "GAP_Property","implied" : ["IsFromAffineCrystGroupToPcpGroup","Tester(IsFromAffineCrystGroupToPcpGroup)"]},"IsColorGroup" : {"type" : "GAP_Property","implied" : ["IsColorGroup","Tester(IsColorGroup)"]},"IsAlmostCrystallographic" : {"type" : "GAP_Property","implied" : ["IsAlmostCrystallographic","Tester(IsAlmostCrystallographic)"]},"IsAlmostBieberbachGroup" : {"type" : "GAP_Property","implied" : ["IsAlmostBieberbachGroup","Tester(IsAlmostBieberbachGroup)"]},"IsIsomorphismByFinitePolycyclicMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsIsomorphismByFinitePolycyclicMatrixGroup","Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"]},"IsIsomorphismByPolycyclicMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsIsomorphismByPolycyclicMatrixGroup","Tester(IsIsomorphismByPolycyclicMatrixGroup)"]},"IsTriangularizableMatGroup" : {"type" : "GAP_Property","implied" : ["IsTriangularizableMatGroup","Tester(IsTriangularizableMatGroup)"]},"IsZ_pi" : {"type" : "GAP_Property","implied" : ["IsZ_pi","Tester(IsZ_pi)"]},"IsResidueClass" : {"type" : "GAP_Property","implied" : ["IsResidueClass","Tester(IsResidueClass)"]},"IsZxZ" : {"type" : "GAP_Property","implied" : ["IsZxZ","Tester(IsZxZ)"]},"IsResidueClassWithFixedRepresentative" : {"type" : "GAP_Property","implied" : ["IsResidueClassWithFixedRepresentative","Tester(IsResidueClassWithFixedRepresentative)"]},"IsOverlappingFree" : {"type" : "GAP_Property","implied" : ["IsOverlappingFree","Tester(IsOverlappingFree)"]},"IsMutable" : {"type" : "GAP_Category","implied" : ["IsMutable","IsCopyable"]},"IsCopyable" : {"type" : "GAP_Category","implied" : ["IsCopyable"]},"IsFunction" : {"type" : "GAP_Category","implied" : ["IsFunction"]},"IsOperation" : {"type" : "GAP_Category","implied" : ["IsFunction","IsOperation"]},"IsInt" : {"type" : "GAP_Category","implied" : ["IsInt","IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},"IsRat" : {"type" : "GAP_Category","implied" : ["IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},"IsCyc" : {"type" : "GAP_Category","implied" : ["IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},"Tester(CONDUCTOR)" : {"type" : "GAP_Attribute","implied" : ["Tester(CONDUCTOR)"]},"IsFFE" : {"type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement"]},"IsPerm" : {"type" : "GAP_Category","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement"]},"IsTransformation" : {"type" : "GAP_Category","implied" : ["IsTransformation","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement"]},"IsPartialPerm" : {"type" : "GAP_Category","implied" : ["IsPartialPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement"]},"IsBool" : {"type" : "GAP_Category","implied" : ["IsBool"]},"IsRecord" : {"type" : "GAP_Category","implied" : ["IsRecord"]},"IsList" : {"type" : "GAP_Category","implied" : ["IsList","IsListOrCollection"]},"IsDenseList" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsListOrCollection"]},"IsHomogeneousList" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection"]},"IsTable" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection"]},"Tester(LENGTH)" : {"type" : "GAP_Attribute","implied" : ["Tester(LENGTH)"]},"Tester(IS_SSORT_LIST)" : {"type" : "GAP_Tester","implied" : ["Tester(IS_SSORT_LIST)"]},"Tester(IS_POSS_LIST)" : {"type" : "GAP_Tester","implied" : ["Tester(IS_POSS_LIST)"]},"IsPlistRep" : {"type" : "GAP_Representation","implied" : ["Tester(LENGTH)","IsPlistRep","IsInternalRep"]},"IsBlist" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsBlist","IsListOrCollection"]},"IsBlistRep" : {"type" : "GAP_Representation","implied" : ["IsBlistRep","IsInternalRep"]},"IsRange" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsRange","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsCyclotomic)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsRangeRep" : {"type" : "GAP_Representation","implied" : ["IsRangeRep","IsInternalRep"]},"IsString" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsString","IsListOrCollection"]},"IsStringRep" : {"type" : "GAP_Representation","implied" : ["IsStringRep","IsInternalRep"]},"IsWeakPointerObject" : {"type" : "GAP_Category","implied" : ["IsList","IsWeakPointerObject","IsListOrCollection","IsFinite","Tester(IsFinite)","IsSmallList","Tester(IsSmallList)"]},"IsNoImmediateMethodsObject" : {"type" : "GAP_Filter","implied" : ["IsNoImmediateMethodsObject"]},"IsInternalRep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep"]},"IsPositionalObjectRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep"]},"IsComponentObjectRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep"]},"IsDataObjectRep" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep"]},"IsNonAtomicComponentObjectRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsNonAtomicComponentObjectRep"]},"IsReadOnlyPositionalObjectRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsReadOnlyPositionalObjectRep"]},"IsAtomicPositionalObjectRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsAtomicPositionalObjectRep"]},"IsAttributeStoringRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep"]},"IsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily"]},"IsType" : {"type" : "GAP_Category","implied" : ["IsType"]},"IsFamilyOfFamilies" : {"type" : "GAP_Category","implied" : ["IsFamily","IsFamilyOfFamilies"]},"IsFamilyOfTypes" : {"type" : "GAP_Category","implied" : ["IsFamily","IsFamilyOfTypes"]},"IsFamilyDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsFamilyDefaultRep"]},"IsTypeDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsTypeDefaultRep"]},"Tester(Name)" : {"type" : "GAP_Attribute","implied" : ["Tester(Name)"]},"Tester(InfoText)" : {"type" : "GAP_Attribute","implied" : ["Tester(InfoText)"]},"Tester(String)" : {"type" : "GAP_Attribute","implied" : ["Tester(String)"]},"Tester(IsImpossible)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsImpossible)"]},"IsPackedElementDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsPackedElementDefaultRep"]},"IsToBeDefinedObj" : {"type" : "GAP_Category","implied" : ["IsToBeDefinedObj"]},"IsLVarsBag" : {"type" : "GAP_Category","implied" : ["IsLVarsBag"]},"IsListOrCollection" : {"type" : "GAP_Category","implied" : ["IsListOrCollection"]},"IsCollection" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection"]},"Tester(CollectionsFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(CollectionsFamily)"]},"CategoryFamily(IsCollection)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsCollection)"]},"Tester(ElementsFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(ElementsFamily)"]},"IsStandardIterator" : {"type" : "GAP_Filter","implied" : ["IsStandardIterator"]},"IsIterator" : {"type" : "GAP_Category","implied" : ["IsIterator"]},"Tester(IsEmpty)" : {"type" : "GAP_Tester","implied" : ["Tester(IsEmpty)"]},"Tester(IsTrivial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTrivial)"]},"Tester(IsNonTrivial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNonTrivial)"]},"Tester(IsFinite)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFinite)"]},"Tester(IsWholeFamily)" : {"type" : "GAP_Tester","implied" : ["Tester(IsWholeFamily)"]},"Tester(Size)" : {"type" : "GAP_Attribute","implied" : ["Tester(Size)","CanComputeSize"]},"Tester(Representative)" : {"type" : "GAP_Attribute","implied" : ["Tester(Representative)"]},"Tester(RepresentativeSmallest)" : {"type" : "GAP_Attribute","implied" : ["Tester(RepresentativeSmallest)"]},"Tester(PseudoRandomSeed)" : {"type" : "GAP_Attribute","implied" : ["Tester(PseudoRandomSeed)"]},"Tester(Enumerator)" : {"type" : "GAP_Attribute","implied" : ["Tester(Enumerator)"]},"Tester(EnumeratorSorted)" : {"type" : "GAP_Attribute","implied" : ["Tester(EnumeratorSorted)"]},"Tester(UnderlyingCollection)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingCollection)"]},"Tester(AsList)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsList)"]},"Tester(AsSortedList)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSortedList)"]},"Tester(AsSSortedList)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSSortedList)"]},"Tester(CanEasilyCompareElements)" : {"type" : "GAP_Tester","implied" : ["Tester(CanEasilyCompareElements)"]},"Tester(CanEasilySortElements)" : {"type" : "GAP_Tester","implied" : ["Tester(CanEasilySortElements)"]},"CanComputeSize" : {"type" : "GAP_Filter","implied" : ["CanComputeSize"]},"Tester(RandomizerAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(RandomizerAttr)"]},"Tester(CheapRandomizerAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(CheapRandomizerAttr)"]},"IsConstantTimeAccessList" : {"type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsConstantTimeAccessList"]},"Tester(IsSmallList)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSmallList)"]},"Tester(ConstantTimeAccessList)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConstantTimeAccessList)"]},"Tester(IsSortedList)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSortedList)"]},"Tester(IsDuplicateFree)" : {"type" : "GAP_Tester","implied" : ["Tester(IsDuplicateFree)"]},"IsQuickPositionList" : {"type" : "GAP_Filter","implied" : ["IsQuickPositionList"]},"Tester(AsDuplicateFreeList)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsDuplicateFreeList)"]},"Tester(SortingPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(SortingPerm)"]},"IsExtAElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement"]},"CategoryCollections(IsExtAElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)"]},"CategoryCollections(CategoryCollections(IsExtAElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtAElement))"]},"IsNearAdditiveElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement"]},"CategoryCollections(IsNearAdditiveElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)"]},"CategoryCollections(CategoryCollections(IsNearAdditiveElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))"]},"IsNearAdditiveElementWithZero" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero"]},"CategoryCollections(IsNearAdditiveElementWithZero)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)"]},"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))"]},"IsNearAdditiveElementWithInverse" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse"]},"CategoryCollections(IsNearAdditiveElementWithInverse)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)"]},"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))"]},"IsAdditiveElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsAdditiveElement"]},"CategoryCollections(IsAdditiveElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsAdditiveElement)"]},"CategoryCollections(CategoryCollections(IsAdditiveElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditiveElement))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))"]},"IsExtLElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement"]},"CategoryCollections(IsExtLElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)"]},"CategoryCollections(CategoryCollections(IsExtLElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtLElement))"]},"IsExtRElement" : {"type" : "GAP_Category","implied" : ["IsExtRElement"]},"CategoryCollections(IsExtRElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtRElement","CategoryCollections(IsExtRElement)"]},"CategoryCollections(CategoryCollections(IsExtRElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtRElement))"]},"IsMultiplicativeElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement"]},"CategoryCollections(IsMultiplicativeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)"]},"CategoryCollections(CategoryCollections(IsMultiplicativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))"]},"IsMultiplicativeElementWithOne" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne"]},"CategoryCollections(IsMultiplicativeElementWithOne)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)"]},"CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))"]},"IsMultiplicativeElementWithInverse" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse"]},"CategoryCollections(IsMultiplicativeElementWithInverse)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)"]},"CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))"]},"IsOddAdditiveNestingDepthFamily" : {"type" : "GAP_Filter","implied" : ["IsOddAdditiveNestingDepthFamily"]},"IsOddAdditiveNestingDepthObject" : {"type" : "GAP_Filter","implied" : ["IsOddAdditiveNestingDepthObject"]},"IsGeneralizedRowVector" : {"type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsGeneralizedRowVector"]},"IsMultiplicativeGeneralizedRowVector" : {"type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVector"]},"Tester(NestingDepthA)" : {"type" : "GAP_Attribute","implied" : ["Tester(NestingDepthA)"]},"Tester(NestingDepthM)" : {"type" : "GAP_Attribute","implied" : ["Tester(NestingDepthM)"]},"CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))"]},"CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))"]},"IsZDFRE" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE"]},"CategoryCollections(IsZDFRE)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)"]},"CategoryCollections(CategoryCollections(IsZDFRE))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))"]},"CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))"]},"IsOrdinaryMatrix" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","IsMultiplicativeElement","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVector","IsOrdinaryMatrix"]},"CategoryCollections(IsOrdinaryMatrix)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))","CategoryCollections(IsOrdinaryMatrix)"]},"IsLieMatrix" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","IsMultiplicativeElement","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVector","IsLieMatrix"]},"IsAssociativeElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement"]},"CategoryCollections(IsAssociativeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"CategoryCollections(CategoryCollections(IsAssociativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsAssociativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsAdditivelyCommutativeElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsAdditivelyCommutativeElement"]},"CategoryCollections(IsAdditivelyCommutativeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsAdditivelyCommutativeElement)"]},"CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))"]},"CategoryFamily(IsAdditivelyCommutativeElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsAdditivelyCommutativeElement)"]},"IsCommutativeElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsCommutativeElement"]},"CategoryCollections(IsCommutativeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsCommutativeElement)"]},"CategoryCollections(CategoryCollections(IsCommutativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))"]},"IsFiniteOrderElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsFiniteOrderElement"]},"CategoryCollections(IsFiniteOrderElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsFiniteOrderElement)"]},"CategoryCollections(CategoryCollections(IsFiniteOrderElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsFiniteOrderElement))"]},"IsJacobianElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement"]},"CategoryCollections(IsJacobianElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)"]},"CategoryCollections(CategoryCollections(IsJacobianElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsJacobianElement))"]},"IsRestrictedJacobianElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement","IsRestrictedJacobianElement"]},"CategoryCollections(IsRestrictedJacobianElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)","CategoryCollections(IsRestrictedJacobianElement)"]},"CategoryCollections(CategoryCollections(IsRestrictedJacobianElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsJacobianElement))","CategoryCollections(CategoryCollections(IsRestrictedJacobianElement))"]},"IsZeroSquaredElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsZeroSquaredElement"]},"CategoryCollections(IsZeroSquaredElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsZeroSquaredElement)"]},"CategoryCollections(CategoryCollections(IsZeroSquaredElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsZeroSquaredElement))"]},"Tester(IsZero)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZero)"]},"Tester(IsOne)" : {"type" : "GAP_Tester","implied" : ["Tester(IsOne)"]},"Tester(ZeroImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(ZeroImmutable)"]},"Tester(AdditiveInverseImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdditiveInverseImmutable)"]},"Tester(OneImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(OneImmutable)"]},"Tester(InverseImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(InverseImmutable)"]},"Tester(Int)" : {"type" : "GAP_Attribute","implied" : ["Tester(Int)"]},"Tester(Rat)" : {"type" : "GAP_Attribute","implied" : ["Tester(Rat)"]},"Tester(Characteristic)" : {"type" : "GAP_Attribute","implied" : ["Tester(Characteristic)"]},"Tester(Order)" : {"type" : "GAP_Attribute","implied" : ["Tester(Order)"]},"Tester(NormedRowVector)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormedRowVector)"]},"Tester(IsCommutativeFamily)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCommutativeFamily)"]},"Tester(IsSkewFieldFamily)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSkewFieldFamily)"]},"Tester(IsUFDFamily)" : {"type" : "GAP_Tester","implied" : ["Tester(IsUFDFamily)"]},"IsAdditiveElementAsMultiplicativeElementRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAdditiveElementAsMultiplicativeElementRep"]},"Tester(AdditiveElementsAsMultiplicativeElementsFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdditiveElementsAsMultiplicativeElementsFamily)"]},"Tester(AdditiveElementAsMultiplicativeElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdditiveElementAsMultiplicativeElement)"]},"Tester(IsIdempotent)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIdempotent)"]},"CategoryCollections(IsFFE)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsFFE)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"CategoryCollections(CategoryCollections(IsFFE))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))"]},"IsLexOrderedFFE" : {"type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsLexOrderedFFE"]},"IsLogOrderedFFE" : {"type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsLogOrderedFFE"]},"CategoryFamily(IsFFE)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsAdditivelyCommutativeElement)","CategoryFamily(IsFFE)"]},"Tester(DegreeFFE)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeFFE)"]},"Tester(IntFFE)" : {"type" : "GAP_Attribute","implied" : ["Tester(IntFFE)"]},"Tester(IntFFESymm)" : {"type" : "GAP_Attribute","implied" : ["Tester(IntFFESymm)"]},"Tester(AsInternalFFE)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsInternalFFE)"]},"IsGeneralizedDomain" : {"type" : "GAP_Category","implied" : ["IsGeneralizedDomain"]},"Tester(GeneratorsOfDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfDomain)"]},"Tester(ParentAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(ParentAttr)"]},"IsChar" : {"type" : "GAP_Category","implied" : ["IsChar"]},"CategoryCollections(IsChar)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsChar)"]},"IsCyclotomic" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},"CategoryCollections(IsCyclotomic)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsCyclotomic)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"CategoryCollections(CategoryCollections(IsCyclotomic))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))"]},"IsPosRat" : {"type" : "GAP_Category","implied" : ["IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsPosRat"]},"IsNegRat" : {"type" : "GAP_Category","implied" : ["IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsNegRat"]},"IsZeroCyc" : {"type" : "GAP_Category","implied" : ["IsInt","IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsZero","Tester(IsZero)","IsCyclotomic","IsZeroCyc"]},"IsSmallIntRep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsSmallIntRep"]},"IsInfinity" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsInfinity"]},"IsNegInfinity" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsNegInfinity"]},"Tester(IsIntegralCyclotomic)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIntegralCyclotomic)"]},"CategoryCollections(IsRecord)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsRecord)"]},"CategoryCollections(CategoryCollections(IsRecord))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsRecord))"]},"Tester(RecNames)" : {"type" : "GAP_Attribute","implied" : ["Tester(RecNames)"]},"IsEnumeratorByFunctionsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsEnumeratorByFunctionsRep"]},"IsIteratorByFunctionsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsIteratorByFunctionsRep"]},"IsListDefault" : {"type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVector","IsListDefault"]},"Tester(IsRectangularTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRectangularTable)"]},"CategoryCollections(IsPerm)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsFiniteOrderElement)","CategoryCollections(IsPerm)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)"]},"CategoryCollections(CategoryCollections(IsPerm))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsFiniteOrderElement))","CategoryCollections(CategoryCollections(IsPerm))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"Tester(SmallestGeneratorPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(SmallestGeneratorPerm)"]},"Tester(SmallestMovedPoint)" : {"type" : "GAP_Attribute","implied" : ["Tester(SmallestMovedPoint)"]},"Tester(LargestMovedPoint)" : {"type" : "GAP_Attribute","implied" : ["Tester(LargestMovedPoint)"]},"Tester(NrMovedPoints)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrMovedPoints)"]},"Tester(MovedPoints)" : {"type" : "GAP_Attribute","implied" : ["Tester(MovedPoints)"]},"Tester(SignPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(SignPerm)"]},"Tester(CycleStructurePerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(CycleStructurePerm)"]},"IsPerm2Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsPerm2Rep"]},"IsPerm4Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsPerm4Rep"]},"CategoryCollections(IsTransformation)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsTransformation)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"CategoryCollections(CategoryCollections(IsTransformation))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsTransformation))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsTrans2Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsTrans2Rep"]},"IsTrans4Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsTrans4Rep"]},"CategoryCollections(IsPartialPerm)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsPartialPerm)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsGeneratorsOfInverseSemigroup","Tester(IsGeneratorsOfInverseSemigroup)"]},"CategoryCollections(CategoryCollections(IsPartialPerm))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsPartialPerm))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsPPerm2Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsPPerm2Rep"]},"IsPPerm4Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsPPerm4Rep"]},"IsInfoClass" : {"type" : "GAP_Category","implied" : ["IsInfoClass"]},"CategoryCollections(IsInfoClass)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsInfoClass)"]},"IsDirectory" : {"type" : "GAP_Category","implied" : ["IsDirectory"]},"IsInputTextStringRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputTextStringRep"]},"IsClosedStream" : {"type" : "GAP_Category","implied" : ["IsClosedStream"]},"IsStream" : {"type" : "GAP_Category","implied" : ["IsStream"]},"IsInputStream" : {"type" : "GAP_Category","implied" : ["IsStream","IsInputStream"]},"IsInputTextStream" : {"type" : "GAP_Category","implied" : ["IsStream","IsInputStream","IsInputTextStream"]},"IsInputTextNone" : {"type" : "GAP_Category","implied" : ["IsStream","IsInputStream","IsInputTextStream","IsInputTextNone"]},"IsOutputStream" : {"type" : "GAP_Category","implied" : ["IsStream","IsOutputStream"]},"IsOutputTextStream" : {"type" : "GAP_Category","implied" : ["IsStream","IsOutputStream","IsOutputTextStream"]},"IsOutputTextNone" : {"type" : "GAP_Category","implied" : ["IsStream","IsOutputStream","IsOutputTextStream","IsOutputTextNone"]},"IsInputOutputStream" : {"type" : "GAP_Category","implied" : ["IsStream","IsInputStream","IsOutputStream","IsInputOutputStream"]},"IsRowVectorObj" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj"]},"IsMatrixObj" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj"]},"IsRowListMatrix" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix"]},"IsFlatMatrix" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsFlatMatrix"]},"IsGF2VectorRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsDataObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","IsGF2VectorRep"]},"IsGF2MatrixRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","IsGF2MatrixRep"]},"Is8BitVectorRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsDataObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","Is8BitVectorRep"]},"Is8BitMatrixRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","Is8BitMatrixRep"]},"IsInfoClassListRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInfoClassListRep"]},"IsRandomSource" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource"]},"IsGlobalRandomSource" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource","IsGlobalRandomSource"]},"IsGAPRandomSource" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource","IsGAPRandomSource"]},"IsMersenneTwister" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource","IsMersenneTwister"]},"IsFloat" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat"]},"IsFloatInterval" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsFloatInterval"]},"IsComplexFloat" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsComplexFloat"]},"IsComplexFloatInterval" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsFloatInterval","IsComplexFloat","IsComplexFloatInterval"]},"CategoryFamily(IsFloat)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsFloat)"]},"CategoryCollections(IsFloat)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsFloat)"]},"CategoryCollections(CategoryCollections(IsFloat))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFloat))"]},"Tester(Cos)" : {"type" : "GAP_Attribute","implied" : ["Tester(Cos)"]},"Tester(Sin)" : {"type" : "GAP_Attribute","implied" : ["Tester(Sin)"]},"Tester(Tan)" : {"type" : "GAP_Attribute","implied" : ["Tester(Tan)"]},"Tester(Sec)" : {"type" : "GAP_Attribute","implied" : ["Tester(Sec)"]},"Tester(Csc)" : {"type" : "GAP_Attribute","implied" : ["Tester(Csc)"]},"Tester(Cot)" : {"type" : "GAP_Attribute","implied" : ["Tester(Cot)"]},"Tester(Asin)" : {"type" : "GAP_Attribute","implied" : ["Tester(Asin)"]},"Tester(Acos)" : {"type" : "GAP_Attribute","implied" : ["Tester(Acos)"]},"Tester(Atan)" : {"type" : "GAP_Attribute","implied" : ["Tester(Atan)"]},"Tester(Cosh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Cosh)"]},"Tester(Sinh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Sinh)"]},"Tester(Tanh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Tanh)"]},"Tester(Sech)" : {"type" : "GAP_Attribute","implied" : ["Tester(Sech)"]},"Tester(Csch)" : {"type" : "GAP_Attribute","implied" : ["Tester(Csch)"]},"Tester(Coth)" : {"type" : "GAP_Attribute","implied" : ["Tester(Coth)"]},"Tester(Asinh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Asinh)"]},"Tester(Acosh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Acosh)"]},"Tester(Atanh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Atanh)"]},"Tester(Log2)" : {"type" : "GAP_Attribute","implied" : ["Tester(Log2)"]},"Tester(Log10)" : {"type" : "GAP_Attribute","implied" : ["Tester(Log10)"]},"Tester(Log1p)" : {"type" : "GAP_Attribute","implied" : ["Tester(Log1p)"]},"Tester(Exp)" : {"type" : "GAP_Attribute","implied" : ["Tester(Exp)"]},"Tester(Exp2)" : {"type" : "GAP_Attribute","implied" : ["Tester(Exp2)"]},"Tester(Exp10)" : {"type" : "GAP_Attribute","implied" : ["Tester(Exp10)"]},"Tester(Expm1)" : {"type" : "GAP_Attribute","implied" : ["Tester(Expm1)"]},"Tester(CubeRoot)" : {"type" : "GAP_Attribute","implied" : ["Tester(CubeRoot)"]},"Tester(Square)" : {"type" : "GAP_Attribute","implied" : ["Tester(Square)"]},"Tester(Ceil)" : {"type" : "GAP_Attribute","implied" : ["Tester(Ceil)"]},"Tester(Floor)" : {"type" : "GAP_Attribute","implied" : ["Tester(Floor)"]},"Tester(Round)" : {"type" : "GAP_Attribute","implied" : ["Tester(Round)"]},"Tester(Trunc)" : {"type" : "GAP_Attribute","implied" : ["Tester(Trunc)"]},"Tester(FrExp)" : {"type" : "GAP_Attribute","implied" : ["Tester(FrExp)"]},"Tester(Argument)" : {"type" : "GAP_Attribute","implied" : ["Tester(Argument)"]},"Tester(AbsoluteValue)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbsoluteValue)"]},"Tester(Frac)" : {"type" : "GAP_Attribute","implied" : ["Tester(Frac)"]},"Tester(SinCos)" : {"type" : "GAP_Attribute","implied" : ["Tester(SinCos)"]},"Tester(Erf)" : {"type" : "GAP_Attribute","implied" : ["Tester(Erf)"]},"Tester(Zeta)" : {"type" : "GAP_Attribute","implied" : ["Tester(Zeta)"]},"Tester(Gamma)" : {"type" : "GAP_Attribute","implied" : ["Tester(Gamma)"]},"Tester(ComplexI)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComplexI)"]},"Tester(PrecisionFloat)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrecisionFloat)"]},"Tester(SignFloat)" : {"type" : "GAP_Attribute","implied" : ["Tester(SignFloat)"]},"Tester(Sup)" : {"type" : "GAP_Attribute","implied" : ["Tester(Sup)"]},"Tester(Inf)" : {"type" : "GAP_Attribute","implied" : ["Tester(Inf)"]},"Tester(Mid)" : {"type" : "GAP_Attribute","implied" : ["Tester(Mid)"]},"Tester(AbsoluteDiameter)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbsoluteDiameter)"]},"Tester(RelativeDiameter)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelativeDiameter)"]},"Tester(IsPInfinity)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPInfinity)"]},"Tester(IsNInfinity)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNInfinity)"]},"Tester(IsXInfinity)" : {"type" : "GAP_Tester","implied" : ["Tester(IsXInfinity)"]},"Tester(IsNaN)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNaN)"]},"IsIEEE754FloatRep" : {"type" : "GAP_Representation","implied" : ["<<unknown>>","IsInternalRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsIEEE754FloatRep"]},"IsDirectoryRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsDirectoryRep"]},"IsInputTextFileRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputTextFileRep"]},"IsInputTextNoneRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputTextNoneRep"]},"IsOutputTextStringRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsOutputTextStringRep"]},"IsOutputTextFileRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsOutputTextFileRep"]},"IsOutputTextNoneRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsOutputTextNoneRep"]},"IsInputOutputStreamByPtyRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputOutputStreamByPtyRep"]},"IsDirectProductElement" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsList","IsDenseList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsDirectProductElement"]},"CategoryFamily(IsDirectProductElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsDirectProductElement)"]},"CategoryCollections(IsDirectProductElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsDirectProductElement)"]},"Tester(ComponentsOfDirectProductElementsFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComponentsOfDirectProductElementsFamily)"]},"IsDefaultDirectProductElementRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsList","IsDenseList","IsPositionalObjectRep","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsDirectProductElement","IsDefaultDirectProductElementRep"]},"Tester(EmptyRowVector)" : {"type" : "GAP_Attribute","implied" : ["Tester(EmptyRowVector)"]},"IsExtASet" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet"]},"IsAssociativeAOpDSum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpDSum"]},"IsAssociativeAOpESum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpESum"]},"IsTrivialAOpEZero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsTrivialAOpEZero"]},"Tester(GeneratorsOfExtASet)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfExtASet)"]},"Tester(AdditivelyActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdditivelyActingDomain)"]},"IsExtLSet" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet"]},"IsAssociativeLOpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd"]},"IsAssociativeLOpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd"]},"IsDistributiveLOpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpDProd"]},"IsDistributiveLOpDSum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpDSum"]},"IsDistributiveLOpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpEProd"]},"IsDistributiveLOpESum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpESum"]},"IsTrivialLOpEOne" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsTrivialLOpEOne"]},"IsTrivialLOpEZero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsTrivialLOpEZero"]},"IsLeftActedOnByRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsLeftActedOnByRing"]},"Tester(IsLeftActedOnByDivisionRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLeftActedOnByDivisionRing)"]},"IsLeftActedOnBySuperset" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsLeftActedOnBySuperset"]},"Tester(GeneratorsOfExtLSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfExtLSet)"]},"Tester(LeftActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeftActingDomain)"]},"IsExtRSet" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet"]},"IsAssociativeROpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsAssociativeROpDProd"]},"IsAssociativeROpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsAssociativeROpEProd"]},"IsDistributiveROpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpDProd"]},"IsDistributiveROpDSum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpDSum"]},"IsDistributiveROpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpEProd"]},"IsDistributiveROpESum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpESum"]},"IsTrivialROpEOne" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsTrivialROpEOne"]},"IsTrivialROpEZero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsTrivialROpEZero"]},"IsRightActedOnByRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsRightActedOnByRing"]},"IsRightActedOnByDivisionRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsRightActedOnByRing","IsRightActedOnByDivisionRing"]},"IsRightActedOnBySuperset" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsRightActedOnBySuperset"]},"Tester(GeneratorsOfExtRSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfExtRSet)"]},"Tester(RightActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightActingDomain)"]},"IsExtUSet" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet"]},"IsAssociativeUOpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsAssociativeUOpDProd"]},"IsAssociativeUOpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsAssociativeUOpEProd"]},"IsDistributiveUOpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpDProd"]},"IsDistributiveUOpDSum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpDSum"]},"IsDistributiveUOpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpEProd"]},"IsDistributiveUOpESum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpESum"]},"IsTrivialUOpEOne" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsTrivialUOpEOne"]},"IsTrivialUOpEZero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsTrivialUOpEZero"]},"IsUpperActedOnByGroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsUpperActedOnByGroup"]},"IsUpperActedOnBySuperset" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsUpperActedOnBySuperset"]},"Tester(GeneratorsOfExtUSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfExtUSet)"]},"Tester(UpperActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(UpperActingDomain)"]},"IsDictionary" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary"]},"IsLookupDictionary" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary"]},"IsHash" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsHash"]},"IsDictionaryDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDefaultRep"]},"IsListDictionary" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDefaultRep","IsListDictionary"]},"IsListLookupDictionary" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsDictionaryDefaultRep","IsListDictionary","IsListLookupDictionary"]},"IsSortDictionary" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDefaultRep","IsListDictionary","IsSortDictionary"]},"IsSortLookupDictionary" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsDictionaryDefaultRep","IsListDictionary","IsListLookupDictionary","IsSortDictionary","IsSortLookupDictionary"]},"IsPositionDictionary" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsDictionaryDefaultRep","IsPositionDictionary","IsPositionDictionary"]},"TableHasIntKeyFun" : {"type" : "GAP_Filter","implied" : ["TableHasIntKeyFun"]},"IsDenseHashRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsHash","IsDenseHashRep"]},"IsSparseHashRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsHash","IsSparseHashRep"]},"IsGeneralMapping" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping"]},"IsSPGeneralMapping" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping"]},"IsNonSPGeneralMapping" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping"]},"CategoryCollections(IsGeneralMapping)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsGeneralMapping)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"CategoryFamily(IsGeneralMapping)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsGeneralMapping)"]},"Tester(FamilyRange)" : {"type" : "GAP_Attribute","implied" : ["Tester(FamilyRange)"]},"Tester(FamilySource)" : {"type" : "GAP_Attribute","implied" : ["Tester(FamilySource)"]},"Tester(FamiliesOfGeneralMappingsAndRanges)" : {"type" : "GAP_Attribute","implied" : ["Tester(FamiliesOfGeneralMappingsAndRanges)"]},"Tester(IsConstantTimeAccessGeneralMapping)" : {"type" : "GAP_Tester","implied" : ["Tester(IsConstantTimeAccessGeneralMapping)"]},"Tester(IsEndoGeneralMapping)" : {"type" : "GAP_Tester","implied" : ["Tester(IsEndoGeneralMapping)"]},"Tester(IsTotal)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTotal)"]},"Tester(IsSingleValued)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSingleValued)"]},"Tester(IsInjective)" : {"type" : "GAP_Tester","implied" : ["Tester(IsInjective)"]},"Tester(IsSurjective)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSurjective)"]},"Tester(Range)" : {"type" : "GAP_Attribute","implied" : ["Tester(Range)"]},"Tester(Source)" : {"type" : "GAP_Attribute","implied" : ["Tester(Source)"]},"Tester(UnderlyingRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingRelation)"]},"Tester(UnderlyingGeneralMapping)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingGeneralMapping)"]},"Tester(IdentityMapping)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdentityMapping)"]},"Tester(InverseGeneralMapping)" : {"type" : "GAP_Attribute","implied" : ["Tester(InverseGeneralMapping)"]},"Tester(ImagesSource)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImagesSource)"]},"Tester(PreImagesRange)" : {"type" : "GAP_Attribute","implied" : ["Tester(PreImagesRange)"]},"IsCompositionMappingRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsCompositionMappingRep"]},"IsGeneralRestrictedMappingRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsGeneralRestrictedMappingRep"]},"Tester(MappingGeneratorsImages)" : {"type" : "GAP_Attribute","implied" : ["Tester(MappingGeneratorsImages)"]},"Tester(RespectsMultiplication)" : {"type" : "GAP_Tester","implied" : ["Tester(RespectsMultiplication)"]},"Tester(RespectsOne)" : {"type" : "GAP_Tester","implied" : ["Tester(RespectsOne)"]},"Tester(RespectsInverses)" : {"type" : "GAP_Tester","implied" : ["Tester(RespectsInverses)"]},"Tester(KernelOfMultiplicativeGeneralMapping)" : {"type" : "GAP_Attribute","implied" : ["Tester(KernelOfMultiplicativeGeneralMapping)"]},"Tester(CoKernelOfMultiplicativeGeneralMapping)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoKernelOfMultiplicativeGeneralMapping)"]},"Tester(RespectsAddition)" : {"type" : "GAP_Tester","implied" : ["Tester(RespectsAddition)"]},"Tester(RespectsZero)" : {"type" : "GAP_Tester","implied" : ["Tester(RespectsZero)"]},"Tester(RespectsAdditiveInverses)" : {"type" : "GAP_Tester","implied" : ["Tester(RespectsAdditiveInverses)"]},"Tester(KernelOfAdditiveGeneralMapping)" : {"type" : "GAP_Attribute","implied" : ["Tester(KernelOfAdditiveGeneralMapping)"]},"Tester(CoKernelOfAdditiveGeneralMapping)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoKernelOfAdditiveGeneralMapping)"]},"Tester(RespectsScalarMultiplication)" : {"type" : "GAP_Tester","implied" : ["Tester(RespectsScalarMultiplication)"]},"Tester(IsFieldHomomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFieldHomomorphism)"]},"Tester(TransformsMultiplicationIntoAddition)" : {"type" : "GAP_Tester","implied" : ["Tester(TransformsMultiplicationIntoAddition)"]},"Tester(TranformsOneIntoZero)" : {"type" : "GAP_Tester","implied" : ["Tester(TranformsOneIntoZero)"]},"Tester(TransformsInversesIntoAdditiveInverses)" : {"type" : "GAP_Tester","implied" : ["Tester(TransformsInversesIntoAdditiveInverses)"]},"Tester(TransformsAdditionIntoMultiplication)" : {"type" : "GAP_Tester","implied" : ["Tester(TransformsAdditionIntoMultiplication)"]},"Tester(TransformsZeroIntoOne)" : {"type" : "GAP_Tester","implied" : ["Tester(TransformsZeroIntoOne)"]},"Tester(TransformsAdditiveInversesIntoInverses)" : {"type" : "GAP_Tester","implied" : ["Tester(TransformsAdditiveInversesIntoInverses)"]},"Tester(Successors)" : {"type" : "GAP_Attribute","implied" : ["Tester(Successors)"]},"Tester(DegreeOfBinaryRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOfBinaryRelation)"]},"Tester(IsReflexiveBinaryRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsReflexiveBinaryRelation)"]},"Tester(IsSymmetricBinaryRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSymmetricBinaryRelation)"]},"Tester(IsTransitiveBinaryRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTransitiveBinaryRelation)"]},"Tester(IsAntisymmetricBinaryRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAntisymmetricBinaryRelation)"]},"Tester(IsPreOrderBinaryRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPreOrderBinaryRelation)"]},"Tester(IsPartialOrderBinaryRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPartialOrderBinaryRelation)"]},"Tester(IsLatticeOrderBinaryRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLatticeOrderBinaryRelation)"]},"Tester(IsEquivalenceRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsEquivalenceRelation)"]},"Tester(IsHasseDiagram)" : {"type" : "GAP_Tester","implied" : ["Tester(IsHasseDiagram)"]},"Tester(PartialOrderOfHasseDiagram)" : {"type" : "GAP_Attribute","implied" : ["Tester(PartialOrderOfHasseDiagram)"]},"Tester(EquivalenceRelationPartition)" : {"type" : "GAP_Attribute","implied" : ["Tester(EquivalenceRelationPartition)"]},"Tester(GeneratorsOfEquivalenceRelationPartition)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfEquivalenceRelationPartition)"]},"IsEquivalenceClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass"]},"Tester(EquivalenceClassRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(EquivalenceClassRelation)"]},"Tester(EquivalenceClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(EquivalenceClasses)"]},"IsMagma" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma"]},"IsMagmaWithOne" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)"]},"IsMagmaWithInversesIfNonzero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","Tester(MultiplicativeNeutralElement)"]},"IsMagmaWithInverses" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","Tester(MultiplicativeNeutralElement)"]},"Tester(AsMagma)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsMagma)"]},"Tester(GeneratorsOfMagma)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfMagma)"]},"Tester(GeneratorsOfMagmaWithOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfMagmaWithOne)"]},"Tester(GeneratorsOfMagmaWithInverses)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfMagmaWithInverses)"]},"Tester(IsGeneratorsOfMagmaWithInverses)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGeneratorsOfMagmaWithInverses)"]},"Tester(TrivialSubmagmaWithOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(TrivialSubmagmaWithOne)"]},"Tester(IsAssociative)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAssociative)"]},"Tester(IsCommutative)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCommutative)"]},"Tester(MultiplicativeNeutralElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(MultiplicativeNeutralElement)"]},"Tester(Centre)" : {"type" : "GAP_Attribute","implied" : ["Tester(Centre)"]},"Tester(Idempotents)" : {"type" : "GAP_Attribute","implied" : ["Tester(Idempotents)"]},"Tester(CentralizerInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(CentralizerInParent)"]},"Tester(MagmaGeneratorsOfFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(MagmaGeneratorsOfFamily)"]},"Tester(GeneratorsOfMagmaIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfMagmaIdeal)"]},"IsMultiplicativeElementWithZero" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithZero"]},"CategoryCollections(IsMultiplicativeElementWithZero)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithZero)"]},"Tester(MultiplicativeZero)" : {"type" : "GAP_Attribute","implied" : ["Tester(MultiplicativeZero)"]},"IsMagmaWithZeroAdjoinedElementRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithZero","IsMagmaWithZeroAdjoinedElementRep"]},"IsMagmaWithZeroAdjoined" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsMagmaWithZeroAdjoined"]},"Tester(InjectionZeroMagma)" : {"type" : "GAP_Attribute","implied" : ["Tester(InjectionZeroMagma)"]},"Tester(MagmaWithZeroAdjoined)" : {"type" : "GAP_Attribute","implied" : ["Tester(MagmaWithZeroAdjoined)"]},"Tester(UnderlyingInjectionZeroMagma)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingInjectionZeroMagma)"]},"IsLeftMagmaCongruence" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsLeftMagmaCongruence"]},"Tester(GeneratingPairsOfLeftMagmaCongruence)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratingPairsOfLeftMagmaCongruence)"]},"Tester(PartialClosureOfCongruence)" : {"type" : "GAP_Attribute","implied" : ["Tester(PartialClosureOfCongruence)"]},"IsRightMagmaCongruence" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsRightMagmaCongruence"]},"Tester(GeneratingPairsOfRightMagmaCongruence)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratingPairsOfRightMagmaCongruence)"]},"IsMagmaCongruence" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","RespectsMultiplication","Tester(RespectsMultiplication)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsLeftMagmaCongruence","IsRightMagmaCongruence","IsMagmaCongruence"]},"Tester(GeneratingPairsOfMagmaCongruence)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratingPairsOfMagmaCongruence)"]},"IsCongruenceClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsGeneralizedDomain","IsEquivalenceClass","IsCongruenceClass"]},"Tester(IsLeftSemigroupCongruence)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLeftSemigroupCongruence)"]},"Tester(IsRightSemigroupCongruence)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRightSemigroupCongruence)"]},"Tester(IsSemigroupCongruence)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSemigroupCongruence)"]},"Tester(IsReesCongruence)" : {"type" : "GAP_Tester","implied" : ["Tester(IsReesCongruence)"]},"Tester(AsSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSemigroup)"]},"Tester(IsGeneratorsOfSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGeneratorsOfSemigroup)"]},"Tester(CayleyGraphSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(CayleyGraphSemigroup)"]},"Tester(CayleyGraphDualSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(CayleyGraphDualSemigroup)"]},"Tester(IsZeroGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZeroGroup)"]},"Tester(IsSimpleSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSimpleSemigroup)"]},"Tester(IsZeroSimpleSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZeroSimpleSemigroup)"]},"Tester(ANonReesCongruenceOfSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(ANonReesCongruenceOfSemigroup)"]},"Tester(IsReesCongruenceSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsReesCongruenceSemigroup)"]},"Tester(IsRegularSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRegularSemigroup)"]},"Tester(IsInverseSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsInverseSemigroup)"]},"Tester(NilpotencyDegree)" : {"type" : "GAP_Attribute","implied" : ["Tester(NilpotencyDegree)"]},"Tester(IsBand)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBand)"]},"Tester(IsBrandtSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBrandtSemigroup)"]},"Tester(IsCliffordSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCliffordSemigroup)"]},"Tester(IsCommutativeSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCommutativeSemigroup)"]},"Tester(IsCompletelyRegularSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCompletelyRegularSemigroup)"]},"Tester(IsCompletelySimpleSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCompletelySimpleSemigroup)"]},"Tester(IsGroupAsSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupAsSemigroup)"]},"Tester(IsIdempotentGenerated)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIdempotentGenerated)"]},"Tester(IsLeftZeroSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLeftZeroSemigroup)"]},"Tester(IsMonogenicSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMonogenicSemigroup)"]},"Tester(IsMonoidAsSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMonoidAsSemigroup)"]},"Tester(IsNilpotentSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNilpotentSemigroup)"]},"Tester(IsOrthodoxSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsOrthodoxSemigroup)"]},"Tester(IsRectangularBand)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRectangularBand)"]},"Tester(IsRightZeroSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRightZeroSemigroup)"]},"Tester(IsSemiband)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSemiband)"]},"Tester(IsSemilattice)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSemilattice)"]},"Tester(IsZeroSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZeroSemigroup)"]},"Tester(IsLeftSemigroupIdeal)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLeftSemigroupIdeal)"]},"Tester(IsRightSemigroupIdeal)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRightSemigroupIdeal)"]},"Tester(IsSemigroupIdeal)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSemigroupIdeal)"]},"Tester(ReesCongruenceOfSemigroupIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(ReesCongruenceOfSemigroupIdeal)"]},"Tester(AsMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsMonoid)"]},"Tester(NameIsomorphismClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(NameIsomorphismClass)"]},"Tester(IsCyclic)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCyclic)"]},"Tester(IsElementaryAbelian)" : {"type" : "GAP_Tester","implied" : ["Tester(IsElementaryAbelian)"]},"Tester(IsFinitelyGeneratedGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFinitelyGeneratedGroup)"]},"Tester(IsSubsetLocallyFiniteGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSubsetLocallyFiniteGroup)"]},"CanEasilyTestMembership" : {"type" : "GAP_Filter","implied" : ["CanEasilyTestMembership"]},"CanEasilyComputeWithIndependentGensAbelianGroup" : {"type" : "GAP_Filter","implied" : ["CanEasilyComputeWithIndependentGensAbelianGroup"]},"CanComputeSizeAnySubgroup" : {"type" : "GAP_Filter","implied" : ["CanComputeSize","CanComputeSizeAnySubgroup"]},"Tester(KnowsHowToDecompose)" : {"type" : "GAP_Tester","implied" : ["Tester(KnowsHowToDecompose)"]},"Tester(IsPGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPGroup)"]},"Tester(PrimePGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimePGroup)"]},"Tester(PClassPGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(PClassPGroup)"]},"Tester(RankPGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RankPGroup)"]},"Tester(IsNilpotentGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNilpotentGroup)"]},"Tester(IsPerfectGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPerfectGroup)"]},"Tester(IsSporadicSimpleGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSporadicSimpleGroup)"]},"Tester(IsSimpleGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSimpleGroup)"]},"Tester(IsAlmostSimpleGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAlmostSimpleGroup)"]},"Tester(IsSupersolvableGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSupersolvableGroup)"]},"Tester(IsMonomialGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMonomialGroup)"]},"Tester(IsSolvableGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSolvableGroup)"]},"Tester(IsPolycyclicGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPolycyclicGroup)"]},"Tester(AbelianInvariants)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbelianInvariants)"]},"Tester(IsInfiniteAbelianizationGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsInfiniteAbelianizationGroup)"]},"Tester(AsGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsGroup)"]},"Tester(ChiefSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(ChiefSeries)"]},"Tester(CommutatorFactorGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(CommutatorFactorGroup)"]},"Tester(CompositionSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(CompositionSeries)"]},"Tester(ConjugacyClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConjugacyClasses)"]},"Tester(ConjugacyClassesMaximalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConjugacyClassesMaximalSubgroups)"]},"Tester(MaximalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalSubgroups)"]},"Tester(MaximalSubgroupClassReps)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalSubgroupClassReps)"]},"Tester(PerfectResiduum)" : {"type" : "GAP_Attribute","implied" : ["Tester(PerfectResiduum)"]},"Tester(RepresentativesPerfectSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(RepresentativesPerfectSubgroups)"]},"Tester(RepresentativesSimpleSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(RepresentativesSimpleSubgroups)"]},"Tester(ConjugacyClassesPerfectSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConjugacyClassesPerfectSubgroups)"]},"Tester(ConjugacyClassesSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConjugacyClassesSubgroups)"]},"Tester(LatticeSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(LatticeSubgroups)"]},"Tester(DerivedLength)" : {"type" : "GAP_Attribute","implied" : ["Tester(DerivedLength)"]},"Tester(HirschLength)" : {"type" : "GAP_Attribute","implied" : ["Tester(HirschLength)"]},"Tester(DerivedSeriesOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DerivedSeriesOfGroup)"]},"Tester(DerivedSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DerivedSubgroup)"]},"Tester(MaximalAbelianQuotient)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalAbelianQuotient)"]},"Tester(CommutatorLength)" : {"type" : "GAP_Attribute","implied" : ["Tester(CommutatorLength)"]},"Tester(DimensionsLoewyFactors)" : {"type" : "GAP_Attribute","implied" : ["Tester(DimensionsLoewyFactors)"]},"Tester(ElementaryAbelianSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(ElementaryAbelianSeries)"]},"Tester(ElementaryAbelianSeriesLargeSteps)" : {"type" : "GAP_Attribute","implied" : ["Tester(ElementaryAbelianSeriesLargeSteps)"]},"Tester(Exponent)" : {"type" : "GAP_Attribute","implied" : ["Tester(Exponent)"]},"Tester(FittingSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FittingSubgroup)"]},"Tester(PrefrattiniSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrefrattiniSubgroup)"]},"Tester(FrattiniSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FrattiniSubgroup)"]},"Tester(InvariantForm)" : {"type" : "GAP_Attribute","implied" : ["Tester(InvariantForm)"]},"Tester(JenningsSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(JenningsSeries)"]},"Tester(LowerCentralSeriesOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(LowerCentralSeriesOfGroup)"]},"Tester(NilpotencyClassOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NilpotencyClassOfGroup)"]},"Tester(MaximalNormalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalNormalSubgroups)"]},"Tester(NormalMaximalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalMaximalSubgroups)"]},"Tester(MinimalNormalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimalNormalSubgroups)"]},"Tester(NormalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalSubgroups)"]},"Tester(NrConjugacyClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrConjugacyClasses)"]},"Tester(ComputedOmegas)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedOmegas)"]},"Tester(ComputedAgemos)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedAgemos)"]},"Tester(RadicalGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RadicalGroup)"]},"Tester(RationalClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(RationalClasses)"]},"Tester(GeneratorsSmallest)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsSmallest)"]},"Tester(LargestElementGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(LargestElementGroup)"]},"Tester(MinimalGeneratingSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimalGeneratingSet)"]},"Tester(SmallGeneratingSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(SmallGeneratingSet)"]},"Tester(SupersolvableResiduum)" : {"type" : "GAP_Attribute","implied" : ["Tester(SupersolvableResiduum)"]},"Tester(ComplementSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComplementSystem)"]},"Tester(SylowSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(SylowSystem)"]},"Tester(HallSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(HallSystem)"]},"Tester(Socle)" : {"type" : "GAP_Attribute","implied" : ["Tester(Socle)"]},"Tester(UpperCentralSeriesOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(UpperCentralSeriesOfGroup)"]},"Tester(CoreInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoreInParent)"]},"Tester(IndexInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndexInParent)"]},"Tester(IndexInWholeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndexInWholeGroup)"]},"Tester(IndependentGeneratorsOfAbelianGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndependentGeneratorsOfAbelianGroup)"]},"Tester(IsNormalInParent)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNormalInParent)"]},"Tester(ComputedIsPNilpotents)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedIsPNilpotents)"]},"Tester(ComputedIsPSolvables)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedIsPSolvables)"]},"Tester(NormalClosureInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalClosureInParent)"]},"Tester(NormalizerInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizerInParent)"]},"Tester(ComputedPCentralSeriess)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedPCentralSeriess)"]},"Tester(ComputedPRumps)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedPRumps)"]},"Tester(ComputedPCores)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedPCores)"]},"Tester(SubnormalSeriesInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(SubnormalSeriesInParent)"]},"Tester(ComputedSylowSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedSylowSubgroups)"]},"Tester(ComputedSylowComplements)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedSylowComplements)"]},"Tester(ComputedHallSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedHallSubgroups)"]},"Tester(GrowthFunctionOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(GrowthFunctionOfGroup)"]},"Tester(ElementTestFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(ElementTestFunction)"]},"IsRightTransversal" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsRightTransversal"]},"CategoryCollections(IsRightTransversal)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(IsRightTransversal)"]},"Tester(RightTransversalInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightTransversalInParent)"]},"Tester(IsomorphismTypeInfoFiniteSimpleGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismTypeInfoFiniteSimpleGroup)"]},"Tester(IsomorphismPcGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismPcGroup)"]},"Tester(IsomorphismSpecialPcGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismSpecialPcGroup)"]},"Tester(IsomorphismPermGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismPermGroup)"]},"Tester(IsomorphismFpGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismFpGroup)"]},"Tester(PrimePowerComponents)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimePowerComponents)"]},"IsGroupOfFamily" : {"type" : "GAP_Filter","implied" : ["IsGroupOfFamily"]},"Tester(IsGeneratorsOfInverseSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGeneratorsOfInverseSemigroup)"]},"Tester(GeneratorsOfInverseMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfInverseMonoid)"]},"Tester(GeneratorsOfInverseSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfInverseSemigroup)"]},"Tester(AsInverseSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsInverseSemigroup)"]},"Tester(AsInverseMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsInverseMonoid)"]},"Tester(ReverseNaturalPartialOrder)" : {"type" : "GAP_Attribute","implied" : ["Tester(ReverseNaturalPartialOrder)"]},"Tester(NaturalPartialOrder)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalPartialOrder)"]},"IsNearAdditiveMagma" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","IsGeneralizedDomain","IsNearAdditiveMagma"]},"IsNearAdditiveMagmaWithZero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","IsGeneralizedDomain","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero"]},"IsNearAdditiveGroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","IsGeneralizedDomain","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup"]},"Tester(IsAdditivelyCommutative)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAdditivelyCommutative)"]},"Tester(GeneratorsOfNearAdditiveMagma)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfNearAdditiveMagma)"]},"Tester(GeneratorsOfNearAdditiveMagmaWithZero)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfNearAdditiveMagmaWithZero)"]},"Tester(GeneratorsOfNearAdditiveGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfNearAdditiveGroup)"]},"Tester(TrivialSubnearAdditiveMagmaWithZero)" : {"type" : "GAP_Attribute","implied" : ["Tester(TrivialSubnearAdditiveMagmaWithZero)"]},"Tester(AdditiveNeutralElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdditiveNeutralElement)"]},"IsAdditiveCoset" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpESum","IsTrivialAOpEZero","IsAdditiveCoset"]},"Tester(IsLDistributive)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLDistributive)"]},"Tester(IsRDistributive)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRDistributive)"]},"Tester(GeneratorsOfSemiring)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfSemiring)"]},"Tester(GeneratorsOfSemiringWithOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfSemiringWithOne)"]},"Tester(GeneratorsOfSemiringWithZero)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfSemiringWithZero)"]},"Tester(GeneratorsOfSemiringWithOneAndZero)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfSemiringWithOneAndZero)"]},"Tester(AsSemiring)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSemiring)"]},"Tester(AsSemiringWithOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSemiringWithOne)"]},"Tester(AsSemiringWithZero)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSemiringWithZero)"]},"Tester(AsSemiringWithOneAndZero)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSemiringWithOneAndZero)"]},"Tester(CentralIdempotentsOfSemiring)" : {"type" : "GAP_Attribute","implied" : ["Tester(CentralIdempotentsOfSemiring)"]},"Tester(AsNearRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsNearRing)"]},"Tester(AsRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsRing)"]},"Tester(GeneratorsOfRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfRing)"]},"Tester(GeneratorsOfRingWithOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfRingWithOne)"]},"IsUniqueFactorizationRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing"]},"IsEuclideanRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing"]},"Tester(IsAnticommutative)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAnticommutative)"]},"Tester(IsIntegralRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIntegralRing)"]},"Tester(IsJacobianRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsJacobianRing)"]},"Tester(IsZeroSquaredRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZeroSquaredRing)"]},"Tester(IsZeroMultiplicationRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZeroMultiplicationRing)"]},"Tester(Units)" : {"type" : "GAP_Attribute","implied" : ["Tester(Units)"]},"Tester(IsGeneralizedCartanMatrix)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGeneralizedCartanMatrix)"]},"Tester(BaseMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(BaseMat)"]},"Tester(BaseOrthogonalSpaceMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(BaseOrthogonalSpaceMat)"]},"Tester(DefaultFieldOfMatrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(DefaultFieldOfMatrix)"]},"Tester(DepthOfUpperTriangularMatrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(DepthOfUpperTriangularMatrix)"]},"Tester(DeterminantMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(DeterminantMat)"]},"Tester(DimensionsMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(DimensionsMat)"]},"Tester(NullspaceMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(NullspaceMat)"]},"Tester(TriangulizedNullspaceMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(TriangulizedNullspaceMat)"]},"Tester(ProjectiveOrder)" : {"type" : "GAP_Attribute","implied" : ["Tester(ProjectiveOrder)"]},"Tester(RankMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(RankMat)"]},"Tester(SemiEchelonMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemiEchelonMat)"]},"Tester(SemiEchelonMatTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemiEchelonMatTransformation)"]},"Tester(TransposedMatImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(TransposedMatImmutable)"]},"Tester(IsMonomialMatrix)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMonomialMatrix)"]},"Tester(JordanDecomposition)" : {"type" : "GAP_Attribute","implied" : ["Tester(JordanDecomposition)"]},"Tester(CharacteristicPolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(CharacteristicPolynomial)"]},"Tester(BaseIntMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(BaseIntMat)"]},"Tester(NullspaceIntMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(NullspaceIntMat)"]},"Tester(AbelianInvariantsOfList)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbelianInvariantsOfList)"]},"Tester(MatrixByBlockMatrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(MatrixByBlockMatrix)"]},"Tester(IsTwoSidedIdealInParent)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTwoSidedIdealInParent)"]},"Tester(IsLeftIdealInParent)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLeftIdealInParent)"]},"Tester(IsRightIdealInParent)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRightIdealInParent)"]},"Tester(GeneratorsOfTwoSidedIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfTwoSidedIdeal)"]},"Tester(GeneratorsOfLeftIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfLeftIdeal)"]},"Tester(GeneratorsOfRightIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfRightIdeal)"]},"Tester(LeftActingRingOfIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeftActingRingOfIdeal)"]},"Tester(RightActingRingOfIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightActingRingOfIdeal)"]},"IsFreeLeftModule" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule"]},"Tester(IsFiniteDimensional)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFiniteDimensional)"]},"Tester(IsFullRowModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullRowModule)"]},"Tester(IsFullMatrixModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullMatrixModule)"]},"IsHandledByNiceBasis" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis"]},"Tester(Dimension)" : {"type" : "GAP_Attribute","implied" : ["Tester(Dimension)"]},"Tester(GeneratorsOfLeftOperatorAdditiveGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfLeftOperatorAdditiveGroup)"]},"Tester(GeneratorsOfRightOperatorAdditiveGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfRightOperatorAdditiveGroup)"]},"Tester(IsRowModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRowModule)"]},"Tester(IsMatrixModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMatrixModule)"]},"Tester(DimensionOfVectors)" : {"type" : "GAP_Attribute","implied" : ["Tester(DimensionOfVectors)"]},"IsBasis" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis"]},"Tester(IsCanonicalBasis)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCanonicalBasis)"]},"Tester(IsCanonicalBasisFullRowModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCanonicalBasisFullRowModule)"]},"Tester(IsCanonicalBasisFullMatrixModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCanonicalBasisFullMatrixModule)"]},"Tester(IsIntegralBasis)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIntegralBasis)"]},"Tester(IsNormalBasis)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNormalBasis)"]},"Tester(IsSemiEchelonized)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSemiEchelonized)"]},"Tester(BasisVectors)" : {"type" : "GAP_Attribute","implied" : ["Tester(BasisVectors)"]},"Tester(EnumeratorByBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(EnumeratorByBasis)"]},"Tester(StructureConstantsTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(StructureConstantsTable)"]},"Tester(UnderlyingLeftModule)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingLeftModule)"]},"Tester(Basis)" : {"type" : "GAP_Attribute","implied" : ["Tester(Basis)"]},"Tester(SemiEchelonBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemiEchelonBasis)"]},"IsGenericFiniteSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsGenericFiniteSpace"]},"IsSpaceOfRationalFunctions" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsSpaceOfRationalFunctions"]},"IsBasisByNiceBasis" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsFinite","Tester(IsFinite)","IsSmallList","Tester(IsSmallList)","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisByNiceBasis"]},"Tester(NiceBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceBasis)"]},"Tester(NiceFreeLeftModule)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceFreeLeftModule)"]},"Tester(NiceFreeLeftModuleInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceFreeLeftModuleInfo)"]},"IsMutableBasis" : {"type" : "GAP_Category","implied" : ["IsMutableBasis"]},"IsGaussianSpace" : {"type" : "GAP_Filter","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsGaussianSpace"]},"Tester(CanonicalBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalBasis)"]},"IsNonGaussianRowSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsNonGaussianRowSpace"]},"IsNonGaussianMatrixSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsNonGaussianMatrixSpace"]},"Tester(NormedRowVectors)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormedRowVectors)"]},"IsSubspacesVectorSpace" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsSubspacesVectorSpace"]},"Tester(Subspaces)" : {"type" : "GAP_Attribute","implied" : ["Tester(Subspaces)"]},"Tester(OrthogonalSpaceInFullRowSpace)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrthogonalSpaceInFullRowSpace)"]},"Tester(IsVectorSpaceHomomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsVectorSpaceHomomorphism)"]},"Tester(AsLeftModuleGeneralMappingByImages)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsLeftModuleGeneralMappingByImages)"]},"Tester(IsFullHomModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullHomModule)"]},"Tester(IsPseudoCanonicalBasisFullHomModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPseudoCanonicalBasisFullHomModule)"]},"IsLinearMappingsModule" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsFiniteDimensional","Tester(IsFiniteDimensional)","IsHandledByNiceBasis","IsLinearMappingsModule"]},"Tester(IsSimpleAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSimpleAlgebra)"]},"Tester(GeneratorsOfLeftOperatorRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfLeftOperatorRing)"]},"Tester(GeneratorsOfLeftOperatorRingWithOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfLeftOperatorRingWithOne)"]},"Tester(PowerSubalgebraSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(PowerSubalgebraSeries)"]},"Tester(AdjointBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdjointBasis)"]},"Tester(IndicesOfAdjointBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndicesOfAdjointBasis)"]},"Tester(RadicalOfAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(RadicalOfAlgebra)"]},"Tester(DirectSumDecomposition)" : {"type" : "GAP_Attribute","implied" : ["Tester(DirectSumDecomposition)"]},"Tester(NullAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(NullAlgebra)"]},"Tester(LieAlgebraByDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieAlgebraByDomain)"]},"IsQuaternion" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociative","Tester(IsAssociative)","IsQuaternion"]},"CategoryCollections(IsQuaternion)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsQuaternion)"]},"CategoryCollections(CategoryCollections(IsQuaternion))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsQuaternion))"]},"Tester(LeviMalcevDecomposition)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeviMalcevDecomposition)"]},"Tester(Grading)" : {"type" : "GAP_Attribute","implied" : ["Tester(Grading)"]},"IsElementOfMagmaRingModuloRelations" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsElementOfMagmaRingModuloRelations"]},"CategoryCollections(IsElementOfMagmaRingModuloRelations)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsElementOfMagmaRingModuloRelations)"]},"CategoryFamily(IsElementOfMagmaRingModuloRelations)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)"]},"IsElementOfFreeMagmaRing" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsElementOfMagmaRingModuloRelations","IsElementOfFreeMagmaRing"]},"CategoryCollections(IsElementOfFreeMagmaRing)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsElementOfMagmaRingModuloRelations)","CategoryCollections(IsElementOfFreeMagmaRing)"]},"CategoryFamily(IsElementOfFreeMagmaRing)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)","CategoryFamily(IsElementOfFreeMagmaRing)"]},"Tester(CoefficientsAndMagmaElements)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoefficientsAndMagmaElements)"]},"Tester(ZeroCoefficient)" : {"type" : "GAP_Attribute","implied" : ["Tester(ZeroCoefficient)"]},"IsMagmaRingModuloRelations" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMagmaRingModuloRelations"]},"IsFreeMagmaRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMagmaRingModuloRelations","IsFreeMagmaRing"]},"Tester(IsGroupRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupRing)"]},"Tester(UnderlyingMagma)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingMagma)"]},"Tester(AugmentationIdeal)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentationIdeal)"]},"IsMagmaRingModuloSpanOfZero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsMagmaRingModuloRelations","IsMagmaRingModuloSpanOfZero"]},"IsElementOfMagmaRingModuloSpanOfZeroFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)","IsElementOfMagmaRingModuloSpanOfZeroFamily"]},"IsSpaceOfElementsOfMagmaRing" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsSpaceOfElementsOfMagmaRing"]},"IsElementOfFpAlgebra" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsElementOfFpAlgebra"]},"CategoryCollections(IsElementOfFpAlgebra)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsElementOfFpAlgebra)"]},"CategoryFamily(IsElementOfFpAlgebra)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfFpAlgebra)"]},"IsSubalgebraFpAlgebra" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsSubalgebraFpAlgebra"]},"Tester(IsFullFpAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullFpAlgebra)"]},"Tester(FreeGeneratorsOfFpAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeGeneratorsOfFpAlgebra)"]},"Tester(RelatorsOfFpAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelatorsOfFpAlgebra)"]},"Tester(FreeAlgebraOfFpAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeAlgebraOfFpAlgebra)"]},"Tester(IsNormalForm)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNormalForm)"]},"Tester(NiceNormalFormByExtRepFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceNormalFormByExtRepFunction)"]},"Tester(NiceAlgebraMonomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceAlgebraMonomorphism)"]},"IsFpAlgebraElementsSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsFpAlgebraElementsSpace"]},"Tester(IsLieAbelian)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieAbelian)"]},"Tester(IsLieNilpotent)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieNilpotent)"]},"Tester(IsRestrictedLieAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRestrictedLieAlgebra)"]},"Tester(LieDerivedSubalgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieDerivedSubalgebra)"]},"Tester(LieDerivedSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieDerivedSeries)"]},"Tester(IsLieSolvable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieSolvable)"]},"Tester(LieLowerCentralSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieLowerCentralSeries)"]},"Tester(LieUpperCentralSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieUpperCentralSeries)"]},"Tester(LieCentre)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieCentre)"]},"Tester(RightDerivations)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightDerivations)"]},"Tester(LeftDerivations)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeftDerivations)"]},"Tester(KillingMatrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(KillingMatrix)"]},"Tester(CartanSubalgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(CartanSubalgebra)"]},"Tester(PthPowerImages)" : {"type" : "GAP_Attribute","implied" : ["Tester(PthPowerImages)"]},"Tester(NonNilpotentElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(NonNilpotentElement)"]},"Tester(LieNilRadical)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieNilRadical)"]},"Tester(LieSolvableRadical)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieSolvableRadical)"]},"Tester(SemiSimpleType)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemiSimpleType)"]},"Tester(LieCentralizerInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieCentralizerInParent)"]},"Tester(LieNormalizerInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieNormalizerInParent)"]},"Tester(PowerS)" : {"type" : "GAP_Attribute","implied" : ["Tester(PowerS)"]},"IsRootSystem" : {"type" : "GAP_Category","implied" : ["IsRootSystem"]},"IsRootSystemFromLieAlgebra" : {"type" : "GAP_Category","implied" : ["IsRootSystem","IsRootSystemFromLieAlgebra"]},"Tester(UnderlyingLieAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingLieAlgebra)"]},"Tester(RootSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(RootSystem)"]},"Tester(PositiveRoots)" : {"type" : "GAP_Attribute","implied" : ["Tester(PositiveRoots)"]},"Tester(NegativeRoots)" : {"type" : "GAP_Attribute","implied" : ["Tester(NegativeRoots)"]},"Tester(PositiveRootVectors)" : {"type" : "GAP_Attribute","implied" : ["Tester(PositiveRootVectors)"]},"Tester(NegativeRootVectors)" : {"type" : "GAP_Attribute","implied" : ["Tester(NegativeRootVectors)"]},"Tester(SimpleSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(SimpleSystem)"]},"Tester(CartanMatrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(CartanMatrix)"]},"Tester(BilinearFormMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(BilinearFormMat)"]},"Tester(CanonicalGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalGenerators)"]},"Tester(ChevalleyBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(ChevalleyBasis)"]},"Tester(UniversalEnvelopingAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(UniversalEnvelopingAlgebra)"]},"IsFamilyElementOfFreeLieAlgebra" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsElementOfMagmaRingModuloRelations)","IsFamilyElementOfFreeLieAlgebra"]},"IsFptoSCAMorphism" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsFptoSCAMorphism"]},"Tester(JenningsLieAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(JenningsLieAlgebra)"]},"Tester(PCentralLieAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(PCentralLieAlgebra)"]},"Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalHomomorphismOfLieAlgebraFromNilpotentGroup)"]},"IsFamilyOverFullCoefficientsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","IsFamilyOverFullCoefficientsFamily"]},"IsSCAlgebraObj" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsSCAlgebraObj"]},"CategoryCollections(IsSCAlgebraObj)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsSCAlgebraObj)"]},"CategoryCollections(CategoryCollections(IsSCAlgebraObj))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsSCAlgebraObj))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsSCAlgebraObj)))"]},"CategoryFamily(IsSCAlgebraObj)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsSCAlgebraObj)"]},"Tester(IsFullSCAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullSCAlgebra)"]},"Tester(IsCanonicalBasisFullSCAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCanonicalBasisFullSCAlgebra)"]},"IsSCAlgebraObjSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsSCAlgebraObjSpace"]},"Tester(IsomorphismFpFLMLOR)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismFpFLMLOR)"]},"Tester(IsomorphismMatrixFLMLOR)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismMatrixFLMLOR)"]},"Tester(IsomorphismSCFLMLOR)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismSCFLMLOR)"]},"IsLieObject" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement","IsZeroSquaredElement","IsLieObject"]},"CategoryCollections(IsLieObject)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)","CategoryCollections(IsZeroSquaredElement)","CategoryCollections(IsLieObject)"]},"CategoryCollections((IsLieObject and IsRestrictedJacobianElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)","CategoryCollections(IsRestrictedJacobianElement)","CategoryCollections(IsZeroSquaredElement)","CategoryCollections(IsLieObject)","CategoryCollections((IsLieObject and IsRestrictedJacobianElement))"]},"Tester(LieFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieFamily)"]},"Tester(UnderlyingFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingFamily)"]},"Tester(LieObject)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieObject)"]},"Tester(UnderlyingRingElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingRingElement)"]},"IsLieObjectsModule" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsLieObjectsModule"]},"IsAlgebraModuleElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsAlgebraModuleElement"]},"CategoryCollections(IsAlgebraModuleElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsAlgebraModuleElement)"]},"CategoryFamily(IsAlgebraModuleElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsAlgebraModuleElement)"]},"IsLeftAlgebraModuleElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsAlgebraModuleElement","IsLeftAlgebraModuleElement"]},"CategoryCollections(IsLeftAlgebraModuleElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsAlgebraModuleElement)","CategoryCollections(IsLeftAlgebraModuleElement)"]},"IsRightAlgebraModuleElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsAlgebraModuleElement","IsRightAlgebraModuleElement"]},"CategoryCollections(IsRightAlgebraModuleElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsAlgebraModuleElement)","CategoryCollections(IsRightAlgebraModuleElement)"]},"Tester(IsAlgebraModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAlgebraModule)"]},"Tester(IsLeftAlgebraModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLeftAlgebraModule)"]},"Tester(IsRightAlgebraModule)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRightAlgebraModule)"]},"Tester(LeftActingAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeftActingAlgebra)"]},"Tester(RightActingAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightActingAlgebra)"]},"Tester(GeneratorsOfAlgebraModule)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfAlgebraModule)"]},"IsBasisOfAlgebraModuleElementSpace" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisOfAlgebraModuleElementSpace"]},"Tester(AdjointModule)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdjointModule)"]},"Tester(FaithfulModule)" : {"type" : "GAP_Attribute","implied" : ["Tester(FaithfulModule)"]},"IsMonomialElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement"]},"CategoryCollections(IsMonomialElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)"]},"CategoryFamily(IsMonomialElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsMonomialElement)"]},"IsTensorElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement","IsTensorElement"]},"CategoryCollections(IsTensorElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)","CategoryCollections(IsTensorElement)"]},"IsWedgeElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement","IsWedgeElement"]},"CategoryCollections(IsWedgeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)","CategoryCollections(IsWedgeElement)"]},"IsSymmetricPowerElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMonomialElement","IsSymmetricPowerElement"]},"CategoryCollections(IsSymmetricPowerElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMonomialElement)","CategoryCollections(IsSymmetricPowerElement)"]},"IsDirectSumElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsDirectSumElement"]},"CategoryCollections(IsDirectSumElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsDirectSumElement)"]},"CategoryFamily(IsDirectSumElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsDirectSumElement)"]},"IsSparseRowSpaceElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsSparseRowSpaceElement"]},"CategoryCollections(IsSparseRowSpaceElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsSparseRowSpaceElement)"]},"CategoryFamily(IsSparseRowSpaceElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsSparseRowSpaceElement)"]},"IsDirectSumElementsSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsDirectSumElementsSpace"]},"IsCochain" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsCochain"]},"CategoryCollections(IsCochain)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsCochain)"]},"Tester(IsWeylGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsWeylGroup)"]},"Tester(WeylGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(WeylGroup)"]},"Tester(SparseCartanMatrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(SparseCartanMatrix)"]},"Tester(LongestWeylWordPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(LongestWeylWordPerm)"]},"Tester(PositiveRootsAsWeights)" : {"type" : "GAP_Attribute","implied" : ["Tester(PositiveRootsAsWeights)"]},"IsUEALatticeElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsUEALatticeElement"]},"CategoryCollections(IsUEALatticeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsUEALatticeElement)"]},"CategoryFamily(IsUEALatticeElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsUEALatticeElement)"]},"Tester(LatticeGeneratorsInUEA)" : {"type" : "GAP_Attribute","implied" : ["Tester(LatticeGeneratorsInUEA)"]},"IsWeightRepElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsWeightRepElement"]},"CategoryCollections(IsWeightRepElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsWeightRepElement)"]},"CategoryFamily(IsWeightRepElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsWeightRepElement)"]},"IsBasisOfWeightRepElementSpace" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisOfWeightRepElementSpace"]},"IsCochainsSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsCochainsSpace"]},"IsSearchTable" : {"type" : "GAP_Category","implied" : ["IsSearchTable"]},"IsVectorSearchTable" : {"type" : "GAP_Category","implied" : ["IsSearchTable","IsVectorSearchTable"]},"IsIntegers" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsFreeLeftModule","IsIntegers"]},"IsPositiveIntegers" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPositiveIntegers"]},"IsNonnegativeIntegers" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsNonnegativeIntegers"]},"IsGaussianIntegers" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsMagma","IsMagmaWithOne","Tester(MultiplicativeNeutralElement)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsFreeLeftModule","IsFiniteDimensional","Tester(IsFiniteDimensional)","IsGaussianIntegers"]},"Tester(PrimeDivisors)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimeDivisors)"]},"IsSCRingObj" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsSCRingObj"]},"CategoryCollections(IsSCRingObj)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsSCRingObj)"]},"CategoryCollections(CategoryCollections(IsSCRingObj))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsSCRingObj))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsSCRingObj)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsSCRingObj)))"]},"CategoryFamily(IsSCRingObj)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsSCRingObj)"]},"Tester(StandardGeneratorsSubringSCRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(StandardGeneratorsSubringSCRing)"]},"Tester(Subrings)" : {"type" : "GAP_Attribute","implied" : ["Tester(Subrings)"]},"Tester(Ideals)" : {"type" : "GAP_Attribute","implied" : ["Tester(Ideals)"]},"Tester(DirectSumInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(DirectSumInfo)"]},"IsPolynomialFunction" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction"]},"IsRationalFunction" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction"]},"CategoryCollections(IsPolynomialFunction)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsPolynomialFunction)"]},"CategoryCollections(IsRationalFunction)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsPolynomialFunction)","CategoryCollections(IsRationalFunction)"]},"IsPolynomialFunctionsFamilyElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsPolynomialFunctionsFamilyElement"]},"IsRationalFunctionsFamilyElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsPolynomialFunctionsFamilyElement","IsRationalFunctionsFamilyElement"]},"IsPolynomialFunctionsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","IsPolynomialFunctionsFamily"]},"IsRationalFunctionsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","IsUFDFamily","Tester(IsUFDFamily)","IsPolynomialFunctionsFamily","IsRationalFunctionsFamily"]},"IsRationalFunctionOverField" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsRationalFunctionOverField"]},"Tester(RationalFunctionsFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(RationalFunctionsFamily)"]},"Tester(CoefficientsFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoefficientsFamily)"]},"Tester(NumeratorOfRationalFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(NumeratorOfRationalFunction)"]},"Tester(DenominatorOfRationalFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(DenominatorOfRationalFunction)"]},"Tester(IsPolynomial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPolynomial)"]},"Tester(AsPolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsPolynomial)"]},"Tester(IsUnivariateRationalFunction)" : {"type" : "GAP_Tester","implied" : ["Tester(IsUnivariateRationalFunction)"]},"Tester(IsLaurentPolynomial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLaurentPolynomial)"]},"Tester(IsConstantRationalFunction)" : {"type" : "GAP_Tester","implied" : ["Tester(IsConstantRationalFunction)"]},"IsRationalFunctionDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsRationalFunctionDefaultRep"]},"IsPolynomialDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsPolynomial","Tester(IsPolynomial)","IsPolynomialDefaultRep"]},"IsLaurentPolynomialDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)","IsLaurentPolynomialDefaultRep"]},"IsUnivariateRationalFunctionDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsUnivariateRationalFunctionDefaultRep"]},"Tester(ExtRepNumeratorRatFun)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExtRepNumeratorRatFun)"]},"Tester(ExtRepDenominatorRatFun)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExtRepDenominatorRatFun)"]},"Tester(ExtRepPolynomialRatFun)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExtRepPolynomialRatFun)"]},"Tester(CoefficientsOfLaurentPolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoefficientsOfLaurentPolynomial)"]},"Tester(IndeterminateNumberOfUnivariateRationalFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndeterminateNumberOfUnivariateRationalFunction)"]},"Tester(IndeterminateOfUnivariateRationalFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndeterminateOfUnivariateRationalFunction)"]},"Tester(CoefficientsOfUnivariatePolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoefficientsOfUnivariatePolynomial)"]},"Tester(DegreeOfLaurentPolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOfLaurentPolynomial)"]},"Tester(CoefficientsOfUnivariateRationalFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoefficientsOfUnivariateRationalFunction)"]},"Tester(Derivative)" : {"type" : "GAP_Attribute","implied" : ["Tester(Derivative)"]},"Tester(Discriminant)" : {"type" : "GAP_Attribute","implied" : ["Tester(Discriminant)"]},"IsLaurentPolynomialsFamilyElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsLaurentPolynomialsFamilyElement"]},"IsUnivariatePolynomialsFamilyElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsUnivariatePolynomialsFamilyElement"]},"IsLaurentPolynomialsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","Tester(OneImmutable)","IsCommutativeFamily","Tester(IsCommutativeFamily)","IsLaurentPolynomialsFamily"]},"IsUnivariatePolynomialsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","IsUnivariatePolynomialsFamily"]},"Tester(PrimeField)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimeField)"]},"Tester(IsPrimeField)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPrimeField)"]},"Tester(DefiningPolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(DefiningPolynomial)"]},"Tester(DegreeOverPrimeField)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOverPrimeField)"]},"Tester(GeneratorsOfDivisionRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfDivisionRing)"]},"Tester(NormalBase)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalBase)"]},"Tester(PrimitiveElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimitiveElement)"]},"Tester(PrimitiveRoot)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimitiveRoot)"]},"Tester(RootOfDefiningPolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(RootOfDefiningPolynomial)"]},"Tester(Subfields)" : {"type" : "GAP_Attribute","implied" : ["Tester(Subfields)"]},"IsFieldControlledByGaloisGroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsNonTrivial","Tester(IsNonTrivial)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(MultiplicativeNeutralElement)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsIntegralRing","Tester(IsIntegralRing)","IsFreeLeftModule","IsFieldControlledByGaloisGroup"]},"Tester(Conjugates)" : {"type" : "GAP_Attribute","implied" : ["Tester(Conjugates)"]},"Tester(Norm)" : {"type" : "GAP_Attribute","implied" : ["Tester(Norm)"]},"Tester(Trace)" : {"type" : "GAP_Attribute","implied" : ["Tester(Trace)"]},"Tester(GaloisGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(GaloisGroup)"]},"Tester(ComplexConjugate)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComplexConjugate)"]},"Tester(RealPart)" : {"type" : "GAP_Attribute","implied" : ["Tester(RealPart)"]},"Tester(ImaginaryPart)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImaginaryPart)"]},"Tester(FrobeniusAutomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(FrobeniusAutomorphism)"]},"IsFieldElementsSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsFieldElementsSpace"]},"IsZmodnZObj" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsZmodnZObj"]},"IsZmodnZObjNonprime" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsZmodnZObj","IsZmodnZObjNonprime"]},"CategoryFamily(IsZmodnZObjNonprime)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsAdditivelyCommutativeElement)","CategoryFamily(IsZmodnZObjNonprime)"]},"CategoryCollections(IsZmodnZObjNonprime)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsZmodnZObjNonprime)"]},"CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(CategoryCollections(IsZmodnZObjNonprime))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsZmodnZObjNonprime)))"]},"Tester(ModulusOfZmodnZObj)" : {"type" : "GAP_Attribute","implied" : ["Tester(ModulusOfZmodnZObj)"]},"IsZmodnZepsObj" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZmodnZepsObj"]},"CategoryCollections(IsZmodnZepsObj)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZmodnZepsObj)"]},"IsZmodnZepsRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsZmodnZepsRep"]},"Tester(Cyclotomic)" : {"type" : "GAP_Attribute","implied" : ["Tester(Cyclotomic)"]},"Tester(IsRingOfIntegralCyclotomics)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsRingOfIntegralCyclotomics)"]},"Tester(GaloisMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(GaloisMat)"]},"Tester(RationalizedMat)" : {"type" : "GAP_Attribute","implied" : ["Tester(RationalizedMat)"]},"Tester(IsNumberField)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNumberField)"]},"Tester(IsAbelianNumberField)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAbelianNumberField)"]},"Tester(IsCyclotomicField)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCyclotomicField)"]},"Tester(GaloisStabilizer)" : {"type" : "GAP_Attribute","implied" : ["Tester(GaloisStabilizer)"]},"IsGaussianRationals" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsNonTrivial","Tester(IsNonTrivial)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneralizedDomain","CategoryCollections(IsCyclotomic)","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(MultiplicativeNeutralElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsIntegralRing","Tester(IsIntegralRing)","IsFreeLeftModule","IsGaussianRationals"]},"Tester(ExponentOfPowering)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExponentOfPowering)"]},"IsPadicNumber" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsCommutativeElement","IsPadicNumber"]},"CategoryCollections(IsPadicNumber)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsPadicNumber)"]},"CategoryCollections(CategoryCollections(IsPadicNumber))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(CategoryCollections(IsPadicNumber))"]},"CategoryFamily(IsPadicNumber)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsPadicNumber)"]},"IsPurePadicNumber" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsCommutativeElement","IsPadicNumber","IsPurePadicNumber"]},"CategoryFamily(IsPurePadicNumber)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsPadicNumber)","CategoryFamily(IsPurePadicNumber)"]},"IsPadicExtensionNumber" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsCommutativeElement","IsPadicNumber","IsPadicExtensionNumber"]},"CategoryFamily(IsPadicExtensionNumber)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsPadicNumber)","CategoryFamily(IsPadicExtensionNumber)"]},"IsPolynomialRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing"]},"IsFunctionField" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFunctionField"]},"IsUnivariatePolynomialRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsUnivariatePolynomialRing"]},"IsFiniteFieldPolynomialRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsFiniteFieldPolynomialRing"]},"IsAbelianNumberFieldPolynomialRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsAbelianNumberFieldPolynomialRing"]},"IsAlgebraicExtensionPolynomialRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsAlgebraicExtensionPolynomialRing"]},"IsRationalsPolynomialRing" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsPolynomialRing","IsAbelianNumberFieldPolynomialRing","IsRationalsPolynomialRing"]},"Tester(CoefficientsRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoefficientsRing)"]},"Tester(IndeterminatesOfPolynomialRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndeterminatesOfPolynomialRing)"]},"Tester(SplittingField)" : {"type" : "GAP_Attribute","implied" : ["Tester(SplittingField)"]},"Tester(IrrFacsPol)" : {"type" : "GAP_Attribute","implied" : ["Tester(IrrFacsPol)"]},"Tester(MinimizedBombieriNorm)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimizedBombieriNorm)"]},"IsAlgebraicElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsAlgebraicElement"]},"CategoryCollections(IsAlgebraicElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","CategoryCollections(IsCommutativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsAlgebraicElement)"]},"CategoryCollections(CategoryCollections(IsAlgebraicElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(CategoryCollections(IsAlgebraicElement))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAlgebraicElement)))"]},"CategoryFamily(IsAlgebraicElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsAdditivelyCommutativeElement)","CategoryFamily(IsAlgebraicElement)"]},"IsAlgebraicExtension" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsNonTrivial","Tester(IsNonTrivial)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsAssociative","Tester(IsAssociative)","IsCommutative","Tester(IsCommutative)","Tester(MultiplicativeNeutralElement)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsUniqueFactorizationRing","IsEuclideanRing","IsIntegralRing","Tester(IsIntegralRing)","IsFreeLeftModule","IsAlgebraicExtension"]},"Tester(AlgebraicElementsFamilies)" : {"type" : "GAP_Attribute","implied" : ["Tester(AlgebraicElementsFamilies)"]},"Tester(DefectApproximation)" : {"type" : "GAP_Attribute","implied" : ["Tester(DefectApproximation)"]},"IsUnknown" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsUnknown"]},"IsWord" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsWord"]},"CategoryCollections(IsWord)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsWord)"]},"IsNonassocWord" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsWord","IsNonassocWord"]},"CategoryCollections(IsNonassocWord)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsWord)","CategoryCollections(IsNonassocWord)"]},"CategoryCollections((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsWord)","CategoryCollections(IsNonassocWord)","CategoryCollections((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))"]},"CategoryFamily(IsNonassocWord)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsNonassocWord)"]},"CategoryFamily((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsNonassocWord)","CategoryFamily((IsNonassocWord and (IsWord and IsMultiplicativeElementWithOne)))"]},"CategoryCollections((IsWord and IsAssociativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))"]},"CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]},"CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]},"CategoryFamily((IsWord and IsAssociativeElement))" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))"]},"CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))"]},"CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","CategoryFamily(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))"]},"IsSyllableWordsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily"]},"Is8BitsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","Is8BitsFamily"]},"Is16BitsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","Is16BitsFamily"]},"Is32BitsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","Is32BitsFamily"]},"IsInfBitsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsSyllableWordsFamily","IsInfBitsFamily"]},"IsSyllableAssocWordRep" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep"]},"IsLetterAssocWordRep" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsLetterAssocWordRep"]},"IsBLetterAssocWordRep" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsLetterAssocWordRep","IsBLetterAssocWordRep"]},"IsWLetterAssocWordRep" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsLetterAssocWordRep","IsWLetterAssocWordRep"]},"IsLetterWordsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily"]},"IsBLetterWordsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily","IsBLetterWordsFamily"]},"IsWLetterWordsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsWord and IsAssociativeElement))","IsLetterWordsFamily","IsWLetterWordsFamily"]},"Tester(IsFreeSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFreeSemigroup)"]},"Tester(IsFreeMonoid)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFreeMonoid)"]},"Tester(NumberSyllables)" : {"type" : "GAP_Attribute","implied" : ["Tester(NumberSyllables)"]},"Tester(BaseDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(BaseDomain)"]},"Tester(RowLength)" : {"type" : "GAP_Attribute","implied" : ["Tester(RowLength)"]},"IsPlistVectorRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","IsPlistVectorRep"]},"IsPlistMatrixRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","IsPlistMatrixRep"]},"IsIntVector" : {"type" : "GAP_Filter","implied" : ["IsIntVector"]},"IsFFEVector" : {"type" : "GAP_Filter","implied" : ["IsFFEVector"]},"IsCheckingVector" : {"type" : "GAP_Filter","implied" : ["IsCheckingVector"]},"IsCheckingMatrix" : {"type" : "GAP_Filter","implied" : ["IsCheckingMatrix"]},"IsRewritingSystem" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem"]},"IsReducedConfluentRewritingSystem" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsReducedConfluentRewritingSystem"]},"Tester(IsBuiltFromAdditiveMagmaWithInverses)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBuiltFromAdditiveMagmaWithInverses)"]},"Tester(IsBuiltFromMagma)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBuiltFromMagma)"]},"Tester(IsBuiltFromMagmaWithOne)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBuiltFromMagmaWithOne)"]},"Tester(IsBuiltFromMagmaWithInverses)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBuiltFromMagmaWithInverses)"]},"Tester(IsBuiltFromGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBuiltFromGroup)"]},"Tester(IsBuiltFromSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBuiltFromSemigroup)"]},"Tester(IsBuiltFromMonoid)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBuiltFromMonoid)"]},"Tester(SemigroupOfRewritingSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemigroupOfRewritingSystem)"]},"Tester(MonoidOfRewritingSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(MonoidOfRewritingSystem)"]},"Tester(ConfluentRws)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConfluentRws)"]},"Tester(GeneratorsOfRws)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfRws)"]},"Tester(NumberGeneratorsOfRws)" : {"type" : "GAP_Attribute","implied" : ["Tester(NumberGeneratorsOfRws)"]},"Tester(Rules)" : {"type" : "GAP_Attribute","implied" : ["Tester(Rules)"]},"Tester(OrderingOfRewritingSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrderingOfRewritingSystem)"]},"Tester(IsConfluent)" : {"type" : "GAP_Tester","implied" : ["Tester(IsConfluent)"]},"Tester(IsReduced)" : {"type" : "GAP_Tester","implied" : ["Tester(IsReduced)"]},"IsPolycyclicCollector" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector"]},"IsPowerConjugateCollector" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector","IsPowerConjugateCollector"]},"IsPowerCommutatorCollector" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector","IsPowerCommutatorCollector"]},"Tester(RelativeOrders)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelativeOrders)"]},"IsUpToDatePolycyclicCollector" : {"type" : "GAP_Filter","implied" : ["IsUpToDatePolycyclicCollector"]},"IsElementsFamilyByRws" : {"type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws"]},"IsMultiplicativeElementWithInverseByRws" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMultiplicativeElementWithInverseByRws"]},"IsElementFinitePolycyclicGroup" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsElementFinitePolycyclicGroup"]},"CategoryCollections(IsElementFinitePolycyclicGroup)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)","CategoryCollections(IsElementFinitePolycyclicGroup)"]},"IsMultiplicativeElementWithInverseByPolycyclicCollector" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsMultiplicativeElementWithInverseByRws","IsMultiplicativeElementWithInverseByPolycyclicCollector"]},"CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsMultiplicativeElementWithInverseByPolycyclicCollector)"]},"Tester(DefiningPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(DefiningPcgs)"]},"IsKernelPcWord" : {"type" : "GAP_Filter","implied" : ["IsKernelPcWord"]},"IsElementsFamilyBy8BitsSingleCollector" : {"type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws","IsElementsFamilyBy8BitsSingleCollector"]},"IsElementsFamilyBy16BitsSingleCollector" : {"type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws","IsElementsFamilyBy16BitsSingleCollector"]},"IsElementsFamilyBy32BitsSingleCollector" : {"type" : "GAP_Category","implied" : ["IsFamily","IsElementsFamilyByRws","IsElementsFamilyBy32BitsSingleCollector"]},"IsMonomialOrdering" : {"type" : "GAP_Category","implied" : ["IsMonomialOrdering"]},"IsMonomialOrderingDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsComponentObjectRep","IsAttributeStoringRep","IsMonomialOrdering","IsMonomialOrderingDefaultRep"]},"Tester(MonomialComparisonFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(MonomialComparisonFunction)"]},"Tester(MonomialExtrepComparisonFun)" : {"type" : "GAP_Attribute","implied" : ["Tester(MonomialExtrepComparisonFun)"]},"Tester(OccuringVariableIndices)" : {"type" : "GAP_Attribute","implied" : ["Tester(OccuringVariableIndices)"]},"Tester(StoredGroebnerBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(StoredGroebnerBasis)"]},"IsGeneralPcgs" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs"]},"IsModuloPcgs" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs"]},"IsPcgs" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs","IsPcgs"]},"IsPcgsFamily" : {"type" : "GAP_Category","implied" : ["IsFamily","IsPcgsFamily"]},"IsPcgsDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep"]},"Tester(PcGroupWithPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcGroupWithPcgs)"]},"Tester(GroupOfPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(GroupOfPcgs)"]},"Tester(OneOfPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(OneOfPcgs)"]},"Tester(PcSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcSeries)"]},"Tester(IsPcgsElementaryAbelianSeries)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPcgsElementaryAbelianSeries)"]},"Tester(PcgsElementaryAbelianSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcgsElementaryAbelianSeries)"]},"Tester(IndicesEANormalSteps)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndicesEANormalSteps)"]},"Tester(EANormalSeriesByPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(EANormalSeriesByPcgs)"]},"Tester(IsPcgsCentralSeries)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPcgsCentralSeries)"]},"Tester(PcgsCentralSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcgsCentralSeries)"]},"Tester(IndicesCentralNormalSteps)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndicesCentralNormalSteps)"]},"Tester(CentralNormalSeriesByPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(CentralNormalSeriesByPcgs)"]},"Tester(IsPcgsPCentralSeriesPGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPcgsPCentralSeriesPGroup)"]},"Tester(PcgsPCentralSeriesPGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcgsPCentralSeriesPGroup)"]},"Tester(IndicesPCentralNormalStepsPGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndicesPCentralNormalStepsPGroup)"]},"Tester(PCentralNormalSeriesByPcgsPGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(PCentralNormalSeriesByPcgsPGroup)"]},"Tester(IsPcgsChiefSeries)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPcgsChiefSeries)"]},"Tester(PcgsChiefSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcgsChiefSeries)"]},"Tester(IndicesChiefNormalSteps)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndicesChiefNormalSteps)"]},"Tester(ChiefNormalSeriesByPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(ChiefNormalSeriesByPcgs)"]},"Tester(IndicesNormalSteps)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndicesNormalSteps)"]},"Tester(NormalSeriesByPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalSeriesByPcgs)"]},"Tester(IsPrimeOrdersPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPrimeOrdersPcgs)"]},"Tester(IsFiniteOrdersPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFiniteOrdersPcgs)"]},"Tester(RefinedPcGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RefinedPcGroup)"]},"Tester(IsomorphismRefinedPcGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismRefinedPcGroup)"]},"IsInducedPcgs" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs","IsPcgs","IsInducedPcgs"]},"Tester(LeadCoeffsIGS)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeadCoeffsIGS)"]},"Tester(ParentPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(ParentPcgs)"]},"Tester(CanonicalPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalPcgs)"]},"Tester(IsCanonicalPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCanonicalPcgs)"]},"Tester(IsParentPcgsFamilyPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsParentPcgsFamilyPcgs)"]},"Tester(ElementaryAbelianSubseries)" : {"type" : "GAP_Attribute","implied" : ["Tester(ElementaryAbelianSubseries)"]},"Tester(IsFamilyPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFamilyPcgs)"]},"Tester(DenominatorOfModuloPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(DenominatorOfModuloPcgs)"]},"Tester(NumeratorOfModuloPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(NumeratorOfModuloPcgs)"]},"Tester(IsNumeratorParentPcgsFamilyPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNumeratorParentPcgsFamilyPcgs)"]},"IsPcgsPermGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)","IsPcgsPermGroupRep"]},"IsModuloPcgsPermGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)","IsPcgsPermGroupRep","IsModuloPcgsPermGroupRep"]},"Tester(IsSpecialPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSpecialPcgs)"]},"Tester(SpecialPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(SpecialPcgs)"]},"Tester(LGHeads)" : {"type" : "GAP_Attribute","implied" : ["Tester(LGHeads)"]},"Tester(LGTails)" : {"type" : "GAP_Attribute","implied" : ["Tester(LGTails)"]},"Tester(LGWeights)" : {"type" : "GAP_Attribute","implied" : ["Tester(LGWeights)"]},"Tester(LGLayers)" : {"type" : "GAP_Attribute","implied" : ["Tester(LGLayers)"]},"Tester(LGFirst)" : {"type" : "GAP_Attribute","implied" : ["Tester(LGFirst)"]},"Tester(LGLength)" : {"type" : "GAP_Attribute","implied" : ["Tester(LGLength)"]},"Tester(InducedPcgsWrtSpecialPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(InducedPcgsWrtSpecialPcgs)"]},"Tester(CanonicalPcgsWrtSpecialPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalPcgsWrtSpecialPcgs)"]},"Tester(IsInducedPcgsWrtSpecialPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsInducedPcgsWrtSpecialPcgs)"]},"Tester(IsCanonicalPcgsWrtSpecialPcgs)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCanonicalPcgsWrtSpecialPcgs)"]},"Tester(CanonicalPcgsWrtFamilyPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalPcgsWrtFamilyPcgs)"]},"Tester(CanonicalPcgsWrtHomePcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalPcgsWrtHomePcgs)"]},"Tester(FamilyPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(FamilyPcgs)"]},"Tester(HomePcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(HomePcgs)"]},"Tester(InducedPcgsWrtFamilyPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(InducedPcgsWrtFamilyPcgs)"]},"Tester(ComputedInducedPcgses)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedInducedPcgses)"]},"Tester(InducedPcgsWrtHomePcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(InducedPcgsWrtHomePcgs)"]},"Tester(Pcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(Pcgs)"]},"Tester(GeneralizedPcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneralizedPcgs)"]},"CanEasilyComputePcgs" : {"type" : "GAP_Filter","implied" : ["IsListOrCollection","IsCollection","CanComputeSize","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","CanComputeSizeAnySubgroup","IsSolvableGroup","Tester(IsSolvableGroup)","CanEasilyComputePcgs"]},"Tester(OmegaSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(OmegaSeries)"]},"Tester(NormalizerInHomePcgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizerInHomePcgs)"]},"Tester(MultiplicationTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(MultiplicationTable)"]},"Tester(AllBlocks)" : {"type" : "GAP_Attribute","implied" : ["Tester(AllBlocks)"]},"Tester(TransitiveIdentification)" : {"type" : "GAP_Attribute","implied" : ["Tester(TransitiveIdentification)"]},"Tester(PrimitiveIdentification)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimitiveIdentification)"]},"Tester(ONanScottType)" : {"type" : "GAP_Attribute","implied" : ["Tester(ONanScottType)"]},"Tester(SocleTypePrimitiveGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(SocleTypePrimitiveGroup)"]},"Tester(TwoClosure)" : {"type" : "GAP_Attribute","implied" : ["Tester(TwoClosure)"]},"IsGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages"]},"IsPreimagesByAsGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages"]},"IsGroupGeneralMappingByAsGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsGroupGeneralMappingByAsGroupGeneralMappingByImages"]},"Tester(AsGroupGeneralMappingByImages)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsGroupGeneralMappingByImages)"]},"Tester(MappingOfWhichItIsAsGGMBI)" : {"type" : "GAP_Attribute","implied" : ["Tester(MappingOfWhichItIsAsGGMBI)"]},"Tester(NaturalHomomorphismByNormalSubgroupNCInParent)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalHomomorphismByNormalSubgroupNCInParent)"]},"Tester(IsConjugatorIsomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsConjugatorIsomorphism)"]},"Tester(IsInnerAutomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsInnerAutomorphism)"]},"Tester(ConjugatorOfConjugatorIsomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConjugatorOfConjugatorIsomorphism)"]},"Tester(ImagesSmallestGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImagesSmallestGenerators)"]},"Tester(RegularActionHomomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(RegularActionHomomorphism)"]},"IsGroupGeneralMappingByPcgs" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsGroupGeneralMappingByPcgs"]},"IsPcGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsGroupGeneralMappingByPcgs","IsPcGroupGeneralMappingByImages"]},"IsToPcGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsToPcGroupGeneralMappingByImages"]},"IsNaturalHomomorphismPcGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsNaturalHomomorphismPcGroupRep"]},"IsPcgsToPcgsGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsGroupGeneralMappingByPcgs","IsPcGroupGeneralMappingByImages","IsToPcGroupGeneralMappingByImages","IsPcgsToPcgsGeneralMappingByImages"]},"Tester(DirectProductInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(DirectProductInfo)"]},"Tester(SubdirectProductInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(SubdirectProductInfo)"]},"Tester(SemidirectProductInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemidirectProductInfo)"]},"Tester(WreathProductInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(WreathProductInfo)"]},"Tester(FreeProductInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeProductInfo)"]},"IsWreathProductElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWreathProductElement"]},"CategoryCollections(IsWreathProductElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsWreathProductElement)"]},"IsWreathProductElementDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsWreathProductElement","IsWreathProductElementDefaultRep"]},"IsPermGroupGeneralMapping" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPermGroupGeneralMapping"]},"IsPermGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsPermGroupGeneralMapping","IsPermGroupGeneralMappingByImages"]},"IsToPermGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsToPermGroupGeneralMappingByImages"]},"Tester(IsNaturalSymmetricGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNaturalSymmetricGroup)"]},"Tester(IsNaturalAlternatingGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNaturalAlternatingGroup)"]},"Tester(IsAlternatingGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAlternatingGroup)"]},"Tester(IsSymmetricGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSymmetricGroup)"]},"Tester(SymmetricParentGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(SymmetricParentGroup)"]},"Tester(AlternatingSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AlternatingSubgroup)"]},"Tester(OrbitStabilizingParentGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrbitStabilizingParentGroup)"]},"Tester(DirectFactorsOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DirectFactorsOfGroup)"]},"Tester(SemidirectFactorsOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemidirectFactorsOfGroup)"]},"Tester(DecompositionTypesOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DecompositionTypesOfGroup)"]},"Tester(IsDihedralGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsDihedralGroup)"]},"Tester(DihedralGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(DihedralGenerators)"]},"Tester(IsQuaternionGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsQuaternionGroup)"]},"Tester(QuaternionGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(QuaternionGenerators)"]},"Tester(IsQuasiDihedralGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsQuasiDihedralGroup)"]},"Tester(QuasiDihedralGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(QuasiDihedralGenerators)"]},"Tester(IsPSL)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPSL)"]},"Tester(ParametersOfGroupViewedAsPSL)" : {"type" : "GAP_Attribute","implied" : ["Tester(ParametersOfGroupViewedAsPSL)"]},"Tester(ParametersOfGroupViewedAsSL)" : {"type" : "GAP_Attribute","implied" : ["Tester(ParametersOfGroupViewedAsSL)"]},"Tester(ParametersOfGroupViewedAsGL)" : {"type" : "GAP_Attribute","implied" : ["Tester(ParametersOfGroupViewedAsGL)"]},"Tester(AlternatingDegree)" : {"type" : "GAP_Attribute","implied" : ["Tester(AlternatingDegree)"]},"Tester(SymmetricDegree)" : {"type" : "GAP_Attribute","implied" : ["Tester(SymmetricDegree)"]},"Tester(PSLDegree)" : {"type" : "GAP_Attribute","implied" : ["Tester(PSLDegree)"]},"Tester(PSLUnderlyingField)" : {"type" : "GAP_Attribute","implied" : ["Tester(PSLUnderlyingField)"]},"Tester(SLDegree)" : {"type" : "GAP_Attribute","implied" : ["Tester(SLDegree)"]},"Tester(SLUnderlyingField)" : {"type" : "GAP_Attribute","implied" : ["Tester(SLUnderlyingField)"]},"Tester(GLDegree)" : {"type" : "GAP_Attribute","implied" : ["Tester(GLDegree)"]},"Tester(GLUnderlyingField)" : {"type" : "GAP_Attribute","implied" : ["Tester(GLUnderlyingField)"]},"Tester(StructureDescription)" : {"type" : "GAP_Attribute","implied" : ["Tester(StructureDescription)"]},"IsQuotientSystem" : {"type" : "GAP_Category","implied" : ["IsQuotientSystem"]},"Tester(IsPQuotientSystem)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPQuotientSystem)"]},"Tester(IsNilpQuotientSystem)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNilpQuotientSystem)"]},"IsExternalSet" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet"]},"IsExternalSubset" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset"]},"IsExternalOrbit" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit"]},"IsExternalSetByPcgs" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSetByPcgs"]},"IsExternalSetDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSetDefaultRep"]},"IsExternalSetByActorsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSetByActorsRep"]},"Tester(ActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(ActingDomain)"]},"Tester(HomeEnumerator)" : {"type" : "GAP_Attribute","implied" : ["Tester(HomeEnumerator)"]},"IsActionHomomorphism" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism"]},"IsActionHomomorphismByActors" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismByActors"]},"IsActionHomomorphismSubset" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismSubset"]},"Tester(ActionKernelExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(ActionKernelExternalSet)"]},"IsActionHomomorphismByBase" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismByBase"]},"IsConstituentHomomorphism" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsConstituentHomomorphism"]},"IsBlocksHomomorphism" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsBlocksHomomorphism"]},"IsLinearActionHomomorphism" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsLinearActionHomomorphism"]},"IsProjectiveActionHomomorphism" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsProjectiveActionHomomorphism"]},"Tester(LinearActionBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(LinearActionBasis)"]},"Tester(FunctionAction)" : {"type" : "GAP_Attribute","implied" : ["Tester(FunctionAction)"]},"Tester(StabilizerOfExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(StabilizerOfExternalSet)"]},"Tester(CanonicalRepresentativeOfExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalRepresentativeOfExternalSet)","Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]},"Tester(CanonicalRepresentativeDeterminatorOfExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalRepresentativeDeterminatorOfExternalSet)","Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]},"Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanEasilyDetermineCanonicalRepresentativeExternalSet)"]},"Tester(ActorOfExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(ActorOfExternalSet)"]},"Tester(ActionHomomorphismAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(ActionHomomorphismAttr)"]},"Tester(SurjectiveActionHomomorphismAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(SurjectiveActionHomomorphismAttr)"]},"Tester(UnderlyingExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingExternalSet)"]},"Tester(ExternalSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExternalSet)"]},"Tester(Orbits)" : {"type" : "GAP_Attribute","implied" : ["Tester(Orbits)"]},"Tester(OrbitsDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrbitsDomain)"]},"Tester(OrbitLengths)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrbitLengths)"]},"Tester(OrbitLengthsDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrbitLengthsDomain)"]},"Tester(ExternalOrbits)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExternalOrbits)"]},"Tester(ExternalOrbitsStabilizers)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExternalOrbitsStabilizers)"]},"Tester(Transitivity)" : {"type" : "GAP_Attribute","implied" : ["Tester(Transitivity)"]},"Tester(BlocksAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(BlocksAttr)"]},"Tester(MaximalBlocksAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalBlocksAttr)"]},"Tester(RepresentativesMinimalBlocksAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(RepresentativesMinimalBlocksAttr)"]},"Tester(Earns)" : {"type" : "GAP_Attribute","implied" : ["Tester(Earns)"]},"Tester(IsTransitive)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTransitive)"]},"Tester(IsPrimitive)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPrimitive)"]},"Tester(IsPrimitiveAffine)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPrimitiveAffine)"]},"Tester(IsSemiRegular)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSemiRegular)"]},"Tester(IsRegular)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRegular)"]},"Tester(RankAction)" : {"type" : "GAP_Attribute","implied" : ["Tester(RankAction)"]},"Tester(StabChainMutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(StabChainMutable)"]},"Tester(StabChainImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(StabChainImmutable)"]},"Tester(StabChainOptions)" : {"type" : "GAP_Attribute","implied" : ["Tester(StabChainOptions)"]},"Tester(BaseOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(BaseOfGroup)"]},"Tester(MinimalStabChain)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimalStabChain)"]},"IsPermOnEnumerator" : {"type" : "GAP_Category","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement","IsPermOnEnumerator"]},"IsExternalOrbitByStabilizerRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsExternalOrbitByStabilizerRep"]},"IsConjugacyClassGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsConjugacyClassGroupRep"]},"IsConjugacyClassPermGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsExternalOrbitByStabilizerRep","IsConjugacyClassGroupRep","IsConjugacyClassPermGroupRep"]},"IsRationalClassGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsRationalClassGroupRep"]},"IsRationalClassPermGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsRationalClassGroupRep","IsRationalClassPermGroupRep"]},"Tester(DecomposedRationalClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(DecomposedRationalClass)"]},"Tester(StoredPermliftSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(StoredPermliftSeries)"]},"Tester(ComputedAscendingChains)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedAscendingChains)"]},"IsDoubleCoset" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsExtRSet","IsDoubleCoset"]},"Tester(LeftActingGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeftActingGroup)"]},"Tester(RightActingGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightActingGroup)"]},"Tester(RepresentativesContainedRightCosets)" : {"type" : "GAP_Attribute","implied" : ["Tester(RepresentativesContainedRightCosets)"]},"IsRightCoset" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsRightCoset"]},"Tester(NaturalHomomorphismsPool)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalHomomorphismsPool)"]},"Tester(SocleComplement)" : {"type" : "GAP_Attribute","implied" : ["Tester(SocleComplement)"]},"Tester(SocleDimensions)" : {"type" : "GAP_Attribute","implied" : ["Tester(SocleDimensions)"]},"Tester(ModuleOfExtension)" : {"type" : "GAP_Attribute","implied" : ["Tester(ModuleOfExtension)"]},"Tester(OmegaAndLowerPCentralSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(OmegaAndLowerPCentralSeries)"]},"Tester(SchurCover)" : {"type" : "GAP_Attribute","implied" : ["Tester(SchurCover)"]},"Tester(EpimorphismSchurCover)" : {"type" : "GAP_Attribute","implied" : ["Tester(EpimorphismSchurCover)"]},"Tester(AbelianInvariantsMultiplier)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbelianInvariantsMultiplier)"]},"Tester(Epicentre)" : {"type" : "GAP_Attribute","implied" : ["Tester(Epicentre)"]},"Tester(IsCentralFactor)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCentralFactor)"]},"IsConjugacyClassSubgroupsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsConjugacyClassSubgroupsRep"]},"IsConjugacyClassSubgroupsByStabilizerRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsExternalOrbitByStabilizerRep","IsConjugacyClassSubgroupsRep","IsConjugacyClassSubgroupsByStabilizerRep"]},"IsLatticeSubgroupsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLatticeSubgroupsRep"]},"Tester(Zuppos)" : {"type" : "GAP_Attribute","implied" : ["Tester(Zuppos)"]},"Tester(MaximalSubgroupsLattice)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalSubgroupsLattice)"]},"Tester(MinimalSupergroupsLattice)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimalSupergroupsLattice)"]},"Tester(TomDataAlmostSimpleRecognition)" : {"type" : "GAP_Attribute","implied" : ["Tester(TomDataAlmostSimpleRecognition)"]},"Tester(IsFrattiniFree)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFrattiniFree)"]},"IsStraightLineProgram" : {"type" : "GAP_Category","implied" : ["IsStraightLineProgram"]},"Tester(LinesOfStraightLineProgram)" : {"type" : "GAP_Attribute","implied" : ["Tester(LinesOfStraightLineProgram)"]},"Tester(NrInputsOfStraightLineProgram)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrInputsOfStraightLineProgram)"]},"StraightLineProgramElmRankFilter" : {"type" : "GAP_Filter","implied" : ["StraightLineProgramElmRankFilter"]},"IsStraightLineProgElm" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","StraightLineProgramElmRankFilter","IsStraightLineProgElm"]},"Tester(StraightLineProgElmType)" : {"type" : "GAP_Attribute","implied" : ["Tester(StraightLineProgElmType)"]},"Tester(SlotUsagePattern)" : {"type" : "GAP_Attribute","implied" : ["Tester(SlotUsagePattern)"]},"Tester(LargestNrSlots)" : {"type" : "GAP_Attribute","implied" : ["Tester(LargestNrSlots)"]},"IsObjWithMemoryRankFilter" : {"type" : "GAP_Filter","implied" : ["IsObjWithMemoryRankFilter"]},"IsObjWithMemory" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsObjWithMemoryRankFilter","IsObjWithMemory"]},"Tester(TypeOfObjWithMemory)" : {"type" : "GAP_Attribute","implied" : ["Tester(TypeOfObjWithMemory)"]},"IsSubgroupFgGroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSubgroupFgGroup"]},"IsSubgroupFpGroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSubgroupFgGroup","IsSubgroupFpGroup"]},"IsElementOfFpGroup" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsElementOfFpGroup"]},"CategoryCollections(IsElementOfFpGroup)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsElementOfFpGroup)"]},"CategoryFamily(IsElementOfFpGroup)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsElementOfFpGroup)"]},"Tester(FpElmEqualityMethod)" : {"type" : "GAP_Attribute","implied" : ["Tester(FpElmEqualityMethod)"]},"Tester(FpElmComparisonMethod)" : {"type" : "GAP_Attribute","implied" : ["Tester(FpElmComparisonMethod)"]},"Tester(FpElementNFFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(FpElementNFFunction)"]},"Tester(CosetTableInWholeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(CosetTableInWholeGroup)"]},"Tester(CosetTableNormalClosureInWholeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(CosetTableNormalClosureInWholeGroup)"]},"IsSubgroupOfWholeGroupByQuotientRep" : {"type" : "GAP_Representation","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsSubgroupFgGroup","IsSubgroupFpGroup","IsSubgroupOfWholeGroupByQuotientRep"]},"Tester(AsSubgroupOfWholeGroupByQuotient)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSubgroupOfWholeGroupByQuotient)"]},"Tester(FreeGeneratorsOfFpGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeGeneratorsOfFpGroup)"]},"Tester(RelatorsOfFpGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelatorsOfFpGroup)"]},"Tester(FreeGroupOfFpGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeGroupOfFpGroup)"]},"Tester(IndicesInvolutaryGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndicesInvolutaryGenerators)"]},"Tester(StoredExcludedOrders)" : {"type" : "GAP_Attribute","implied" : ["Tester(StoredExcludedOrders)"]},"Tester(FPFaithHom)" : {"type" : "GAP_Attribute","implied" : ["Tester(FPFaithHom)"]},"Tester(AugmentedCosetTableMtcInWholeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentedCosetTableMtcInWholeGroup)"]},"Tester(AugmentedCosetTableRrsInWholeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentedCosetTableRrsInWholeGroup)"]},"Tester(AugmentedCosetTableNormalClosureInWholeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentedCosetTableNormalClosureInWholeGroup)"]},"IsPresentation" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsPresentation"]},"Tester(PrimaryGeneratorWords)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimaryGeneratorWords)"]},"Tester(TietzeOrigin)" : {"type" : "GAP_Attribute","implied" : ["Tester(TietzeOrigin)"]},"Tester(TzOptions)" : {"type" : "GAP_Attribute","implied" : ["Tester(TzOptions)"]},"Extrarankfilter" : {"type" : "GAP_Filter","implied" : ["Extrarankfilter"]},"IsFromFpGroupGeneralMapping" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","Extrarankfilter","IsFromFpGroupGeneralMapping"]},"IsFromFpGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsFromFpGroupGeneralMapping","IsFromFpGroupGeneralMappingByImages"]},"IsFromFpGroupStdGensGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsFromFpGroupGeneralMapping","IsFromFpGroupGeneralMappingByImages","IsFromFpGroupStdGensGeneralMappingByImages"]},"IsToFpGroupGeneralMappingByImages" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsToFpGroupGeneralMappingByImages"]},"Tester(IsWordDecompHomomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsWordDecompHomomorphism)"]},"Tester(CosetTableFpHom)" : {"type" : "GAP_Attribute","implied" : ["Tester(CosetTableFpHom)"]},"Tester(IsomorphismSimplifiedFpGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismSimplifiedFpGroup)"]},"Tester(EpimorphismFromFreeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(EpimorphismFromFreeGroup)"]},"IsCanonicalBasisIntegersRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisIntegersRep"]},"Tester(NiceMonomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceMonomorphism)"]},"IsNiceMonomorphism" : {"type" : "GAP_Filter","implied" : ["IsNiceMonomorphism"]},"Tester(IsCanonicalNiceMonomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCanonicalNiceMonomorphism)"]},"Tester(CanonicalNiceMonomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalNiceMonomorphism)"]},"Tester(NiceObject)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceObject)"]},"Tester(IsHandledByNiceMonomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsHandledByNiceMonomorphism)"]},"Tester(SeedFaithfulAction)" : {"type" : "GAP_Attribute","implied" : ["Tester(SeedFaithfulAction)"]},"Tester(AutomorphismGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AutomorphismGroup)"]},"Tester(IsGroupOfAutomorphisms)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupOfAutomorphisms)"]},"Tester(IsGroupOfAutomorphismsFiniteGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupOfAutomorphismsFiniteGroup)"]},"Tester(AutomorphismDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(AutomorphismDomain)"]},"Tester(IsAutomorphismGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAutomorphismGroup)"]},"Tester(InnerAutomorphismsAutomorphismGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(InnerAutomorphismsAutomorphismGroup)"]},"Tester(DefaultFieldOfMatrixGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DefaultFieldOfMatrixGroup)"]},"Tester(DimensionOfMatrixGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DimensionOfMatrixGroup)"]},"Tester(FieldOfMatrixGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FieldOfMatrixGroup)"]},"Tester(TransposedMatrixGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(TransposedMatrixGroup)"]},"Tester(IsGeneralLinearGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGeneralLinearGroup)"]},"Tester(IsNaturalGL)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNaturalGL)"]},"Tester(IsSpecialLinearGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSpecialLinearGroup)"]},"Tester(IsNaturalSL)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNaturalSL)"]},"Tester(IsSubgroupSL)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSubgroupSL)"]},"Tester(InvariantBilinearForm)" : {"type" : "GAP_Attribute","implied" : ["Tester(InvariantBilinearForm)"]},"Tester(IsFullSubgroupGLorSLRespectingBilinearForm)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"]},"Tester(InvariantSesquilinearForm)" : {"type" : "GAP_Attribute","implied" : ["Tester(InvariantSesquilinearForm)"]},"Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]},"Tester(InvariantQuadraticForm)" : {"type" : "GAP_Attribute","implied" : ["Tester(InvariantQuadraticForm)"]},"Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullSubgroupGLorSLRespectingQuadraticForm)"]},"CanComputeFittingFree" : {"type" : "GAP_Filter","implied" : ["IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsFiniteOrderElement)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsCompletelySimpleSemigroup","Tester(IsCompletelySimpleSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)","CanComputeFittingFree","IsNilpotentByFinite","Tester(IsNilpotentByFinite)"]},"Tester(FittingFreeLiftSetup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FittingFreeLiftSetup)"]},"Tester(RecogDecompinfoHomomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(RecogDecompinfoHomomorphism)"]},"Tester(DirectFactorsFittingFreeSocle)" : {"type" : "GAP_Attribute","implied" : ["Tester(DirectFactorsFittingFreeSocle)"]},"Tester(ChiefSeriesTF)" : {"type" : "GAP_Attribute","implied" : ["Tester(ChiefSeriesTF)"]},"Tester(IsRationalMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRationalMatrixGroup)"]},"Tester(IsIntegerMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIntegerMatrixGroup)"]},"Tester(ZClassRepsQClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(ZClassRepsQClass)"]},"Tester(NormalizerInGLnZ)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizerInGLnZ)"]},"Tester(CentralizerInGLnZ)" : {"type" : "GAP_Attribute","implied" : ["Tester(CentralizerInGLnZ)"]},"Tester(IsBravaisGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBravaisGroup)"]},"Tester(BravaisGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(BravaisGroup)"]},"Tester(BravaisSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(BravaisSubgroups)"]},"Tester(BravaisSupergroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(BravaisSupergroups)"]},"Tester(NormalizerInGLnZBravaisGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizerInGLnZBravaisGroup)"]},"Tester(InvariantLattice)" : {"type" : "GAP_Attribute","implied" : ["Tester(InvariantLattice)"]},"IsPerfectLibraryGroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsPerfectLibraryGroup"]},"Tester(PerfectIdentification)" : {"type" : "GAP_Attribute","implied" : ["Tester(PerfectIdentification)"]},"Tester(DataAboutSimpleGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DataAboutSimpleGroup)"]},"IsImfMatrixGroup" : {"type" : "GAP_Filter","implied" : ["IsImfMatrixGroup"]},"Tester(ImfRecord)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImfRecord)"]},"IsOrdering" : {"type" : "GAP_Category","implied" : ["IsOrdering"]},"Tester(OrderingsFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrderingsFamily)"]},"Tester(IsWellFoundedOrdering)" : {"type" : "GAP_Tester","implied" : ["Tester(IsWellFoundedOrdering)"]},"Tester(IsTotalOrdering)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTotalOrdering)"]},"Tester(FamilyForOrdering)" : {"type" : "GAP_Attribute","implied" : ["Tester(FamilyForOrdering)"]},"Tester(LessThanFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(LessThanFunction)"]},"Tester(LessThanOrEqualFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(LessThanOrEqualFunction)"]},"Tester(IsOrderingOnFamilyOfAssocWords)" : {"type" : "GAP_Tester","implied" : ["Tester(IsOrderingOnFamilyOfAssocWords)"]},"Tester(LetterRepWordsLessFunc)" : {"type" : "GAP_Attribute","implied" : ["Tester(LetterRepWordsLessFunc)"]},"Tester(IsTranslationInvariantOrdering)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTranslationInvariantOrdering)"]},"Tester(OrderingOnGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrderingOnGenerators)"]},"Tester(IsShortLexOrdering)" : {"type" : "GAP_Tester","implied" : ["Tester(IsShortLexOrdering)"]},"Tester(WeightOfGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(WeightOfGenerators)"]},"Tester(IsWeightLexOrdering)" : {"type" : "GAP_Tester","implied" : ["Tester(IsWeightLexOrdering)"]},"Tester(IsBasicWreathProductOrdering)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBasicWreathProductOrdering)"]},"Tester(IsWreathProductOrdering)" : {"type" : "GAP_Tester","implied" : ["Tester(IsWreathProductOrdering)"]},"Tester(LevelsOfGenerators)" : {"type" : "GAP_Attribute","implied" : ["Tester(LevelsOfGenerators)"]},"Tester(LargestImageOfMovedPoint)" : {"type" : "GAP_Attribute","implied" : ["Tester(LargestImageOfMovedPoint)"]},"Tester(SmallestImageOfMovedPoint)" : {"type" : "GAP_Attribute","implied" : ["Tester(SmallestImageOfMovedPoint)"]},"Tester(RankOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(RankOfTransformation)"]},"Tester(AsPermutation)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsPermutation)"]},"Tester(AsTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsTransformation)"]},"Tester(PermutationOfImage)" : {"type" : "GAP_Attribute","implied" : ["Tester(PermutationOfImage)"]},"Tester(DegreeOfTransformationCollection)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOfTransformationCollection)"]},"Tester(FlatKernelOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(FlatKernelOfTransformation)"]},"Tester(ImageSetOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImageSetOfTransformation)"]},"Tester(IndexPeriodOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndexPeriodOfTransformation)"]},"Tester(KernelOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(KernelOfTransformation)"]},"Tester(SmallestIdempotentPower)" : {"type" : "GAP_Attribute","implied" : ["Tester(SmallestIdempotentPower)"]},"Tester(ComponentRepsOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComponentRepsOfTransformation)"]},"Tester(NrComponentsOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrComponentsOfTransformation)"]},"Tester(ComponentsOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComponentsOfTransformation)"]},"Tester(CyclesOfTransformation)" : {"type" : "GAP_Attribute","implied" : ["Tester(CyclesOfTransformation)"]},"Tester(LeftOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeftOne)"]},"Tester(RightOne)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightOne)"]},"Tester(DomainOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(DomainOfPartialPerm)"]},"Tester(ImageListOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImageListOfPartialPerm)"]},"Tester(ImageSetOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImageSetOfPartialPerm)"]},"Tester(IndexPeriodOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(IndexPeriodOfPartialPerm)"]},"Tester(ComponentRepsOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComponentRepsOfPartialPerm)"]},"Tester(NrComponentsOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrComponentsOfPartialPerm)"]},"Tester(ComponentsOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComponentsOfPartialPerm)"]},"Tester(FixedPointsOfPartialPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(FixedPointsOfPartialPerm)"]},"Tester(NrFixedPoints)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrFixedPoints)"]},"Tester(DegreeOfPartialPermCollection)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOfPartialPermCollection)"]},"Tester(CodegreeOfPartialPermCollection)" : {"type" : "GAP_Attribute","implied" : ["Tester(CodegreeOfPartialPermCollection)"]},"Tester(RankOfPartialPermCollection)" : {"type" : "GAP_Attribute","implied" : ["Tester(RankOfPartialPermCollection)"]},"Tester(DomainOfPartialPermCollection)" : {"type" : "GAP_Attribute","implied" : ["Tester(DomainOfPartialPermCollection)"]},"Tester(ImageOfPartialPermCollection)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImageOfPartialPermCollection)"]},"Tester(TransformationRepresentation)" : {"type" : "GAP_Attribute","implied" : ["Tester(TransformationRepresentation)"]},"IsElementOfFpSemigroup" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsElementOfFpSemigroup"]},"CategoryCollections(IsElementOfFpSemigroup)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsElementOfFpSemigroup)"]},"CategoryFamily(IsElementOfFpSemigroup)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsElementOfFpSemigroup)"]},"Tester(FreeGeneratorsOfFpSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeGeneratorsOfFpSemigroup)"]},"Tester(FreeSemigroupOfFpSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeSemigroupOfFpSemigroup)"]},"Tester(RelationsOfFpSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelationsOfFpSemigroup)"]},"Tester(IsomorphismFpSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismFpSemigroup)"]},"IsElementOfFpMonoid" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsAssociativeElement","IsElementOfFpMonoid"]},"CategoryCollections(IsElementOfFpMonoid)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsElementOfFpMonoid)"]},"CategoryFamily(IsElementOfFpMonoid)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsElementOfFpMonoid)"]},"Tester(FreeGeneratorsOfFpMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeGeneratorsOfFpMonoid)"]},"Tester(FreeMonoidOfFpMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeMonoidOfFpMonoid)"]},"Tester(RelationsOfFpMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelationsOfFpMonoid)"]},"Tester(IsomorphismFpMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismFpMonoid)"]},"Tester(ReducedConfluentRewritingSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(ReducedConfluentRewritingSystem)"]},"Tester(FreeMonoidOfRewritingSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeMonoidOfRewritingSystem)"]},"Tester(FamilyForRewritingSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(FamilyForRewritingSystem)"]},"Tester(FreeSemigroupOfRewritingSystem)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeSemigroupOfRewritingSystem)"]},"IsKnuthBendixRewritingSystem" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsRewritingSystem","IsKnuthBendixRewritingSystem"]},"Tester(TzRules)" : {"type" : "GAP_Attribute","implied" : ["Tester(TzRules)"]},"Tester(CosetTableOfFpSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(CosetTableOfFpSemigroup)"]},"IsMonoidByAdjoiningIdentityElt" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsAssociativeElement","IsMonoidByAdjoiningIdentityElt"]},"IsMonoidByAdjoiningIdentity" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsMonoidByAdjoiningIdentity"]},"Tester(AdjoinedIdentityFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdjoinedIdentityFamily)"]},"Tester(UnderlyingSemigroupFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingSemigroupFamily)"]},"Tester(AdjoinedIdentityDefaultType)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdjoinedIdentityDefaultType)"]},"IsMonoidByAdjoiningIdentityEltRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsMonoidByAdjoiningIdentityEltRep"]},"Tester(MonoidByAdjoiningIdentity)" : {"type" : "GAP_Attribute","implied" : ["Tester(MonoidByAdjoiningIdentity)"]},"Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingSemigroupOfMonoidByAdjoiningIdentity)"]},"Tester(MonoidByAdjoiningIdentityElt)" : {"type" : "GAP_Attribute","implied" : ["Tester(MonoidByAdjoiningIdentityElt)"]},"Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt)"]},"IsGreensRelation" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation"]},"IsGreensRRelation" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensRRelation"]},"IsGreensLRelation" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensLRelation"]},"IsGreensJRelation" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensJRelation"]},"IsGreensHRelation" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensHRelation"]},"IsGreensDRelation" : {"type" : "GAP_Category","implied" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)","IsGreensRelation","IsGreensDRelation"]},"Tester(IsFiniteSemigroupGreensRelation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFiniteSemigroupGreensRelation)"]},"Tester(GreensRRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensRRelation)"]},"Tester(GreensLRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensLRelation)"]},"Tester(GreensJRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensJRelation)"]},"Tester(GreensDRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensDRelation)"]},"Tester(GreensHRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensHRelation)"]},"Tester(AssociatedConcreteSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AssociatedConcreteSemigroup)"]},"Tester(AssociatedFpSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AssociatedFpSemigroup)"]},"IsGreensClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass"]},"IsGreensRClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensRClass"]},"IsGreensLClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensLClass"]},"IsGreensJClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensJClass"]},"IsGreensHClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensHClass"]},"IsGreensDClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsEquivalenceClass","IsGreensClass","IsGreensDClass"]},"Tester(GreensRClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensRClasses)"]},"Tester(GreensLClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensLClasses)"]},"Tester(GreensJClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensJClasses)"]},"Tester(GreensDClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensDClasses)"]},"Tester(GreensHClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(GreensHClasses)"]},"Tester(RClassOfHClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(RClassOfHClass)"]},"Tester(LClassOfHClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(LClassOfHClass)"]},"Tester(DClassOfHClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(DClassOfHClass)"]},"Tester(DClassOfLClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(DClassOfLClass)"]},"Tester(DClassOfRClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(DClassOfRClass)"]},"Tester(GroupHClassOfGreensDClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(GroupHClassOfGreensDClass)"]},"Tester(IsRegularDClass)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRegularDClass)"]},"Tester(IsGroupHClass)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupHClass)"]},"Tester(EggBoxOfDClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(EggBoxOfDClass)"]},"Tester(InternalRepGreensRelation)" : {"type" : "GAP_Attribute","implied" : ["Tester(InternalRepGreensRelation)"]},"Tester(CanonicalGreensClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(CanonicalGreensClass)"]},"IsSemigroupGeneralMappingRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","IsSemigroupGeneralMappingRep"]},"IsSemigroupHomomorphismByImagesRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsSemigroupHomomorphismByImagesRep"]},"Tester(IsFpSemigpReducedElt)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFpSemigpReducedElt)"]},"Tester(IsFpMonoidReducedElt)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFpMonoidReducedElt)"]},"Tester(IsFullTransformationSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFullTransformationSemigroup)"]},"Tester(DegreeOfTransformationSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOfTransformationSemigroup)"]},"Tester(IsomorphismTransformationSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismTransformationSemigroup)"]},"Tester(IsomorphismTransformationMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismTransformationMonoid)"]},"Tester(AntiIsomorphismTransformationSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AntiIsomorphismTransformationSemigroup)"]},"IsReesMatrixSemigroupElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsReesMatrixSemigroupElement"]},"IsReesZeroMatrixSemigroupElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsReesZeroMatrixSemigroupElement"]},"CategoryCollections(IsReesMatrixSemigroupElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsReesMatrixSemigroupElement)"]},"CategoryCollections(IsReesZeroMatrixSemigroupElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","CategoryCollections(IsReesZeroMatrixSemigroupElement)"]},"Tester(IsReesMatrixSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsReesMatrixSemigroup)"]},"Tester(IsReesZeroMatrixSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsReesZeroMatrixSemigroup)"]},"Tester(Matrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(Matrix)"]},"Tester(Rows)" : {"type" : "GAP_Attribute","implied" : ["Tester(Rows)"]},"Tester(Columns)" : {"type" : "GAP_Attribute","implied" : ["Tester(Columns)"]},"Tester(UnderlyingSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingSemigroup)"]},"Tester(AssociatedReesMatrixSemigroupOfDClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(AssociatedReesMatrixSemigroupOfDClass)"]},"Tester(IsomorphismReesMatrixSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismReesMatrixSemigroup)"]},"Tester(IsomorphismReesZeroMatrixSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismReesZeroMatrixSemigroup)"]},"Tester(ReesMatrixSemigroupOfFamily)" : {"type" : "GAP_Attribute","implied" : ["Tester(ReesMatrixSemigroupOfFamily)"]},"Tester(TypeReesMatrixSemigroupElements)" : {"type" : "GAP_Attribute","implied" : ["Tester(TypeReesMatrixSemigroupElements)"]},"IsQuotientSemigroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsMagma","IsAssociative","Tester(IsAssociative)","IsQuotientSemigroup"]},"Tester(QuotientSemigroupPreimage)" : {"type" : "GAP_Attribute","implied" : ["Tester(QuotientSemigroupPreimage)"]},"Tester(QuotientSemigroupCongruence)" : {"type" : "GAP_Attribute","implied" : ["Tester(QuotientSemigroupCongruence)"]},"Tester(QuotientSemigroupHomomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(QuotientSemigroupHomomorphism)"]},"Tester(DegreeOfPartialPermSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOfPartialPermSemigroup)"]},"Tester(CodegreeOfPartialPermSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(CodegreeOfPartialPermSemigroup)"]},"Tester(RankOfPartialPermSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RankOfPartialPermSemigroup)"]},"Tester(IsSymmetricInverseSemigroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSymmetricInverseSemigroup)"]},"Tester(IsomorphismPartialPermSemigroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismPartialPermSemigroup)"]},"Tester(IsomorphismPartialPermMonoid)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismPartialPermMonoid)"]},"IsNearlyCharacterTable" : {"type" : "GAP_Category","implied" : ["IsNearlyCharacterTable"]},"IsCharacterTable" : {"type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable"]},"IsOrdinaryTable" : {"type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable","IsOrdinaryTable"]},"IsBrauerTable" : {"type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable","IsBrauerTable"]},"IsCharacterTableInProgress" : {"type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTableInProgress"]},"Tester(UnderlyingGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingGroup)"]},"Tester(IdentificationOfConjugacyClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdentificationOfConjugacyClasses)"]},"Tester(CharacterDegrees)" : {"type" : "GAP_Attribute","implied" : ["Tester(CharacterDegrees)"]},"Tester(Irr)" : {"type" : "GAP_Attribute","implied" : ["Tester(Irr)"]},"Tester(LinearCharacters)" : {"type" : "GAP_Attribute","implied" : ["Tester(LinearCharacters)"]},"Tester(IBr)" : {"type" : "GAP_Attribute","implied" : ["Tester(IBr)"]},"Tester(OrdinaryCharacterTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrdinaryCharacterTable)"]},"Tester(IsAlmostSimpleCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAlmostSimpleCharacterTable)"]},"Tester(IsMonomialCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMonomialCharacterTable)"]},"Tester(IsNilpotentCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNilpotentCharacterTable)"]},"Tester(IsPerfectCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPerfectCharacterTable)"]},"Tester(IsSimpleCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSimpleCharacterTable)"]},"Tester(IsSolvableCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSolvableCharacterTable)"]},"Tester(IsSporadicSimpleCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSporadicSimpleCharacterTable)"]},"Tester(IsSupersolvableCharacterTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSupersolvableCharacterTable)"]},"Tester(OrdersClassRepresentatives)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrdersClassRepresentatives)"]},"Tester(SizesCentralizers)" : {"type" : "GAP_Attribute","implied" : ["Tester(SizesCentralizers)"]},"Tester(SizesConjugacyClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(SizesConjugacyClasses)"]},"Tester(AutomorphismsOfTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(AutomorphismsOfTable)"]},"Tester(UnderlyingCharacteristic)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingCharacteristic)"]},"Tester(ClassNames)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassNames)"]},"Tester(CharacterNames)" : {"type" : "GAP_Attribute","implied" : ["Tester(CharacterNames)"]},"Tester(ClassParameters)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassParameters)"]},"Tester(CharacterParameters)" : {"type" : "GAP_Attribute","implied" : ["Tester(CharacterParameters)"]},"Tester(Identifier)" : {"type" : "GAP_Attribute","implied" : ["Tester(Identifier)"]},"Tester(InverseClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(InverseClasses)"]},"Tester(RealClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(RealClasses)"]},"Tester(ClassRoots)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassRoots)"]},"Tester(ClassPositionsOfNormalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfNormalSubgroups)"]},"Tester(ClassPositionsOfMaximalNormalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfMaximalNormalSubgroups)"]},"Tester(ClassPositionsOfMinimalNormalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfMinimalNormalSubgroups)"]},"Tester(ClassPositionsOfCentre)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfCentre)"]},"Tester(ClassPositionsOfDirectProductDecompositions)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfDirectProductDecompositions)"]},"Tester(ClassPositionsOfDerivedSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfDerivedSubgroup)"]},"Tester(ClassPositionsOfElementaryAbelianSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfElementaryAbelianSeries)"]},"Tester(ClassPositionsOfFittingSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfFittingSubgroup)"]},"Tester(ClassPositionsOfSolvableRadical)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfSolvableRadical)"]},"Tester(ClassPositionsOfLowerCentralSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfLowerCentralSeries)"]},"Tester(ClassPositionsOfUpperCentralSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfUpperCentralSeries)"]},"Tester(ClassPositionsOfSolvableResiduum)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfSolvableResiduum)"]},"Tester(ClassPositionsOfSupersolvableResiduum)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfSupersolvableResiduum)"]},"Tester(ComputedPrimeBlockss)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedPrimeBlockss)"]},"Tester(BlocksInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(BlocksInfo)"]},"Tester(DecompositionMatrix)" : {"type" : "GAP_Attribute","implied" : ["Tester(DecompositionMatrix)"]},"Tester(ComputedIsPSolvableCharacterTables)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedIsPSolvableCharacterTables)"]},"Tester(ComputedIndicators)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedIndicators)"]},"Tester(ComputedBrauerTables)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedBrauerTables)"]},"Tester(DisplayOptions)" : {"type" : "GAP_Attribute","implied" : ["Tester(DisplayOptions)"]},"Tester(FactorsOfDirectProduct)" : {"type" : "GAP_Attribute","implied" : ["Tester(FactorsOfDirectProduct)"]},"Tester(CharacterTableIsoclinic)" : {"type" : "GAP_Attribute","implied" : ["Tester(CharacterTableIsoclinic)"]},"Tester(SourceOfIsoclinicTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(SourceOfIsoclinicTable)"]},"Tester(ClassPermutation)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPermutation)"]},"Tester(NormalSubgroupClassesInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalSubgroupClassesInfo)"]},"IsLibraryCharacterTableRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLibraryCharacterTableRep"]},"IsGenericCharacterTableRep" : {"type" : "GAP_Representation","implied" : ["IsNearlyCharacterTable","IsGenericCharacterTableRep"]},"IsClassFunction" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsExtAElement","CategoryCollections(IsExtAElement)","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","IsMultiplicativeElement","CategoryCollections(IsMultiplicativeElement)","IsMultiplicativeElementWithOne","CategoryCollections(IsMultiplicativeElementWithOne)","IsMultiplicativeElementWithInverse","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralizedRowVector","IsAssociativeElement","IsCommutativeElement","IsClassFunction"]},"Tester(UnderlyingCharacterTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingCharacterTable)"]},"Tester(ValuesOfClassFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(ValuesOfClassFunction)"]},"Tester(GlobalPartitionOfClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(GlobalPartitionOfClasses)"]},"Tester(TrivialCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(TrivialCharacter)"]},"Tester(NaturalCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalCharacter)"]},"Tester(IsCharacter)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCharacter)"]},"Tester(IsVirtualCharacter)" : {"type" : "GAP_Tester","implied" : ["Tester(IsVirtualCharacter)"]},"Tester(IsIrreducibleCharacter)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIrreducibleCharacter)"]},"Tester(CentreOfCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(CentreOfCharacter)"]},"Tester(ConstituentsOfCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConstituentsOfCharacter)"]},"Tester(DegreeOfCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeOfCharacter)"]},"Tester(KernelOfCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(KernelOfCharacter)"]},"Tester(ClassPositionsOfKernel)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassPositionsOfKernel)"]},"Tester(CentralCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(CentralCharacter)"]},"Tester(DeterminantOfCharacter)" : {"type" : "GAP_Attribute","implied" : ["Tester(DeterminantOfCharacter)"]},"Tester(BrauerCharacterValue)" : {"type" : "GAP_Attribute","implied" : ["Tester(BrauerCharacterValue)"]},"IsClassFunctionsSpace" : {"type" : "GAP_Filter","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsFreeLeftModule","IsHandledByNiceBasis","IsClassFunctionsSpace"]},"Tester(ComputedPowerMaps)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedPowerMaps)"]},"Tester(FusionConjugacyClassesOp)" : {"type" : "GAP_Attribute","implied" : ["Tester(FusionConjugacyClassesOp)"]},"Tester(ComputedClassFusions)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedClassFusions)"]},"Tester(NamesOfFusionSources)" : {"type" : "GAP_Attribute","implied" : ["Tester(NamesOfFusionSources)"]},"Tester(BaumClausenInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(BaumClausenInfo)"]},"Tester(IrreducibleRepresentations)" : {"type" : "GAP_Attribute","implied" : ["Tester(IrreducibleRepresentations)"]},"Tester(IrrBaumClausen)" : {"type" : "GAP_Attribute","implied" : ["Tester(IrrBaumClausen)"]},"Tester(IrrConlon)" : {"type" : "GAP_Attribute","implied" : ["Tester(IrrConlon)"]},"Tester(MolienSeriesInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(MolienSeriesInfo)"]},"Tester(Alpha)" : {"type" : "GAP_Attribute","implied" : ["Tester(Alpha)"]},"Tester(Delta)" : {"type" : "GAP_Attribute","implied" : ["Tester(Delta)"]},"Tester(IsBergerCondition)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBergerCondition)"]},"Tester(IsPrimitiveCharacter)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPrimitiveCharacter)"]},"Tester(TestQuasiPrimitive)" : {"type" : "GAP_Attribute","implied" : ["Tester(TestQuasiPrimitive)"]},"Tester(IsQuasiPrimitive)" : {"type" : "GAP_Tester","implied" : ["Tester(IsQuasiPrimitive)"]},"Tester(IsInducedFromNormalSubgroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsInducedFromNormalSubgroup)"]},"Tester(IsMonomialCharacter)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMonomialCharacter)"]},"Tester(IsMonomialNumber)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMonomialNumber)"]},"Tester(TestMonomialQuick)" : {"type" : "GAP_Attribute","implied" : ["Tester(TestMonomialQuick)"]},"Tester(TestMonomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(TestMonomial)"]},"Tester(TestSubnormallyMonomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(TestSubnormallyMonomial)"]},"Tester(IsSubnormallyMonomial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSubnormallyMonomial)"]},"Tester(TestRelativelySM)" : {"type" : "GAP_Attribute","implied" : ["Tester(TestRelativelySM)"]},"Tester(IsRelativelySM)" : {"type" : "GAP_Tester","implied" : ["Tester(IsRelativelySM)"]},"Tester(IsMinimalNonmonomial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMinimalNonmonomial)"]},"Tester(DixonRecord)" : {"type" : "GAP_Attribute","implied" : ["Tester(DixonRecord)"]},"Tester(IrrDixonSchneider)" : {"type" : "GAP_Attribute","implied" : ["Tester(IrrDixonSchneider)"]},"Tester(TableOfMarks)" : {"type" : "GAP_Attribute","implied" : ["Tester(TableOfMarks)"]},"IsTableOfMarks" : {"type" : "GAP_Category","implied" : ["IsTableOfMarks"]},"Tester(PermutationTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(PermutationTom)"]},"Tester(MarksTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(MarksTom)"]},"Tester(SubsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(SubsTom)"]},"Tester(NrSubsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrSubsTom)"]},"Tester(OrdersTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrdersTom)"]},"Tester(LengthsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(LengthsTom)"]},"Tester(ClassTypesTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassTypesTom)"]},"Tester(ClassNamesTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(ClassNamesTom)"]},"Tester(FusionsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(FusionsTom)"]},"Tester(IdempotentsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdempotentsTom)"]},"Tester(IdempotentsTomInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdempotentsTomInfo)"]},"Tester(MatTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(MatTom)"]},"Tester(MoebiusTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(MoebiusTom)"]},"Tester(WeightsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(WeightsTom)"]},"Tester(IsAbelianTom)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAbelianTom)"]},"Tester(IsCyclicTom)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCyclicTom)"]},"Tester(IsNilpotentTom)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNilpotentTom)"]},"Tester(IsPerfectTom)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPerfectTom)"]},"Tester(IsSolvableTom)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSolvableTom)"]},"Tester(DerivedSubgroupsTomPossible)" : {"type" : "GAP_Attribute","implied" : ["Tester(DerivedSubgroupsTomPossible)"]},"Tester(DerivedSubgroupsTomUnique)" : {"type" : "GAP_Attribute","implied" : ["Tester(DerivedSubgroupsTomUnique)"]},"Tester(NormalizersTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizersTom)"]},"Tester(CyclicExtensionsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(CyclicExtensionsTom)"]},"Tester(ComputedCyclicExtensionsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedCyclicExtensionsTom)"]},"Tester(MaximalSubgroupsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalSubgroupsTom)"]},"Tester(GeneratorsSubgroupsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsSubgroupsTom)"]},"Tester(StraightLineProgramsTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(StraightLineProgramsTom)"]},"IsTableOfMarksWithGens" : {"type" : "GAP_Filter","implied" : ["IsTableOfMarksWithGens"]},"IsUnicodeString" : {"type" : "GAP_Filter","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsString","IsListOrCollection","IsConstantTimeAccessList","IsUnicodeString"]},"IsUnicodeCharacter" : {"type" : "GAP_Filter","implied" : ["IsInt","IsRat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsChar","IsCyclotomic","IsUnicodeCharacter"]},"IsObjToBePrinted" : {"type" : "GAP_Filter","implied" : ["IsObjToBePrinted"]},"IsFile" : {"type" : "GAP_Category","implied" : ["IsFile"]},"Tester(ProcessID)" : {"type" : "GAP_Attribute","implied" : ["Tester(ProcessID)"]},"IO_Result" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IO_Result"]},"IsRealRandomSource" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsRandomSource","IsRealRandomSource"]},"IsBackgroundJob" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBackgroundJob"]},"IsBackgroundJobByFork" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBackgroundJob","IsBackgroundJobByFork"]},"IsWorkerFarm" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsWorkerFarm"]},"IsWorkerFarmByFork" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsWorkerFarm","IsWorkerFarmByFork"]},"IsIOHubCat" : {"type" : "GAP_Category","implied" : ["IsComponentObjectRep","IsIOHubCat"]},"IsIOHub" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsIOHubCat","IsIOHub"]},"IsEmptyRowVectorRep" : {"type" : "GAP_Representation","implied" : ["IsList","IsPositionalObjectRep","IsListOrCollection","IsConstantTimeAccessList","IsEmptyRowVectorRep"]},"IsNullMapMatrix" : {"type" : "GAP_Representation","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","IsMultiplicativeElement","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVector","IsNullMapMatrix"]},"IsBlockMatrixRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsBlockMatrixRep"]},"IsDefaultGeneralMappingRep" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","Tester(Range)","Tester(Source)","IsDefaultGeneralMappingRep"]},"IsMappingByFunctionRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsMappingByFunctionRep"]},"IsMappingByFunctionWithInverseRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsMappingByFunctionRep","IsMappingByFunctionWithInverseRep"]},"IsNonSPMappingByFunctionRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsMappingByFunctionRep","IsNonSPMappingByFunctionRep"]},"IsNonSPMappingByFunctionWithInverseRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsMappingByFunctionRep","IsMappingByFunctionWithInverseRep","IsNonSPMappingByFunctionRep","IsNonSPMappingByFunctionWithInverseRep"]},"IsSPMappingByFunctionRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsMappingByFunctionRep","IsSPMappingByFunctionRep"]},"IsSPMappingByFunctionWithInverseRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsMappingByFunctionRep","IsMappingByFunctionWithInverseRep","IsSPMappingByFunctionRep","IsSPMappingByFunctionWithInverseRep"]},"IsInverseGeneralMappingRep" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsNonSPGeneralMapping","IsInverseGeneralMappingRep"]},"IsBinaryRelationDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBinaryRelationDefaultRep"]},"IsBinaryRelationOnPointsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBinaryRelationOnPointsRep"]},"IsEquivalenceRelationDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEquivalenceRelationDefaultRep"]},"IsEquivalenceClassDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEquivalenceClassDefaultRep"]},"IsRightTransversalRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep"]},"IsAdditiveCosetDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsAdditiveCosetDefaultRep"]},"IsRelativeBasisDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsRelativeBasisDefaultRep"]},"IsBasisWithReplacedLeftModuleRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsBasisWithReplacedLeftModuleRep"]},"IsMutableBasisByImmutableBasisRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisByImmutableBasisRep"]},"IsMutableBasisViaNiceMutableBasisRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisViaNiceMutableBasisRep"]},"IsSubspacesVectorSpaceDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsSubspacesVectorSpaceDefaultRep"]},"IsSemiEchelonBasisOfGaussianRowSpaceRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsSemiEchelonBasisOfGaussianRowSpaceRep"]},"IsSubspacesFullRowSpaceDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsSubspacesVectorSpaceDefaultRep","IsSubspacesFullRowSpaceDefaultRep"]},"IsMutableBasisOfGaussianRowSpaceRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisOfGaussianRowSpaceRep"]},"IsSemiEchelonBasisOfGaussianMatrixSpaceRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsSemiEchelonBasisOfGaussianMatrixSpaceRep"]},"IsMutableBasisOfGaussianMatrixSpaceRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsMutableBasisOfGaussianMatrixSpaceRep"]},"IsLinearGeneralMappingByImagesDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLinearGeneralMappingByImagesDefaultRep"]},"IsLinearMappingByMatrixDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLinearMappingByMatrixDefaultRep"]},"IsMagmaRingObjDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsMagmaRingObjDefaultRep"]},"IsCanonicalBasisFreeMagmaRingRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFreeMagmaRingRep"]},"IsEmbeddingRingMagmaRing" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","IsEmbeddingRingMagmaRing"]},"IsEmbeddingMagmaMagmaRing" : {"type" : "GAP_Representation","implied" : 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["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisRationals"]},"IsCanonicalBasisGaussianIntegersRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisGaussianIntegersRep"]},"IsCanonicalBasisAbelianNumberFieldRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisAbelianNumberFieldRep"]},"IsCanonicalBasisCyclotomicFieldRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsCanonicalBasisAbelianNumberFieldRep","IsCanonicalBasisCyclotomicFieldRep"]},"IsANFAutomorphismRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsANFAutomorphismRep"]},"IsLockedRepresentationVector" : {"type" : "GAP_Filter","implied" : ["IsLockedRepresentationVector"]},"IsBracketRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsBracketRep"]},"Is8BitsAssocWord" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","Is8BitsAssocWord"]},"Is16BitsAssocWord" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","Is16BitsAssocWord"]},"Is32BitsAssocWord" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","Is32BitsAssocWord"]},"IsInfBitsAssocWord" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsAssociativeElement","IsWord","IsSyllableAssocWordRep","IsInfBitsAssocWord"]},"IsInfiniteListOfNamesRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInfiniteListOfNamesRep"]},"IsInfiniteListOfGeneratorsRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInfiniteListOfGeneratorsRep"]},"IsSingleCollectorRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep"]},"Is8BitsSingleCollectorRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","Is8BitsSingleCollectorRep"]},"Is16BitsSingleCollectorRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","Is16BitsSingleCollectorRep"]},"Is32BitsSingleCollectorRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","Is32BitsSingleCollectorRep"]},"IsDefaultRhsTypeSingleCollector" : {"type" : "GAP_Filter","implied" : ["IsDefaultRhsTypeSingleCollector"]},"IsCombinatorialCollectorRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsSingleCollectorRep","IsCombinatorialCollectorRep"]},"IsNBitsPcWordRep" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsNBitsPcWordRep"]},"Is8BitsPcWordRep" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsKernelPcWord","IsNBitsPcWordRep","Is8BitsPcWordRep"]},"Is16BitsPcWordRep" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsKernelPcWord","IsNBitsPcWordRep","Is16BitsPcWordRep"]},"Is32BitsPcWordRep" : {"type" : "GAP_Representation","implied" : ["IsDataObjectRep","IsKernelPcWord","IsNBitsPcWordRep","Is32BitsPcWordRep"]},"IsDeepThoughtCollectorRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsDeepThoughtCollectorRep"]},"IsEnumeratorByPcgsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEnumeratorByPcgsRep"]},"IsPcgsByPcgsRep" : {"type" : "GAP_Representation","implied" : 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["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsModuloTailPcgsRep"]},"IsSubsetInducedNumeratorModuloTailPcgsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsModuloTailPcgsRep","IsSubsetInducedNumeratorModuloTailPcgsRep"]},"IsModuloTailPcgsByListRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsModuloTailPcgsRep","IsModuloTailPcgsByListRep"]},"IsNumeratorParentForExponentsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsNumeratorParentForExponentsRep"]},"IsNumeratorParentLayersForExponentsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsModuloPcgsRep","IsNumeratorParentLayersForExponentsRep"]},"IsUnsortedPcgsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsUnsortedPcgsRep"]},"IsSortedPcgsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPcgsDefaultRep","IsUnsortedPcgsRep","IsSortedPcgsRep"]},"IsMemberPcSeriesPermGroup" : {"type" : "GAP_Representation","implied" : 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["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsProjectionDirectProductPermGroup"]},"IsProjectionSubdirectProductPermGroup" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsProjectionSubdirectProductPermGroup"]},"IsEmbeddingDirectProductMatrixGroup" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsEmbeddingDirectProductMatrixGroup"]},"IsProjectionDirectProductMatrixGroup" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsProjectionDirectProductMatrixGroup"]},"IsEmbeddingImprimitiveWreathProductMatrixGroup" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsEmbeddingImprimitiveWreathProductMatrixGroup"]},"IsSlicedPerm" : {"type" : "GAP_Representation","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement","IsSlicedPerm"]},"IsSlicedPermInv" : {"type" : "GAP_Representation","implied" : ["IsPerm","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsFiniteOrderElement","IsSlicedPermInv"]},"IsRightCosetDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsGeneralizedDomain","IsExternalSet","IsExternalSubset","IsExternalOrbit","IsRightCoset","IsRightCosetDefaultRep"]},"IsDoubleCosetDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsExtRSet","IsDoubleCoset","IsDoubleCosetDefaultRep"]},"IsRightTransversalViaCosetsRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalViaCosetsRep"]},"IsFactoredTransversalRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsFactoredTransversalRep"]},"IsRightTransversalPermGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalPermGroupRep"]},"IsRightTransversalPcGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalPcGroupRep"]},"IsEnumeratorByNiceomorphismRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsEnumeratorByNiceomorphismRep"]},"IsActionHomomorphismAutomGroup" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsPreimagesByAsGroupGeneralMappingByImages","IsActionHomomorphism","IsActionHomomorphismByBase","IsActionHomomorphismAutomGroup"]},"IsBlowUpIsomorphism" : {"type" : "GAP_Filter","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","IsBlowUpIsomorphism"]},"IsRightTransversalFpGroupRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsRightTransversal","IsRightTransversalRep","IsRightTransversalFpGroupRep"]},"IsPresentationDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsPresentationDefaultRep"]},"IsModuloPcgsFpGroupRep" : {"type" : "GAP_Representation","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsNoImmediateMethodsObject","IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsFinite","Tester(IsFinite)","IsConstantTimeAccessList","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneralPcgs","IsModuloPcgs","IsPcgsDefaultRep","IsModuloPcgsFpGroupRep"]},"IsTransformationRepOfEndo" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsTransformationRepOfEndo"]},"IsKnuthBendixRewritingSystemRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsKnuthBendixRewritingSystemRep"]},"IsFloatPseudoField" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFloatPseudoField"]},"IsFloatRationalFunction" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsPolynomialFunction","IsRationalFunction","IsFloatRationalFunction"]},"IsIEEE754PseudoField" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsFreeLeftModule","IsFloatPseudoField","IsIEEE754PseudoField"]},"Tester(IdGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdGroup)"]},"Tester(Gap3CatalogueIdGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(Gap3CatalogueIdGroup)"]},"Tester(FrattinifactorSize)" : {"type" : "GAP_Attribute","implied" : ["Tester(FrattinifactorSize)"]},"Tester(FrattinifactorId)" : {"type" : "GAP_Attribute","implied" : ["Tester(FrattinifactorId)"]},"Tester(GaloisType)" : {"type" : "GAP_Attribute","implied" : ["Tester(GaloisType)"]},"Tester(SimsNo)" : {"type" : "GAP_Attribute","implied" : ["Tester(SimsNo)"]},"Tester(MinimalBlockDimension)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimalBlockDimension)"]},"Tester(IsPrimitiveMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPrimitiveMatrixGroup)"]},"IsPrimGrpIterRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsPrimGrpIterRep"]},"IsPGAutomorphismRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","IsPGAutomorphismRep"]},"Tester(IrrFacsAlgExtPol)" : {"type" : "GAP_Attribute","implied" : ["Tester(IrrFacsAlgExtPol)"]},"IsBasisOfMatrixField" : {"type" : "GAP_Representation","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsBasis","IsBasisOfMatrixField"]},"Tester(IsUnitGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsUnitGroup)"]},"Tester(IsUnitGroupIsomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsUnitGroupIsomorphism)"]},"Tester(IsNumberFieldByMatrices)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNumberFieldByMatrices)"]},"Tester(IsMultGroupByFieldElemsIsomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMultGroupByFieldElemsIsomorphism)"]},"Tester(IntegerDefiningPolynomial)" : {"type" : "GAP_Attribute","implied" : ["Tester(IntegerDefiningPolynomial)"]},"Tester(IntegerPrimitiveElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(IntegerPrimitiveElement)"]},"Tester(EquationOrderBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(EquationOrderBasis)"]},"Tester(MaximalOrderBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(MaximalOrderBasis)"]},"Tester(UnitGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnitGroup)"]},"Tester(FieldOfUnitGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FieldOfUnitGroup)"]},"IsFromTheLeftCollectorRep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsRewritingSystem","IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromMagmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)","IsPolycyclicCollector","IsPowerConjugateCollector","IsFromTheLeftCollectorRep"]},"Tester(IsWeightedCollector)" : {"type" : "GAP_Tester","implied" : ["Tester(IsWeightedCollector)"]},"Tester(IsPolynomialCollector)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPolynomialCollector)"]},"Tester(UseLibraryCollector)" : {"type" : "GAP_Tester","implied" : ["Tester(UseLibraryCollector)"]},"Tester(IsPolycyclicPresentation)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPolycyclicPresentation)"]},"IsPcpElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsPcpElement"]},"CategoryFamily(IsPcpElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily(IsPcpElement)"]},"CategoryCollections(IsPcpElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","CategoryCollections(IsPcpElement)"]},"IsPcpElementRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsPcpElementRep"]},"Tester(TailOfElm)" : {"type" : "GAP_Attribute","implied" : ["Tester(TailOfElm)"]},"Tester(RelativeOrderPcp)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelativeOrderPcp)"]},"Tester(RelativeIndex)" : {"type" : "GAP_Attribute","implied" : ["Tester(RelativeIndex)"]},"Tester(FactorOrder)" : {"type" : "GAP_Attribute","implied" : ["Tester(FactorOrder)"]},"Tester(Igs)" : {"type" : "GAP_Attribute","implied" : ["Tester(Igs)"]},"Tester(Ngs)" : {"type" : "GAP_Attribute","implied" : ["Tester(Ngs)"]},"Tester(Cgs)" : {"type" : "GAP_Attribute","implied" : ["Tester(Cgs)"]},"IsPcp" : {"type" : "GAP_Category","implied" : ["IsPcp"]},"IsPcpRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsPcpRep"]},"IsFromPcpGHBI" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsFromPcpGHBI"]},"IsToPcpGHBI" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","IsSPGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsGroupGeneralMappingByImages","Extrarankfilter","IsToPcpGHBI"]},"Tester(EfaSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(EfaSeries)"]},"Tester(PcpsOfEfaSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcpsOfEfaSeries)"]},"Tester(IsomorphismPcpGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismPcpGroup)"]},"Tester(PcpGroupByEfaSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcpGroupByEfaSeries)"]},"Tester(IsHomomorphismIntoMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsHomomorphismIntoMatrixGroup)"]},"Tester(SemiSimpleEfaSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(SemiSimpleEfaSeries)"]},"Tester(FCCentre)" : {"type" : "GAP_Attribute","implied" : ["Tester(FCCentre)"]},"Tester(IsNilpotentByFinite)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNilpotentByFinite)"]},"Tester(ComputedMaximalSubgroupClassesByIndexs)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedMaximalSubgroupClassesByIndexs)"]},"Tester(ComputedLowIndexSubgroupClassess)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedLowIndexSubgroupClassess)"]},"Tester(ComputedLowIndexNormalSubgroupss)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedLowIndexNormalSubgroupss)"]},"Tester(SchurExtension)" : {"type" : "GAP_Attribute","implied" : ["Tester(SchurExtension)"]},"Tester(SchurExtensionEpimorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(SchurExtensionEpimorphism)"]},"Tester(NonAbelianTensorSquare)" : {"type" : "GAP_Attribute","implied" : ["Tester(NonAbelianTensorSquare)"]},"Tester(NonAbelianExteriorSquare)" : {"type" : "GAP_Attribute","implied" : ["Tester(NonAbelianExteriorSquare)"]},"Tester(TorsionSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(TorsionSubgroup)"]},"Tester(NormalTorsionSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalTorsionSubgroup)"]},"Tester(FiniteSubgroupClasses)" : {"type" : "GAP_Attribute","implied" : ["Tester(FiniteSubgroupClasses)"]},"Tester(IsTorsionFree)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTorsionFree)"]},"Tester(IsFreeAbelian)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFreeAbelian)"]},"IsClass" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsClass"]},"Tester(MemberFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(MemberFunction)"]},"Tester(ComputedIsMembers)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedIsMembers)"]},"Tester(IsGroupClass)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupClass)"]},"Tester(GroupClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(GroupClass)"]},"Tester(ContainsTrivialGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(ContainsTrivialGroup)"]},"Tester(IsSubgroupClosed)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSubgroupClosed)"]},"Tester(IsNormalSubgroupClosed)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNormalSubgroupClosed)"]},"Tester(IsQuotientClosed)" : {"type" : "GAP_Tester","implied" : ["Tester(IsQuotientClosed)"]},"Tester(IsResiduallyClosed)" : {"type" : "GAP_Tester","implied" : ["Tester(IsResiduallyClosed)"]},"Tester(IsNormalProductClosed)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNormalProductClosed)"]},"Tester(IsDirectProductClosed)" : {"type" : "GAP_Tester","implied" : ["Tester(IsDirectProductClosed)"]},"Tester(IsSchunckClass)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSchunckClass)"]},"Tester(IsSaturated)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSaturated)"]},"Tester(FittingClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(FittingClass)"]},"Tester(InjectorFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(InjectorFunction)"]},"Tester(RadicalFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(RadicalFunction)"]},"Tester(IsPrimitiveSolvableGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPrimitiveSolvableGroup)"]},"Tester(SchunckClass)" : {"type" : "GAP_Attribute","implied" : ["Tester(SchunckClass)"]},"Tester(Boundary)" : {"type" : "GAP_Attribute","implied" : ["Tester(Boundary)"]},"Tester(ProjectorFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(ProjectorFunction)"]},"Tester(BoundaryFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(BoundaryFunction)"]},"Tester(OrdinaryFormation)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrdinaryFormation)"]},"Tester(SaturatedFormation)" : {"type" : "GAP_Attribute","implied" : ["Tester(SaturatedFormation)"]},"Tester(FittingFormation)" : {"type" : "GAP_Attribute","implied" : ["Tester(FittingFormation)"]},"Tester(SaturatedFittingFormation)" : {"type" : "GAP_Attribute","implied" : ["Tester(SaturatedFittingFormation)"]},"Tester(ResidualFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(ResidualFunction)"]},"Tester(LocalDefinitionFunction)" : {"type" : "GAP_Attribute","implied" : ["Tester(LocalDefinitionFunction)"]},"Tester(ComputedProjectors)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedProjectors)"]},"Tester(ComputedCoveringSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedCoveringSubgroups)"]},"Tester(ComputedInjectors)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedInjectors)"]},"Tester(ComputedRadicals)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedRadicals)"]},"Tester(ComputedResiduals)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedResiduals)"]},"Tester(CharacteristicSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(CharacteristicSubgroups)"]},"Tester(NormalGeneratorsOfNilpotentResidual)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalGeneratorsOfNilpotentResidual)"]},"Tester(PrimePowerGensPcSequence)" : {"type" : "GAP_Attribute","implied" : ["Tester(PrimePowerGensPcSequence)"]},"Tester(NilpotentProjector)" : {"type" : "GAP_Attribute","implied" : ["Tester(NilpotentProjector)"]},"Tester(SupersolvableProjector)" : {"type" : "GAP_Attribute","implied" : ["Tester(SupersolvableProjector)"]},"Tester(SolvableSocle)" : {"type" : "GAP_Attribute","implied" : ["Tester(SolvableSocle)"]},"Tester(SocleComponents)" : {"type" : "GAP_Attribute","implied" : ["Tester(SocleComponents)"]},"Tester(SolvableSocleComponents)" : {"type" : "GAP_Attribute","implied" : ["Tester(SolvableSocleComponents)"]},"Tester(ComputedPSocleComponentss)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedPSocleComponentss)"]},"Tester(ComputedPSocles)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedPSocles)"]},"Tester(AbelianMinimalNormalSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbelianMinimalNormalSubgroups)"]},"IsClassByPropertyRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByPropertyRep"]},"IsClassByComplementRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByComplementRep"]},"IsClassByIntersectionRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByIntersectionRep"]},"IsClassByUnionRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsClassByUnionRep"]},"IsGroupClassByListRep" : {"type" : "GAP_Representation","implied" : ["IsListOrCollection","IsClass","IsGroupClass","Tester(IsGroupClass)","IsGroupClassByListRep"]},"IsFittingProductRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)","IsNormalProductClosed","Tester(IsNormalProductClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsFittingProductRep"]},"IsFittingSetRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsClass","IsClassByPropertyRep","IsFittingSetRep"]},"IsFormationProductRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsClass","IsGroupClass","Tester(IsGroupClass)","ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","IsResiduallyClosed","Tester(IsResiduallyClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)","IsFormationProductRep"]},"IsBBoxProgram" : {"type" : "GAP_Category","implied" : ["IsBBoxProgram"]},"IsStraightLineDecision" : {"type" : "GAP_Category","implied" : ["IsStraightLineDecision"]},"Tester(LinesOfStraightLineDecision)" : {"type" : "GAP_Attribute","implied" : ["Tester(LinesOfStraightLineDecision)"]},"Tester(NrInputsOfStraightLineDecision)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrInputsOfStraightLineDecision)"]},"Tester(AsBBoxProgram)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsBBoxProgram)"]},"Tester(AsStraightLineProgram)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsStraightLineProgram)"]},"Tester(AsStraightLineDecision)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsStraightLineDecision)"]},"Tester(Maxes)" : {"type" : "GAP_Attribute","implied" : ["Tester(Maxes)"]},"Tester(AtlasRepInfoRecord)" : {"type" : "GAP_Attribute","implied" : ["Tester(AtlasRepInfoRecord)"]},"Tester(CASInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(CASInfo)"]},"Tester(ConstructionInfoCharacterTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConstructionInfoCharacterTable)"]},"Tester(FusionToTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(FusionToTom)"]},"Tester(ProjectivesInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(ProjectivesInfo)"]},"Tester(ExtensionInfoCharacterTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(ExtensionInfoCharacterTable)"]},"Tester(GroupInfoForCharacterTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(GroupInfoForCharacterTable)"]},"Tester(KnowsSomeGroupInfo)" : {"type" : "GAP_Tester","implied" : ["Tester(KnowsSomeGroupInfo)"]},"Tester(IsNontrivialDirectProduct)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNontrivialDirectProduct)"]},"Tester(KnowsDeligneLusztigNames)" : {"type" : "GAP_Tester","implied" : ["Tester(KnowsDeligneLusztigNames)"]},"Tester(IsDuplicateTable)" : {"type" : "GAP_Tester","implied" : ["Tester(IsDuplicateTable)"]},"Tester(IdentifierOfMainTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdentifierOfMainTable)"]},"Tester(IdentifiersOfDuplicateTables)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdentifiersOfDuplicateTables)"]},"Tester(DeligneLusztigNames)" : {"type" : "GAP_Attribute","implied" : ["Tester(DeligneLusztigNames)"]},"Tester(DeligneLusztigName)" : {"type" : "GAP_Attribute","implied" : ["Tester(DeligneLusztigName)"]},"Tester(FingerprintOfCharacterTable)" : {"type" : "GAP_Attribute","implied" : ["Tester(FingerprintOfCharacterTable)"]},"Tester(SpinSymIngredients)" : {"type" : "GAP_Attribute","implied" : ["Tester(SpinSymIngredients)"]},"IsSpinSymTable" : {"type" : "GAP_Category","implied" : ["IsNearlyCharacterTable","IsCharacterTable","IsSpinSymTable"]},"IsLibTomRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsLibTomRep"]},"Tester(NamesLibTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(NamesLibTom)"]},"Tester(NotifiedFusionsOfLibTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(NotifiedFusionsOfLibTom)"]},"Tester(FusionsOfLibTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(FusionsOfLibTom)"]},"Tester(NotifiedFusionsToLibTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(NotifiedFusionsToLibTom)"]},"Tester(FusionsToLibTom)" : {"type" : "GAP_Attribute","implied" : ["Tester(FusionsToLibTom)"]},"Tester(StandardGeneratorsInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(StandardGeneratorsInfo)"]},"IsInvAutomatonCategory" : {"type" : "GAP_Category","implied" : ["IsInvAutomatonCategory"]},"Tester(FGA_States)" : {"type" : "GAP_Attribute","implied" : ["Tester(FGA_States)"]},"Tester(FGA_GeneratorsLetterRep)" : {"type" : "GAP_Attribute","implied" : ["Tester(FGA_GeneratorsLetterRep)"]},"Tester(FreeGeneratorsOfGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeGeneratorsOfGroup)"]},"Tester(RankOfFreeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(RankOfFreeGroup)"]},"Tester(FreeGroupAutomaton)" : {"type" : "GAP_Attribute","implied" : ["IsListOrCollection","IsCollection","CanComputeSize","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsAssociativeElement)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsAssociative","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)","IsFinitelyGeneratedGroup","Tester(IsFinitelyGeneratedGroup)","CanEasilyTestMembership","CanComputeSizeAnySubgroup","CategoryCollections(IsWord)","CategoryCollections((IsWord and IsAssociativeElement))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithOne)))","CategoryCollections(((IsWord and IsAssociativeElement) and (IsWord and IsMultiplicativeElementWithInverse)))","IsSubgroupFgGroup","IsSubgroupFpGroup","IsTorsionFree","Tester(IsTorsionFree)","Tester(FreeGroupAutomaton)"]},"Tester(FreeGroupExtendedAutomaton)" : {"type" : "GAP_Attribute","implied" : ["Tester(FreeGroupExtendedAutomaton)"]},"Tester(NormalizerInWholeGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizerInWholeGroup)"]},"Tester(FGA_Source)" : {"type" : "GAP_Attribute","implied" : ["Tester(FGA_Source)"]},"Tester(FGA_Image)" : {"type" : "GAP_Attribute","implied" : ["Tester(FGA_Image)"]},"IsAutomorphismGroupOfFreeGroup" : {"type" : "GAP_Filter","implied" : ["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)","IsAutomorphismGroup","Tester(IsAutomorphismGroup)","IsAutomorphismGroupOfFreeGroup"]},"Tester(FGA_WhiteheadParams)" : {"type" : "GAP_Attribute","implied" : ["Tester(FGA_WhiteheadParams)"]},"Tester(FGA_WhiteheadAutomorphisms)" : {"type" : "GAP_Attribute","implied" : ["Tester(FGA_WhiteheadAutomorphisms)"]},"Tester(FGA_NielsenAutomorphisms)" : {"type" : "GAP_Attribute","implied" : ["Tester(FGA_NielsenAutomorphisms)"]},"IsSimpleInvAutomatonRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsListOrCollection","IsCollection","IsInvAutomatonCategory","IsSimpleInvAutomatonRep"]},"Tester(IsIrreducibleMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIrreducibleMatrixGroup)"]},"Tester(ComputedIsIrreducibleMatrixGroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedIsIrreducibleMatrixGroups)"]},"Tester(IsAbsolutelyIrreducibleMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAbsolutelyIrreducibleMatrixGroup)"]},"Tester(ComputedIsPrimitiveMatrixGroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedIsPrimitiveMatrixGroups)"]},"Tester(MinimalBlockDimensionOfMatrixGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimalBlockDimensionOfMatrixGroup)"]},"Tester(ComputedMinimalBlockDimensionOfMatrixGroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedMinimalBlockDimensionOfMatrixGroups)"]},"Tester(CharacteristicOfField)" : {"type" : "GAP_Attribute","implied" : ["Tester(CharacteristicOfField)"]},"Tester(RepresentationIsomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(RepresentationIsomorphism)"]},"Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup)"]},"Tester(ImprimitivitySystems)" : {"type" : "GAP_Attribute","implied" : ["Tester(ImprimitivitySystems)"]},"Tester(ComputedImprimitivitySystemss)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedImprimitivitySystemss)"]},"Tester(TraceField)" : {"type" : "GAP_Attribute","implied" : ["Tester(TraceField)"]},"Tester(ConjugatingMatTraceField)" : {"type" : "GAP_Attribute","implied" : ["Tester(ConjugatingMatTraceField)"]},"Tester(FingerprintMatrixGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(FingerprintMatrixGroup)"]},"Tester(IdIrreducibleSolvableMatrixGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdIrreducibleSolvableMatrixGroup)"]},"Tester(IdPrimitiveSolvableGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(IdPrimitiveSolvableGroup)"]},"IsNilpotentLieAutomorphismRep" : {"type" : "GAP_Representation","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(RespectsZero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)","IsNilpotentLieAutomorphismRep"]},"Tester(IsLieNilpotentOverFp)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieNilpotentOverFp)"]},"Tester(AutomorphismGroupOfNilpotentLieAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(AutomorphismGroupOfNilpotentLieAlgebra)"]},"Tester(MinimalGeneratorNumber)" : {"type" : "GAP_Attribute","implied" : ["Tester(MinimalGeneratorNumber)"]},"Tester(IsLieCover)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieCover)"]},"Tester(CoverOf)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoverOf)"]},"Tester(CoverHomomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoverHomomorphism)"]},"Tester(LieCover)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieCover)"]},"Tester(LieNucleus)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieNucleus)"]},"Tester(LieMultiplicator)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieMultiplicator)"]},"Tester(IsLieAlgebraWithNB)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieAlgebraWithNB)"]},"Tester(NilpotentBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(NilpotentBasis)"]},"Tester(IsNilpotentBasis)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNilpotentBasis)"]},"Tester(LieNBDefinitions)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieNBDefinitions)"]},"Tester(LieNBWeights)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieNBWeights)"]},"Tester(IsGroupAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupAlgebra)"]},"Tester(IsFModularGroupAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFModularGroupAlgebra)"]},"Tester(IsPModularGroupAlgebra)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPModularGroupAlgebra)"]},"Tester(UnderlyingRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingRing)"]},"Tester(UnderlyingField)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingField)"]},"Tester(Support)" : {"type" : "GAP_Attribute","implied" : ["Tester(Support)"]},"Tester(CoefficientsBySupport)" : {"type" : "GAP_Attribute","implied" : ["Tester(CoefficientsBySupport)"]},"Tester(TraceOfMagmaRingElement)" : {"type" : "GAP_Attribute","implied" : ["Tester(TraceOfMagmaRingElement)"]},"Tester(Augmentation)" : {"type" : "GAP_Attribute","implied" : ["Tester(Augmentation)"]},"Tester(IsSymmetric)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsSymmetric)"]},"Tester(IsUnitary)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsUnitary)"]},"Tester(WeightedBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(WeightedBasis)"]},"Tester(AugmentationIdealPowerSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentationIdealPowerSeries)"]},"Tester(AugmentationIdealNilpotencyIndex)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentationIdealNilpotencyIndex)"]},"Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentationIdealOfDerivedSubgroupNilpotencyIndex)"]},"Tester(IsGroupOfUnitsOfMagmaRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsGroupOfUnitsOfMagmaRing)"]},"Tester(IsUnitGroupOfGroupRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsUnitGroupOfGroupRing)"]},"Tester(IsNormalizedUnitGroupOfGroupRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNormalizedUnitGroupOfGroupRing)"]},"Tester(UnderlyingGroupRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingGroupRing)"]},"Tester(NormalizedUnitGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizedUnitGroup)"]},"Tester(PcNormalizedUnitGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcNormalizedUnitGroup)"]},"Tester(ComputedAugmentationIdealPowerFactorGroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(ComputedAugmentationIdealPowerFactorGroups)"]},"Tester(PcUnits)" : {"type" : "GAP_Attribute","implied" : ["Tester(PcUnits)"]},"Tester(NaturalBijectionToPcNormalizedUnitGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalBijectionToPcNormalizedUnitGroup)"]},"Tester(NaturalBijectionToNormalizedUnitGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalBijectionToNormalizedUnitGroup)"]},"Tester(GroupBases)" : {"type" : "GAP_Attribute","implied" : ["Tester(GroupBases)"]},"Tester(BicyclicUnitGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(BicyclicUnitGroup)"]},"Tester(UnitarySubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnitarySubgroup)"]},"IsLieAlgebraByAssociativeAlgebra" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd","IsAssociativeLOpEProd","IsDistributiveLOpDSum","IsDistributiveLOpESum","IsTrivialLOpEOne","IsLeftActedOnByRing","IsLeftActedOnByDivisionRing","Tester(IsLeftActedOnByDivisionRing)","IsMagma","IsNearAdditiveMagma","IsNearAdditiveMagmaWithZero","IsNearAdditiveGroup","IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)","IsLDistributive","Tester(IsLDistributive)","IsRDistributive","Tester(IsRDistributive)","IsAnticommutative","Tester(IsAnticommutative)","IsJacobianRing","Tester(IsJacobianRing)","IsZeroSquaredRing","Tester(IsZeroSquaredRing)","IsFreeLeftModule","IsLieAlgebraByAssociativeAlgebra"]},"Tester(UnderlyingAssociativeAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingAssociativeAlgebra)"]},"Tester(IsLieAlgebraOfGroupRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieAlgebraOfGroupRing)"]},"Tester(IsBasisOfLieAlgebraOfGroupRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsBasisOfLieAlgebraOfGroupRing)"]},"Tester(NaturalBijectionToLieAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalBijectionToLieAlgebra)"]},"Tester(NaturalBijectionToAssociativeAlgebra)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalBijectionToAssociativeAlgebra)"]},"Tester(AugmentationHomomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(AugmentationHomomorphism)"]},"Tester(IsLieMetabelian)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieMetabelian)"]},"Tester(IsLieCentreByMetabelian)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLieCentreByMetabelian)"]},"Tester(LieUpperNilpotencyIndex)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieUpperNilpotencyIndex)"]},"Tester(LieLowerNilpotencyIndex)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieLowerNilpotencyIndex)"]},"Tester(LieDerivedLength)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieDerivedLength)"]},"Tester(SubgroupsOfIndexTwo)" : {"type" : "GAP_Attribute","implied" : ["Tester(SubgroupsOfIndexTwo)"]},"Tester(DihedralDepth)" : {"type" : "GAP_Attribute","implied" : ["Tester(DihedralDepth)"]},"Tester(DimensionBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(DimensionBasis)"]},"Tester(LieDimensionSubgroups)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieDimensionSubgroups)"]},"Tester(LieUpperCodimensionSeries)" : {"type" : "GAP_Attribute","implied" : ["Tester(LieUpperCodimensionSeries)"]},"Tester(RootsAsMatrices)" : {"type" : "GAP_Attribute","implied" : ["Tester(RootsAsMatrices)"]},"Tester(IsSolvablePolynomial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSolvablePolynomial)"]},"Tester(IsSeparablePolynomial)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSeparablePolynomial)"]},"Tester(IsomorphismMatrixField)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsomorphismMatrixField)"]},"Tester(GaloisGroupOnRoots)" : {"type" : "GAP_Attribute","implied" : ["Tester(GaloisGroupOnRoots)"]},"Tester(IsAffineCrystGroupOnRight)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAffineCrystGroupOnRight)"]},"Tester(IsAffineCrystGroupOnLeft)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAffineCrystGroupOnLeft)"]},"Tester(IsAffineCrystGroupOnLeftOrRight)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAffineCrystGroupOnLeftOrRight)"]},"Tester(IsSpaceGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSpaceGroup)"]},"Tester(IsStandardAffineCrystGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsStandardAffineCrystGroup)"]},"Tester(IsSymmorphicSpaceGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSymmorphicSpaceGroup)"]},"Tester(IsPointGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPointGroup)"]},"Tester(NormalizerPointGroupInGLnZ)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormalizerPointGroupInGLnZ)"]},"Tester(CentralizerPointGroupInGLnZ)" : {"type" : "GAP_Attribute","implied" : ["Tester(CentralizerPointGroupInGLnZ)"]},"Tester(AffineCrystGroupOfPointGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(AffineCrystGroupOfPointGroup)"]},"Tester(PointGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(PointGroup)"]},"Tester(PointHomomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(PointHomomorphism)"]},"Tester(TranslationBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(TranslationBasis)"]},"Tester(InternalBasis)" : {"type" : "GAP_Attribute","implied" : ["Tester(InternalBasis)"]},"Tester(TransParts)" : {"type" : "GAP_Attribute","implied" : ["Tester(TransParts)"]},"Tester(TranslationNormalizer)" : {"type" : "GAP_Attribute","implied" : ["Tester(TranslationNormalizer)"]},"Tester(AffineNormalizer)" : {"type" : "GAP_Attribute","implied" : ["Tester(AffineNormalizer)"]},"Tester(IsPointHomomorphism)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPointHomomorphism)"]},"Tester(NiceToCryst)" : {"type" : "GAP_Attribute","implied" : ["Tester(NiceToCryst)"]},"Tester(IsFromAffineCrystGroupToFpGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFromAffineCrystGroupToFpGroup)"]},"Tester(IsFromAffineCrystGroupToPcpGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsFromAffineCrystGroupToPcpGroup)"]},"IsWyckoffPosition" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsWyckoffPosition"]},"Tester(WyckoffStabilizer)" : {"type" : "GAP_Attribute","implied" : ["Tester(WyckoffStabilizer)"]},"Tester(WyckoffOrbit)" : {"type" : "GAP_Attribute","implied" : ["Tester(WyckoffOrbit)"]},"Tester(WyckoffPositions)" : {"type" : "GAP_Attribute","implied" : ["Tester(WyckoffPositions)"]},"IsWyckoffGraph" : {"type" : "GAP_Filter","implied" : ["IsWyckoffGraph"]},"Tester(CocVecs)" : {"type" : "GAP_Attribute","implied" : ["Tester(CocVecs)"]},"Tester(IsColorGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsColorGroup)"]},"Tester(ColorSubgroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(ColorSubgroup)"]},"Tester(ColorCosetList)" : {"type" : "GAP_Attribute","implied" : ["Tester(ColorCosetList)"]},"Tester(ColorPermGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(ColorPermGroup)"]},"Tester(ColorHomomorphism)" : {"type" : "GAP_Attribute","implied" : ["Tester(ColorHomomorphism)"]},"Tester(CrystCatRecord)" : {"type" : "GAP_Attribute","implied" : ["Tester(CrystCatRecord)"]},"Tester(IsAlmostCrystallographic)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAlmostCrystallographic)"]},"Tester(IsAlmostBieberbachGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsAlmostBieberbachGroup)"]},"Tester(AlmostCrystallographicInfo)" : {"type" : "GAP_Attribute","implied" : ["Tester(AlmostCrystallographicInfo)"]},"Tester(NaturalHomomorphismOnHolonomyGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(NaturalHomomorphismOnHolonomyGroup)"]},"Tester(HolonomyGroup)" : {"type" : "GAP_Attribute","implied" : ["Tester(HolonomyGroup)"]},"Tester(OrientationModule)" : {"type" : "GAP_Attribute","implied" : ["Tester(OrientationModule)"]},"Tester(BettiNumbers)" : {"type" : "GAP_Attribute","implied" : ["Tester(BettiNumbers)"]},"Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"]},"Tester(IsIsomorphismByPolycyclicMatrixGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsIsomorphismByPolycyclicMatrixGroup)"]},"Tester(IsTriangularizableMatGroup)" : {"type" : "GAP_Tester","implied" : ["Tester(IsTriangularizableMatGroup)"]},"Tester(IsZ_pi)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZ_pi)"]},"Tester(NoninvertiblePrimes)" : {"type" : "GAP_Attribute","implied" : ["Tester(NoninvertiblePrimes)"]},"IsResidueClassUnion" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion"]},"IsResidueClassUnionOfZ" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZ","IsResidueClassUnionOfZorZ_pi"]},"IsResidueClassUnionOfZxZ" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZxZ"]},"IsResidueClassUnionOfZ_pi" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZ_pi","IsResidueClassUnionOfZorZ_pi"]},"IsResidueClassUnionOfGFqx" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfGFqx"]},"IsResidueClassUnionOfZorZ_pi" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsResidueClassUnion","IsResidueClassUnionOfZorZ_pi"]},"IsResidueClassUnionResidueListRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsResidueClassUnionResidueListRep"]},"IsResidueClassUnionsIteratorRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsResidueClassUnionsIteratorRep"]},"Tester(IsResidueClass)" : {"type" : "GAP_Tester","implied" : ["Tester(IsResidueClass)"]},"Tester(UnderlyingIndeterminate)" : {"type" : "GAP_Attribute","implied" : ["Tester(UnderlyingIndeterminate)"]},"Tester(IsZxZ)" : {"type" : "GAP_Tester","implied" : ["Tester(IsZxZ)"]},"Tester(SizeOfSmallestResidueClassRing)" : {"type" : "GAP_Attribute","implied" : ["Tester(SizeOfSmallestResidueClassRing)"]},"Tester(Density)" : {"type" : "GAP_Attribute","implied" : ["Tester(Density)"]},"IsUnionOfResidueClassesWithFixedRepresentatives" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives"]},"IsUnionOfResidueClassesOfZWithFixedRepresentatives" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfZWithFixedRepresentatives","IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"]},"IsUnionOfResidueClassesOfZ_piWithFixedRepresentatives" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfZ_piWithFixedRepresentatives","IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"]},"IsUnionOfResidueClassesOfGFqxWithFixedRepresentatives" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfGFqxWithFixedRepresentatives"]},"IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsUnionOfResidueClassesWithFixedRepresentatives","IsUnionOfResidueClassesOfZorZ_piWithFixedRepresentatives"]},"IsUnionOfResidueClassesWithFixedRepsStandardRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttributeStoringRep","IsUnionOfResidueClassesWithFixedRepsStandardRep"]},"Tester(IsResidueClassWithFixedRepresentative)" : {"type" : "GAP_Tester","implied" : ["Tester(IsResidueClassWithFixedRepresentative)"]},"Tester(IsOverlappingFree)" : {"type" : "GAP_Tester","implied" : ["Tester(IsOverlappingFree)"]},"Tester(Rho)" : {"type" : "GAP_Attribute","implied" : ["Tester(Rho)"]}}