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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)"]},"IsWhol\
eFamily" : {"type" : "GAP_Property","implied" : ["IsWholeFamily","Tester(IsWholeFamily)"]},"CanEasilyCompareElements" : {"type" : "GA\
P_Property","implied" : ["CanEasilyCompareElements","Tester(CanEasilyCompareElements)"]},"CanEasilySortElements" : {"type" : "GAP_Pro\
perty","implied" : ["CanEasilyCompareElements","Tester(CanEasilyCompareElements)","CanEasilySortElements","Tester(CanEasilySortElemen\
ts)"]},"IsSmallList" : {"type" : "GAP_Property","implied" : ["IsSmallList","Tester(IsSmallList)"]},"IsSortedList" : {"type" : "GAP_Pr\
operty","implied" : ["IsSortedList","Tester(IsSortedList)"]},"IsSSortedList" : {"type" : "GAP_Property","implied" : ["IsSSortedList",\
"Tester(IS_SSORT_LIST)","IsSortedList","Tester(IsSortedList)"]},"IsDuplicateFree" : {"type" : "GAP_Property","implied" : ["IsDuplicat\
eFree","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" : ["IsOn\
e","Tester(IsOne)"]},"IsCommutativeFamily" : {"type" : "GAP_Property","implied" : ["IsCommutativeFamily","Tester(IsCommutativeFamily)\
"]},"IsSkewFieldFamily" : {"type" : "GAP_Property","implied" : ["IsSkewFieldFamily","Tester(IsSkewFieldFamily)"]},"IsUFDFamily" : {"t\
ype" : "GAP_Property","implied" : ["IsUFDFamily","Tester(IsUFDFamily)"]},"IsIdempotent" : {"type" : "GAP_Property","implied" : ["IsId\
empotent","Tester(IsIdempotent)"]},"IsIntegralCyclotomic" : {"type" : "GAP_Property","implied" : ["IsIntegralCyclotomic","Tester(IsIn\
tegralCyclotomic)"]},"IsRectangularTable" : {"type" : "GAP_Property","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable\
","IsListOrCollection","IsCollection","IsRectangularTable","Tester(IsRectangularTable)"]},"IsPInfinity" : {"type" : "GAP_Property","i\
mplied" : ["IsPInfinity","Tester(IsPInfinity)"]},"IsNInfinity" : {"type" : "GAP_Property","implied" : ["IsNInfinity","Tester(IsNInfin\
ity)"]},"IsXInfinity" : {"type" : "GAP_Property","implied" : ["IsXInfinity","Tester(IsXInfinity)"]},"IsNaN" : {"type" : "GAP_Property\
","implied" : ["IsNaN","Tester(IsNaN)"]},"IsLeftActedOnByDivisionRing" : {"type" : "GAP_Property","implied" : ["IsLeftActedOnByDivisi\
onRing","Tester(IsLeftActedOnByDivisionRing)"]},"IsConstantTimeAccessGeneralMapping" : {"type" : "GAP_Property","implied" : ["IsConst\
antTimeAccessGeneralMapping","Tester(IsConstantTimeAccessGeneralMapping)"]},"IsEndoGeneralMapping" : {"type" : "GAP_Property","implie\
d" : ["IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)"]},"IsTotal" : {"type" : "GAP_Property","implied" : ["IsTotal","Tester(IsT\
otal)"]},"IsSingleValued" : {"type" : "GAP_Property","implied" : ["IsSingleValued","Tester(IsSingleValued)"]},"IsInjective" : {"type"\
: "GAP_Property","implied" : ["IsInjective","Tester(IsInjective)"]},"IsSurjective" : {"type" : "GAP_Property","implied" : ["IsSurjec\
tive","Tester(IsSurjective)"]},"RespectsMultiplication" : {"type" : "GAP_Property","implied" : ["RespectsMultiplication","Tester(Resp\
ectsMultiplication)"]},"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(Respec\
tsAdditiveInverses)"]},"RespectsScalarMultiplication" : {"type" : "GAP_Property","implied" : ["RespectsAdditiveInverses","Tester(Resp\
ectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplication)"]},"IsFieldHomomorphism" : {"type" : "GAP\
_Property","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeE\
lementWithInverse","IsAssociativeElement","IsGeneralMapping","IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","R\
espectsMultiplication","Tester(RespectsMultiplication)","RespectsAddition","Tester(RespectsAddition)","RespectsZero","Tester(Respects\
Zero)","RespectsAdditiveInverses","Tester(RespectsAdditiveInverses)","RespectsScalarMultiplication","Tester(RespectsScalarMultiplicat\
ion)","IsFieldHomomorphism","Tester(IsFieldHomomorphism)"]},"TransformsMultiplicationIntoAddition" : {"type" : "GAP_Property","implie\
d" : ["TransformsMultiplicationIntoAddition","Tester(TransformsMultiplicationIntoAddition)"]},"TranformsOneIntoZero" : {"type" : "GAP\
_Property","implied" : ["TranformsOneIntoZero","Tester(TranformsOneIntoZero)"]},"TransformsInversesIntoAdditiveInverses" : {"type" : \
"GAP_Property","implied" : ["TransformsInversesIntoAdditiveInverses","Tester(TransformsInversesIntoAdditiveInverses)"]},"TransformsAd\
ditionIntoMultiplication" : {"type" : "GAP_Property","implied" : ["TransformsAdditionIntoMultiplication","Tester(TransformsAdditionIn\
toMultiplication)"]},"TransformsZeroIntoOne" : {"type" : "GAP_Property","implied" : ["TransformsZeroIntoOne","Tester(TransformsZeroIn\
toOne)"]},"TransformsAdditiveInversesIntoInverses" : {"type" : "GAP_Property","implied" : ["TransformsAdditiveInversesIntoInverses","\
Tester(TransformsAdditiveInversesIntoInverses)"]},"IsReflexiveBinaryRelation" : {"type" : "GAP_Property","implied" : ["IsTotal","Test\
er(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)"]},"IsSymmetricBinaryRelation" : {"type" : "GAP_Property"\
,"implied" : ["IsSymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)"]},"IsTransitiveBinaryRelation" : {"type" : "GAP_Propert\
y","implied" : ["IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)"]},"IsAntisymmetricBinaryRelation" : {"type" : "GAP_\
Property","implied" : ["IsAntisymmetricBinaryRelation","Tester(IsAntisymmetricBinaryRelation)"]},"IsPreOrderBinaryRelation" : {"type"\
: "GAP_Property","implied" : ["IsPreOrderBinaryRelation","Tester(IsPreOrderBinaryRelation)"]},"IsPartialOrderBinaryRelation" : {"typ\
e" : "GAP_Property","implied" : ["IsPartialOrderBinaryRelation","Tester(IsPartialOrderBinaryRelation)"]},"IsLatticeOrderBinaryRelatio\
n" : {"type" : "GAP_Property","implied" : ["IsPartialOrderBinaryRelation","Tester(IsPartialOrderBinaryRelation)","IsLatticeOrderBinar\
yRelation","Tester(IsLatticeOrderBinaryRelation)"]},"IsEquivalenceRelation" : {"type" : "GAP_Property","implied" : ["IsEndoGeneralMap\
ping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsReflexiveBinaryRelation","Tester(IsReflexiveBinaryRelation)","IsS\
ymmetricBinaryRelation","Tester(IsSymmetricBinaryRelation)","IsTransitiveBinaryRelation","Tester(IsTransitiveBinaryRelation)","IsPreO\
rderBinaryRelation","Tester(IsPreOrderBinaryRelation)","IsEquivalenceRelation","Tester(IsEquivalenceRelation)"]},"IsHasseDiagram" : {\
"type" : "GAP_Property","implied" : ["IsHasseDiagram","Tester(IsHasseDiagram)"]},"IsGeneratorsOfMagmaWithInverses" : {"type" : "GAP_P\
roperty","implied" : ["IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)"]},"IsAssociative" : {"type" : "GAP_\
Property","implied" : ["IsAssociative","Tester(IsAssociative)"]},"IsCommutative" : {"type" : "GAP_Property","implied" : ["IsCommutati\
ve","Tester(IsCommutative)"]},"IsLeftSemigroupCongruence" : {"type" : "GAP_Property","implied" : ["IsLeftSemigroupCongruence","Tester\
(IsLeftSemigroupCongruence)"]},"IsRightSemigroupCongruence" : {"type" : "GAP_Property","implied" : ["IsRightSemigroupCongruence","Tes\
ter(IsRightSemigroupCongruence)"]},"IsSemigroupCongruence" : {"type" : "GAP_Property","implied" : ["IsLeftSemigroupCongruence","Teste\
r(IsLeftSemigroupCongruence)","IsRightSemigroupCongruence","Tester(IsRightSemigroupCongruence)","IsSemigroupCongruence","Tester(IsSem\
igroupCongruence)"]},"IsReesCongruence" : {"type" : "GAP_Property","implied" : ["IsReesCongruence","Tester(IsReesCongruence)"]},"IsGe\
neratorsOfSemigroup" : {"type" : "GAP_Property","implied" : ["IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsZeroGro\
up" : {"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" : {"typ\
e" : "GAP_Property","implied" : ["IsZeroSimpleSemigroup","Tester(IsZeroSimpleSemigroup)"]},"IsReesCongruenceSemigroup" : {"type" : "G\
AP_Property","implied" : ["IsReesCongruenceSemigroup","Tester(IsReesCongruenceSemigroup)"]},"IsRegularSemigroup" : {"type" : "GAP_Pro\
perty","implied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)"]},"IsInverseSemigroup" : {"type" : "GAP_Property","implied" : [\
"IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsOrthodoxSemigroup","Tester(IsO\
rthodoxSemigroup)"]},"IsBand" : {"type" : "GAP_Property","implied" : ["IsBand","Tester(IsBand)"]},"IsBrandtSemigroup" : {"type" : "GA\
P_Property","implied" : ["IsBrandtSemigroup","Tester(IsBrandtSemigroup)"]},"IsCliffordSemigroup" : {"type" : "GAP_Property","implied"\
: ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCliffordSemigroup","Tester\
(IsCliffordSemigroup)","IsCompletelyRegularSemigroup","Tester(IsCompletelyRegularSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodox\
Semigroup)"]},"IsCommutativeSemigroup" : {"type" : "GAP_Property","implied" : ["IsCommutativeSemigroup","Tester(IsCommutativeSemigrou\
p)"]},"IsCompletelyRegularSemigroup" : {"type" : "GAP_Property","implied" : ["IsCompletelyRegularSemigroup","Tester(IsCompletelyRegul\
arSemigroup)"]},"IsCompletelySimpleSemigroup" : {"type" : "GAP_Property","implied" : ["IsCompletelySimpleSemigroup","Tester(IsComplet\
elySimpleSemigroup)"]},"IsGroupAsSemigroup" : {"type" : "GAP_Property","implied" : ["IsSimpleSemigroup","Tester(IsSimpleSemigroup)","\
IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Te\
ster(IsCompletelyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsOrthodoxSemigroup","Tester(IsOrthodoxSemigro\
up)"]},"IsIdempotentGenerated" : {"type" : "GAP_Property","implied" : ["IsIdempotentGenerated","Tester(IsIdempotentGenerated)","IsSem\
iband","Tester(IsSemiband)"]},"IsLeftZeroSemigroup" : {"type" : "GAP_Property","implied" : ["IsLeftZeroSemigroup","Tester(IsLeftZeroS\
emigroup)"]},"IsMonogenicSemigroup" : {"type" : "GAP_Property","implied" : ["IsMonogenicSemigroup","Tester(IsMonogenicSemigroup)"]},"\
IsMonoidAsSemigroup" : {"type" : "GAP_Property","implied" : ["IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)"]},"IsNilpotentSemigr\
oup" : {"type" : "GAP_Property","implied" : ["IsNilpotentSemigroup","Tester(IsNilpotentSemigroup)"]},"IsOrthodoxSemigroup" : {"type" \
: "GAP_Property","implied" : ["IsOrthodoxSemigroup","Tester(IsOrthodoxSemigroup)"]},"IsRectangularBand" : {"type" : "GAP_Property","i\
mplied" : ["IsRectangularBand","Tester(IsRectangularBand)"]},"IsRightZeroSemigroup" : {"type" : "GAP_Property","implied" : ["IsRightZ\
eroSemigroup","Tester(IsRightZeroSemigroup)"]},"IsSemiband" : {"type" : "GAP_Property","implied" : ["IsSemiband","Tester(IsSemiband)"\
]},"IsSemilattice" : {"type" : "GAP_Property","implied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Te\
ster(IsInverseSemigroup)","IsBand","Tester(IsBand)","IsCliffordSemigroup","Tester(IsCliffordSemigroup)","IsCompletelyRegularSemigroup\
","Tester(IsCompletelyRegularSemigroup)","IsIdempotentGenerated","Tester(IsIdempotentGenerated)","IsOrthodoxSemigroup","Tester(IsOrth\
odoxSemigroup)","IsSemiband","Tester(IsSemiband)","IsSemilattice","Tester(IsSemilattice)"]},"IsZeroSemigroup" : {"type" : "GAP_Proper\
ty","implied" : ["IsZeroSemigroup","Tester(IsZeroSemigroup)"]},"IsLeftSemigroupIdeal" : {"type" : "GAP_Property","implied" : ["IsLeft\
SemigroupIdeal","Tester(IsLeftSemigroupIdeal)"]},"IsRightSemigroupIdeal" : {"type" : "GAP_Property","implied" : ["IsRightSemigroupIde\
al","Tester(IsRightSemigroupIdeal)"]},"IsSemigroupIdeal" : {"type" : "GAP_Property","implied" : ["IsSemigroupIdeal","Tester(IsSemigro\
upIdeal)"]},"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","imp\
lied" : ["KnowsHowToDecompose","Tester(KnowsHowToDecompose)"]},"IsPGroup" : {"type" : "GAP_Property","implied" : ["IsPGroup","Tester(\
IsPGroup)"]},"IsNilpotentGroup" : {"type" : "GAP_Property","implied" : ["IsNilpotentGroup","Tester(IsNilpotentGroup)","IsSupersolvabl\
eGroup","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_Proper\
ty","implied" : ["IsSimpleGroup","Tester(IsSimpleGroup)"]},"IsAlmostSimpleGroup" : {"type" : "GAP_Property","implied" : ["IsAlmostSim\
pleGroup","Tester(IsAlmostSimpleGroup)"]},"IsSupersolvableGroup" : {"type" : "GAP_Property","implied" : ["IsSupersolvableGroup","Test\
er(IsSupersolvableGroup)","IsSolvableGroup","Tester(IsSolvableGroup)"]},"IsMonomialGroup" : {"type" : "GAP_Property","implied" : ["Is\
MonomialGroup","Tester(IsMonomialGroup)","IsSolvableGroup","Tester(IsSolvableGroup)"]},"IsSolvableGroup" : {"type" : "GAP_Property","\
implied" : ["IsSolvableGroup","Tester(IsSolvableGroup)"]},"IsPolycyclicGroup" : {"type" : "GAP_Property","implied" : ["IsSolvableGrou\
p","Tester(IsSolvableGroup)","IsPolycyclicGroup","Tester(IsPolycyclicGroup)"]},"IsNormalInParent" : {"type" : "GAP_Property","implied\
" : ["IsNormalInParent","Tester(IsNormalInParent)"]},"IsGeneratorsOfInverseSemigroup" : {"type" : "GAP_Property","implied" : ["IsGene\
ratorsOfInverseSemigroup","Tester(IsGeneratorsOfInverseSemigroup)"]},"IsAdditivelyCommutative" : {"type" : "GAP_Property","implied" :\
["IsAdditivelyCommutative","Tester(IsAdditivelyCommutative)"]},"IsLDistributive" : {"type" : "GAP_Property","implied" : ["IsLDistrib\
utive","Tester(IsLDistributive)"]},"IsRDistributive" : {"type" : "GAP_Property","implied" : ["IsRDistributive","Tester(IsRDistributiv\
e)"]},"IsAnticommutative" : {"type" : "GAP_Property","implied" : ["IsAnticommutative","Tester(IsAnticommutative)"]},"IsIntegralRing" \
: {"type" : "GAP_Property","implied" : ["IsIntegralRing","Tester(IsIntegralRing)"]},"IsJacobianRing" : {"type" : "GAP_Property","impl\
ied" : ["IsJacobianRing","Tester(IsJacobianRing)"]},"IsZeroSquaredRing" : {"type" : "GAP_Property","implied" : ["IsZeroSquaredRing","\
Tester(IsZeroSquaredRing)"]},"IsZeroMultiplicationRing" : {"type" : "GAP_Property","implied" : ["IsZeroMultiplicationRing","Tester(Is\
ZeroMultiplicationRing)"]},"IsGeneralizedCartanMatrix" : {"type" : "GAP_Property","implied" : ["IsGeneralizedCartanMatrix","Tester(Is\
GeneralizedCartanMatrix)"]},"IsMonomialMatrix" : {"type" : "GAP_Property","implied" : ["IsMonomialMatrix","Tester(IsMonomialMatrix)"]\
},"IsTwoSidedIdealInParent" : {"type" : "GAP_Property","implied" : ["IsTwoSidedIdealInParent","Tester(IsTwoSidedIdealInParent)","IsLe\
ftIdealInParent","Tester(IsLeftIdealInParent)","IsRightIdealInParent","Tester(IsRightIdealInParent)"]},"IsLeftIdealInParent" : {"type\
" : "GAP_Property","implied" : ["IsLeftIdealInParent","Tester(IsLeftIdealInParent)"]},"IsRightIdealInParent" : {"type" : "GAP_Propert\
y","implied" : ["IsRightIdealInParent","Tester(IsRightIdealInParent)"]},"IsFiniteDimensional" : {"type" : "GAP_Property","implied" : \
["IsFiniteDimensional","Tester(IsFiniteDimensional)"]},"IsFullRowModule" : {"type" : "GAP_Property","implied" : ["IsFullRowModule","T\
ester(IsFullRowModule)","IsRowModule","Tester(IsRowModule)"]},"IsFullMatrixModule" : {"type" : "GAP_Property","implied" : ["IsFullMat\
rixModule","Tester(IsFullMatrixModule)","IsMatrixModule","Tester(IsMatrixModule)"]},"IsRowModule" : {"type" : "GAP_Property","implied\
" : ["IsRowModule","Tester(IsRowModule)"]},"IsMatrixModule" : {"type" : "GAP_Property","implied" : ["IsMatrixModule","Tester(IsMatrix\
Module)"]},"IsCanonicalBasis" : {"type" : "GAP_Property","implied" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)"]},"IsCanonicalBas\
isFullRowModule" : {"type" : "GAP_Property","implied" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullRowModule\
","Tester(IsCanonicalBasisFullRowModule)"]},"IsCanonicalBasisFullMatrixModule" : {"type" : "GAP_Property","implied" : ["IsCanonicalBa\
sis","Tester(IsCanonicalBasis)","IsCanonicalBasisFullMatrixModule","Tester(IsCanonicalBasisFullMatrixModule)"]},"IsIntegralBasis" : {\
"type" : "GAP_Property","implied" : ["IsIntegralBasis","Tester(IsIntegralBasis)"]},"IsNormalBasis" : {"type" : "GAP_Property","implie\
d" : ["IsNormalBasis","Tester(IsNormalBasis)"]},"IsSemiEchelonized" : {"type" : "GAP_Property","implied" : ["IsSemiEchelonized","Test\
er(IsSemiEchelonized)"]},"IsVectorSpaceHomomorphism" : {"type" : "GAP_Property","implied" : ["IsVectorSpaceHomomorphism","Tester(IsVe\
ctorSpaceHomomorphism)"]},"IsFullHomModule" : {"type" : "GAP_Property","implied" : ["IsFullHomModule","Tester(IsFullHomModule)"]},"Is\
PseudoCanonicalBasisFullHomModule" : {"type" : "GAP_Property","implied" : ["IsPseudoCanonicalBasisFullHomModule","Tester(IsPseudoCano\
nicalBasisFullHomModule)"]},"IsSimpleAlgebra" : {"type" : "GAP_Property","implied" : ["IsSimpleAlgebra","Tester(IsSimpleAlgebra)"]},"\
IsGroupRing" : {"type" : "GAP_Property","implied" : ["IsGroupRing","Tester(IsGroupRing)"]},"IsFullFpAlgebra" : {"type" : "GAP_Propert\
y","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" : ["IsLieNi\
lpotent","Tester(IsLieNilpotent)","IsLieSolvable","Tester(IsLieSolvable)"]},"IsRestrictedLieAlgebra" : {"type" : "GAP_Property","impl\
ied" : ["IsRestrictedLieAlgebra","Tester(IsRestrictedLieAlgebra)"]},"IsLieSolvable" : {"type" : "GAP_Property","implied" : ["IsLieSol\
vable","Tester(IsLieSolvable)"]},"IsFullSCAlgebra" : {"type" : "GAP_Property","implied" : ["IsFullSCAlgebra","Tester(IsFullSCAlgebra)\
"]},"IsCanonicalBasisFullSCAlgebra" : {"type" : "GAP_Property","implied" : ["IsCanonicalBasis","Tester(IsCanonicalBasis)","IsCanonica\
lBasisFullSCAlgebra","Tester(IsCanonicalBasisFullSCAlgebra)"]},"IsAlgebraModule" : {"type" : "GAP_Property","implied" : ["IsAlgebraMo\
dule","Tester(IsAlgebraModule)"]},"IsLeftAlgebraModule" : {"type" : "GAP_Property","implied" : ["IsLeftAlgebraModule","Tester(IsLeftA\
lgebraModule)"]},"IsRightAlgebraModule" : {"type" : "GAP_Property","implied" : ["IsRightAlgebraModule","Tester(IsRightAlgebraModule)"\
]},"IsWeylGroup" : {"type" : "GAP_Property","implied" : ["IsWeylGroup","Tester(IsWeylGroup)"]},"IsPolynomial" : {"type" : "GAP_Proper\
ty","implied" : ["IsPolynomial","Tester(IsPolynomial)"]},"IsUnivariateRationalFunction" : {"type" : "GAP_Property","implied" : ["IsUn\
ivariateRationalFunction","Tester(IsUnivariateRationalFunction)"]},"IsLaurentPolynomial" : {"type" : "GAP_Property","implied" : ["IsU\
nivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsLaurentPolynomial","Tester(IsLaurentPolynomial)"]},"IsConstantRa\
tionalFunction" : {"type" : "GAP_Property","implied" : ["IsUnivariateRationalFunction","Tester(IsUnivariateRationalFunction)","IsCons\
tantRationalFunction","Tester(IsConstantRationalFunction)"]},"IsPrimeField" : {"type" : "GAP_Property","implied" : ["IsPrimeField","T\
ester(IsPrimeField)"]},"IsNumberField" : {"type" : "GAP_Property","implied" : ["IsNumberField","Tester(IsNumberField)"]},"IsAbelianNu\
mberField" : {"type" : "GAP_Property","implied" : ["IsNumberField","Tester(IsNumberField)","IsAbelianNumberField","Tester(IsAbelianNu\
mberField)"]},"IsCyclotomicField" : {"type" : "GAP_Property","implied" : ["IsNumberField","Tester(IsNumberField)","IsAbelianNumberFie\
ld","Tester(IsAbelianNumberField)","IsCyclotomicField","Tester(IsCyclotomicField)"]},"IsFreeSemigroup" : {"type" : "GAP_Property","im\
plied" : ["IsFreeSemigroup","Tester(IsFreeSemigroup)"]},"IsFreeMonoid" : {"type" : "GAP_Property","implied" : ["IsFreeMonoid","Tester\
(IsFreeMonoid)"]},"IsBuiltFromAdditiveMagmaWithInverses" : {"type" : "GAP_Property","implied" : ["IsBuiltFromAdditiveMagmaWithInverse\
s","Tester(IsBuiltFromAdditiveMagmaWithInverses)"]},"IsBuiltFromMagma" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMagma","Te\
ster(IsBuiltFromMagma)"]},"IsBuiltFromMagmaWithOne" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMagma","Tester(IsBuiltFromMag\
ma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)"]},"IsBuiltFromMagmaWithInverses" : {"type" : "GAP_Property","implied\
" : ["IsBuiltFromMagma","Tester(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithI\
nverses","Tester(IsBuiltFromMagmaWithInverses)"]},"IsBuiltFromGroup" : {"type" : "GAP_Property","implied" : ["IsBuiltFromMagma","Test\
er(IsBuiltFromMagma)","IsBuiltFromMagmaWithOne","Tester(IsBuiltFromMagmaWithOne)","IsBuiltFromMagmaWithInverses","Tester(IsBuiltFromM\
agmaWithInverses)","IsBuiltFromGroup","Tester(IsBuiltFromGroup)"]},"IsBuiltFromSemigroup" : {"type" : "GAP_Property","implied" : ["Is\
BuiltFromSemigroup","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_Proper\
ty","implied" : ["IsPcgsCentralSeries","Tester(IsPcgsCentralSeries)"]},"IsPcgsPCentralSeriesPGroup" : {"type" : "GAP_Property","impli\
ed" : ["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","impli\
ed" : ["IsFiniteOrdersPcgs","Tester(IsFiniteOrdersPcgs)"]},"IsCanonicalPcgs" : {"type" : "GAP_Property","implied" : ["IsCanonicalPcgs\
","Tester(IsCanonicalPcgs)"]},"IsParentPcgsFamilyPcgs" : {"type" : "GAP_Property","implied" : ["IsParentPcgsFamilyPcgs","Tester(IsPar\
entPcgsFamilyPcgs)"]},"IsFamilyPcgs" : {"type" : "GAP_Property","implied" : ["IsCanonicalPcgs","Tester(IsCanonicalPcgs)","IsParentPcg\
sFamilyPcgs","Tester(IsParentPcgsFamilyPcgs)","IsFamilyPcgs","Tester(IsFamilyPcgs)"]},"IsNumeratorParentPcgsFamilyPcgs" : {"type" : "\
GAP_Property","implied" : ["IsNumeratorParentPcgsFamilyPcgs","Tester(IsNumeratorParentPcgsFamilyPcgs)"]},"IsSpecialPcgs" : {"type" : \
"GAP_Property","implied" : ["IsPcgsElementaryAbelianSeries","Tester(IsPcgsElementaryAbelianSeries)","IsSpecialPcgs","Tester(IsSpecial\
Pcgs)"]},"IsInducedPcgsWrtSpecialPcgs" : {"type" : "GAP_Property","implied" : ["IsInducedPcgsWrtSpecialPcgs","Tester(IsInducedPcgsWrt\
SpecialPcgs)"]},"IsCanonicalPcgsWrtSpecialPcgs" : {"type" : "GAP_Property","implied" : ["IsCanonicalPcgsWrtSpecialPcgs","Tester(IsCan\
onicalPcgsWrtSpecialPcgs)"]},"IsConjugatorIsomorphism" : {"type" : "GAP_Property","implied" : ["IsExtLElement","IsExtRElement","IsMul\
tiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElement","IsGeneralMapping","\
IsTotal","Tester(IsTotal)","IsSingleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSur\
jective)","RespectsMultiplication","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(Re\
spectsInverses)","IsConjugatorIsomorphism","Tester(IsConjugatorIsomorphism)"]},"IsInnerAutomorphism" : {"type" : "GAP_Property","impl\
ied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInvers\
e","IsAssociativeElement","IsGeneralMapping","IsEndoGeneralMapping","Tester(IsEndoGeneralMapping)","IsTotal","Tester(IsTotal)","IsSin\
gleValued","Tester(IsSingleValued)","IsInjective","Tester(IsInjective)","IsSurjective","Tester(IsSurjective)","RespectsMultiplication\
","Tester(RespectsMultiplication)","RespectsOne","Tester(RespectsOne)","RespectsInverses","Tester(RespectsInverses)","IsConjugatorIso\
morphism","Tester(IsConjugatorIsomorphism)","IsInnerAutomorphism","Tester(IsInnerAutomorphism)"]},"IsNaturalSymmetricGroup" : {"type"\
: "GAP_Property","implied" : ["IsNaturalSymmetricGroup","Tester(IsNaturalSymmetricGroup)","IsSymmetricGroup","Tester(IsSymmetricGrou\
p)"]},"IsNaturalAlternatingGroup" : {"type" : "GAP_Property","implied" : ["IsNaturalAlternatingGroup","Tester(IsNaturalAlternatingGro\
up)","IsAlternatingGroup","Tester(IsAlternatingGroup)"]},"IsAlternatingGroup" : {"type" : "GAP_Property","implied" : ["IsAlternatingG\
roup","Tester(IsAlternatingGroup)"]},"IsSymmetricGroup" : {"type" : "GAP_Property","implied" : ["IsSymmetricGroup","Tester(IsSymmetri\
cGroup)"]},"IsDihedralGroup" : {"type" : "GAP_Property","implied" : ["IsDihedralGroup","Tester(IsDihedralGroup)"]},"IsQuaternionGroup\
" : {"type" : "GAP_Property","implied" : ["IsQuaternionGroup","Tester(IsQuaternionGroup)"]},"IsQuasiDihedralGroup" : {"type" : "GAP_P\
roperty","implied" : ["IsQuasiDihedralGroup","Tester(IsQuasiDihedralGroup)"]},"IsPSL" : {"type" : "GAP_Property","implied" : ["IsPSL"\
,"Tester(IsPSL)"]},"IsPQuotientSystem" : {"type" : "GAP_Property","implied" : ["IsPQuotientSystem","Tester(IsPQuotientSystem)"]},"IsN\
ilpQuotientSystem" : {"type" : "GAP_Property","implied" : ["IsNilpQuotientSystem","Tester(IsNilpQuotientSystem)"]},"IsTransitive" : {\
"type" : "GAP_Property","implied" : ["IsTransitive","Tester(IsTransitive)"]},"IsPrimitive" : {"type" : "GAP_Property","implied" : ["I\
sPrimitive","Tester(IsPrimitive)"]},"IsPrimitiveAffine" : {"type" : "GAP_Property","implied" : ["IsPrimitiveAffine","Tester(IsPrimiti\
veAffine)"]},"IsSemiRegular" : {"type" : "GAP_Property","implied" : ["IsSemiRegular","Tester(IsSemiRegular)"]},"IsRegular" : {"type" \
: "GAP_Property","implied" : ["IsRegular","Tester(IsRegular)"]},"IsCentralFactor" : {"type" : "GAP_Property","implied" : ["IsCentralF\
actor","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(IsCanonicalNiceMonomorph\
ism)"]},"IsHandledByNiceMonomorphism" : {"type" : "GAP_Property","implied" : ["CanEasilyTestMembership","IsHandledByNiceMonomorphism"\
,"Tester(IsHandledByNiceMonomorphism)"]},"IsGroupOfAutomorphisms" : {"type" : "GAP_Property","implied" : ["IsGroupOfAutomorphisms","T\
ester(IsGroupOfAutomorphisms)"]},"IsGroupOfAutomorphismsFiniteGroup" : {"type" : "GAP_Property","implied" : ["IsFinite","Tester(IsFin\
ite)","CanEasilyTestMembership","IsHandledByNiceMonomorphism","Tester(IsHandledByNiceMonomorphism)","IsGroupOfAutomorphisms","Tester(\
IsGroupOfAutomorphisms)","IsGroupOfAutomorphismsFiniteGroup","Tester(IsGroupOfAutomorphismsFiniteGroup)"]},"IsAutomorphismGroup" : {"\
type" : "GAP_Property","implied" : ["IsGroupOfAutomorphisms","Tester(IsGroupOfAutomorphisms)","IsAutomorphismGroup","Tester(IsAutomor\
phismGroup)"]},"IsGeneralLinearGroup" : {"type" : "GAP_Property","implied" : ["IsGeneralLinearGroup","Tester(IsGeneralLinearGroup)"]}\
,"IsNaturalGL" : {"type" : "GAP_Property","implied" : ["IsGeneralLinearGroup","Tester(IsGeneralLinearGroup)","IsNaturalGL","Tester(Is\
NaturalGL)"]},"IsSpecialLinearGroup" : {"type" : "GAP_Property","implied" : ["IsSpecialLinearGroup","Tester(IsSpecialLinearGroup)"]},\
"IsNaturalSL" : {"type" : "GAP_Property","implied" : ["IsSpecialLinearGroup","Tester(IsSpecialLinearGroup)","IsNaturalSL","Tester(IsN\
aturalSL)","IsSubgroupSL","Tester(IsSubgroupSL)"]},"IsSubgroupSL" : {"type" : "GAP_Property","implied" : ["IsSubgroupSL","Tester(IsSu\
bgroupSL)"]},"IsFullSubgroupGLorSLRespectingBilinearForm" : {"type" : "GAP_Property","implied" : ["IsFullSubgroupGLorSLRespectingBili\
nearForm","Tester(IsFullSubgroupGLorSLRespectingBilinearForm)"]},"IsFullSubgroupGLorSLRespectingSesquilinearForm" : {"type" : "GAP_Pr\
operty","implied" : ["IsFullSubgroupGLorSLRespectingSesquilinearForm","Tester(IsFullSubgroupGLorSLRespectingSesquilinearForm)"]},"IsF\
ullSubgroupGLorSLRespectingQuadraticForm" : {"type" : "GAP_Property","implied" : ["IsFullSubgroupGLorSLRespectingQuadraticForm","Test\
er(IsFullSubgroupGLorSLRespectingQuadraticForm)"]},"IsRationalMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsRationalMatrixG\
roup","Tester(IsRationalMatrixGroup)"]},"IsIntegerMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsRationalMatrixGroup","Teste\
r(IsRationalMatrixGroup)","IsIntegerMatrixGroup","Tester(IsIntegerMatrixGroup)"]},"IsBravaisGroup" : {"type" : "GAP_Property","implie\
d" : ["IsBravaisGroup","Tester(IsBravaisGroup)"]},"IsWellFoundedOrdering" : {"type" : "GAP_Property","implied" : ["IsWellFoundedOrder\
ing","Tester(IsWellFoundedOrdering)"]},"IsTotalOrdering" : {"type" : "GAP_Property","implied" : ["IsTotalOrdering","Tester(IsTotalOrd\
ering)"]},"IsOrderingOnFamilyOfAssocWords" : {"type" : "GAP_Property","implied" : ["IsOrderingOnFamilyOfAssocWords","Tester(IsOrderin\
gOnFamilyOfAssocWords)"]},"IsTranslationInvariantOrdering" : {"type" : "GAP_Property","implied" : ["IsTranslationInvariantOrdering","\
Tester(IsTranslationInvariantOrdering)"]},"IsShortLexOrdering" : {"type" : "GAP_Property","implied" : ["IsShortLexOrdering","Tester(I\
sShortLexOrdering)"]},"IsWeightLexOrdering" : {"type" : "GAP_Property","implied" : ["IsWeightLexOrdering","Tester(IsWeightLexOrdering\
)"]},"IsBasicWreathProductOrdering" : {"type" : "GAP_Property","implied" : ["IsBasicWreathProductOrdering","Tester(IsBasicWreathProdu\
ctOrdering)"]},"IsWreathProductOrdering" : {"type" : "GAP_Property","implied" : ["IsWreathProductOrdering","Tester(IsWreathProductOrd\
ering)"]},"IsFiniteSemigroupGreensRelation" : {"type" : "GAP_Property","implied" : ["IsFiniteSemigroupGreensRelation","Tester(IsFinit\
eSemigroupGreensRelation)"]},"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","imp\
lied" : ["IsFullTransformationSemigroup","Tester(IsFullTransformationSemigroup)"]},"IsReesMatrixSemigroup" : {"type" : "GAP_Property"\
,"implied" : ["IsReesMatrixSemigroup","Tester(IsReesMatrixSemigroup)"]},"IsReesZeroMatrixSemigroup" : {"type" : "GAP_Property","impli\
ed" : ["IsReesZeroMatrixSemigroup","Tester(IsReesZeroMatrixSemigroup)"]},"IsSymmetricInverseSemigroup" : {"type" : "GAP_Property","im\
plied" : ["IsRegularSemigroup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsOrthodoxSemigroup","\
Tester(IsOrthodoxSemigroup)","IsSymmetricInverseSemigroup","Tester(IsSymmetricInverseSemigroup)"]},"IsAlmostSimpleCharacterTable" : {\
"type" : "GAP_Property","implied" : ["IsAlmostSimpleCharacterTable","Tester(IsAlmostSimpleCharacterTable)"]},"IsMonomialCharacterTabl\
e" : {"type" : "GAP_Property","implied" : ["IsMonomialCharacterTable","Tester(IsMonomialCharacterTable)"]},"IsNilpotentCharacterTable\
" : {"type" : "GAP_Property","implied" : ["IsNilpotentCharacterTable","Tester(IsNilpotentCharacterTable)"]},"IsPerfectCharacterTable"\
: {"type" : "GAP_Property","implied" : ["IsPerfectCharacterTable","Tester(IsPerfectCharacterTable)"]},"IsSimpleCharacterTable" : {"t\
ype" : "GAP_Property","implied" : ["IsSimpleCharacterTable","Tester(IsSimpleCharacterTable)"]},"IsSolvableCharacterTable" : {"type" :\
"GAP_Property","implied" : ["IsSolvableCharacterTable","Tester(IsSolvableCharacterTable)"]},"IsSporadicSimpleCharacterTable" : {"typ\
e" : "GAP_Property","implied" : ["IsSporadicSimpleCharacterTable","Tester(IsSporadicSimpleCharacterTable)"]},"IsSupersolvableCharacte\
rTable" : {"type" : "GAP_Property","implied" : ["IsSupersolvableCharacterTable","Tester(IsSupersolvableCharacterTable)"]},"IsCharacte\
r" : {"type" : "GAP_Property","implied" : ["IsCharacter","Tester(IsCharacter)"]},"IsVirtualCharacter" : {"type" : "GAP_Property","imp\
lied" : ["IsVirtualCharacter","Tester(IsVirtualCharacter)"]},"IsIrreducibleCharacter" : {"type" : "GAP_Property","implied" : ["IsIrre\
ducibleCharacter","Tester(IsIrreducibleCharacter)"]},"IsBergerCondition" : {"type" : "GAP_Property","implied" : ["IsBergerCondition",\
"Tester(IsBergerCondition)"]},"IsPrimitiveCharacter" : {"type" : "GAP_Property","implied" : ["IsPrimitiveCharacter","Tester(IsPrimiti\
veCharacter)"]},"IsQuasiPrimitive" : {"type" : "GAP_Property","implied" : ["IsQuasiPrimitive","Tester(IsQuasiPrimitive)"]},"IsInduced\
FromNormalSubgroup" : {"type" : "GAP_Property","implied" : ["IsInducedFromNormalSubgroup","Tester(IsInducedFromNormalSubgroup)"]},"Is\
MonomialCharacter" : {"type" : "GAP_Property","implied" : ["IsMonomialCharacter","Tester(IsMonomialCharacter)"]},"IsMonomialNumber" :\
{"type" : "GAP_Property","implied" : ["IsMonomialNumber","Tester(IsMonomialNumber)"]},"IsSubnormallyMonomial" : {"type" : "GAP_Prope\
rty","implied" : ["IsSubnormallyMonomial","Tester(IsSubnormallyMonomial)"]},"IsRelativelySM" : {"type" : "GAP_Property","implied" : [\
"IsRelativelySM","Tester(IsRelativelySM)"]},"IsMinimalNonmonomial" : {"type" : "GAP_Property","implied" : ["IsMinimalNonmonomial","Te\
ster(IsMinimalNonmonomial)"]},"IsAbelianTom" : {"type" : "GAP_Property","implied" : ["IsAbelianTom","Tester(IsAbelianTom)"]},"IsCycli\
cTom" : {"type" : "GAP_Property","implied" : ["IsCyclicTom","Tester(IsCyclicTom)"]},"IsNilpotentTom" : {"type" : "GAP_Property","impl\
ied" : ["IsNilpotentTom","Tester(IsNilpotentTom)"]},"IsPerfectTom" : {"type" : "GAP_Property","implied" : ["IsPerfectTom","Tester(IsP\
erfectTom)"]},"IsSolvableTom" : {"type" : "GAP_Property","implied" : ["IsSolvableTom","Tester(IsSolvableTom)"]},"IsPrimitiveMatrixGro\
up" : {"type" : "GAP_Property","implied" : ["IsPrimitiveMatrixGroup","Tester(IsPrimitiveMatrixGroup)"]},"IsUnitGroup" : {"type" : "GA\
P_Property","implied" : ["IsUnitGroup","Tester(IsUnitGroup)"]},"IsUnitGroupIsomorphism" : {"type" : "GAP_Property","implied" : ["IsUn\
itGroupIsomorphism","Tester(IsUnitGroupIsomorphism)"]},"IsNumberFieldByMatrices" : {"type" : "GAP_Property","implied" : ["IsNumberFie\
ldByMatrices","Tester(IsNumberFieldByMatrices)"]},"IsMultGroupByFieldElemsIsomorphism" : {"type" : "GAP_Property","implied" : ["IsMul\
tGroupByFieldElemsIsomorphism","Tester(IsMultGroupByFieldElemsIsomorphism)"]},"IsWeightedCollector" : {"type" : "GAP_Property","impli\
ed" : ["IsWeightedCollector","Tester(IsWeightedCollector)"]},"IsPolynomialCollector" : {"type" : "GAP_Property","implied" : ["IsPolyn\
omialCollector","Tester(IsPolynomialCollector)"]},"UseLibraryCollector" : {"type" : "GAP_Property","implied" : ["UseLibraryCollector"\
,"Tester(UseLibraryCollector)"]},"IsPolycyclicPresentation" : {"type" : "GAP_Property","implied" : ["IsPolycyclicPresentation","Teste\
r(IsPolycyclicPresentation)"]},"IsHomomorphismIntoMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsHomomorphismIntoMatrixGroup\
","Tester(IsHomomorphismIntoMatrixGroup)"]},"IsNilpotentByFinite" : {"type" : "GAP_Property","implied" : ["IsNilpotentByFinite","Test\
er(IsNilpotentByFinite)"]},"IsTorsionFree" : {"type" : "GAP_Property","implied" : ["IsTorsionFree","Tester(IsTorsionFree)"]},"IsFreeA\
belian" : {"type" : "GAP_Property","implied" : ["IsFreeAbelian","Tester(IsFreeAbelian)"]},"IsGroupClass" : {"type" : "GAP_Property","\
implied" : ["IsGroupClass","Tester(IsGroupClass)"]},"ContainsTrivialGroup" : {"type" : "GAP_Property","implied" : ["ContainsTrivialGr\
oup","Tester(ContainsTrivialGroup)"]},"IsSubgroupClosed" : {"type" : "GAP_Property","implied" : ["IsSubgroupClosed","Tester(IsSubgrou\
pClosed)","IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)"]},"IsNormalSubgroupClosed" : {"type" : "GAP_Property","implied" :\
["IsNormalSubgroupClosed","Tester(IsNormalSubgroupClosed)"]},"IsQuotientClosed" : {"type" : "GAP_Property","implied" : ["IsQuotientC\
losed","Tester(IsQuotientClosed)"]},"IsResiduallyClosed" : {"type" : "GAP_Property","implied" : ["IsResiduallyClosed","Tester(IsResid\
uallyClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)"]},"IsNormalProductClosed" : {"type" : "GAP_Property","implied" \
: ["IsNormalProductClosed","Tester(IsNormalProductClosed)","IsDirectProductClosed","Tester(IsDirectProductClosed)"]},"IsDirectProduct\
Closed" : {"type" : "GAP_Property","implied" : ["IsDirectProductClosed","Tester(IsDirectProductClosed)"]},"IsSchunckClass" : {"type" \
: "GAP_Property","implied" : ["ContainsTrivialGroup","Tester(ContainsTrivialGroup)","IsQuotientClosed","Tester(IsQuotientClosed)","Is\
DirectProductClosed","Tester(IsDirectProductClosed)","IsSchunckClass","Tester(IsSchunckClass)","IsSaturated","Tester(IsSaturated)"]},\
"IsSaturated" : {"type" : "GAP_Property","implied" : ["IsSaturated","Tester(IsSaturated)"]},"IsPrimitiveSolvableGroup" : {"type" : "G\
AP_Property","implied" : ["IsPrimitiveSolvableGroup","Tester(IsPrimitiveSolvableGroup)"]},"KnowsSomeGroupInfo" : {"type" : "GAP_Prope\
rty","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" : ["IsDu\
plicateTable","Tester(IsDuplicateTable)"]},"IsIrreducibleMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsIrreducibleMatrixGro\
up","Tester(IsIrreducibleMatrixGroup)"]},"IsAbsolutelyIrreducibleMatrixGroup" : {"type" : "GAP_Property","implied" : ["IsAbsolutelyIr\
reducibleMatrixGroup","Tester(IsAbsolutelyIrreducibleMatrixGroup)"]},"IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup" : {"type" : \
"GAP_Property","implied" : ["IsMaximalAbsolutelyIrreducibleSolvableMatrixGroup","Tester(IsMaximalAbsolutelyIrreducibleSolvableMatrixG\
roup)"]},"IsLieNilpotentOverFp" : {"type" : "GAP_Property","implied" : ["IsLieNilpotentOverFp","Tester(IsLieNilpotentOverFp)"]},"IsLi\
eCover" : {"type" : "GAP_Property","implied" : ["IsLieCover","Tester(IsLieCover)"]},"IsLieAlgebraWithNB" : {"type" : "GAP_Property","\
implied" : ["IsLieAlgebraWithNB","Tester(IsLieAlgebraWithNB)"]},"IsNilpotentBasis" : {"type" : "GAP_Property","implied" : ["IsNilpote\
ntBasis","Tester(IsNilpotentBasis)"]},"IsGroupAlgebra" : {"type" : "GAP_Property","implied" : ["IsGroupAlgebra","Tester(IsGroupAlgebr\
a)"]},"IsFModularGroupAlgebra" : {"type" : "GAP_Property","implied" : ["IsFModularGroupAlgebra","Tester(IsFModularGroupAlgebra)"]},"I\
sPModularGroupAlgebra" : {"type" : "GAP_Property","implied" : ["IsPModularGroupAlgebra","Tester(IsPModularGroupAlgebra)"]},"IsGroupOf\
UnitsOfMagmaRing" : {"type" : "GAP_Property","implied" : ["IsGroupOfUnitsOfMagmaRing","Tester(IsGroupOfUnitsOfMagmaRing)"]},"IsUnitGr\
oupOfGroupRing" : {"type" : "GAP_Property","implied" : ["IsUnitGroupOfGroupRing","Tester(IsUnitGroupOfGroupRing)"]},"IsNormalizedUnit\
GroupOfGroupRing" : {"type" : "GAP_Property","implied" : ["IsListOrCollection","IsCollection","CanComputeSize","IsDuplicateFree","Tes\
ter(IsDuplicateFree)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","Cate\
goryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicative\
ElementWithInverse)","IsGeneralizedDomain","IsMagma","IsMagmaWithOne","IsMagmaWithInversesIfNonzero","IsMagmaWithInverses","IsAssocia\
tive","Tester(IsAssociative)","Tester(MultiplicativeNeutralElement)","IsSimpleSemigroup","Tester(IsSimpleSemigroup)","IsRegularSemigr\
oup","Tester(IsRegularSemigroup)","IsInverseSemigroup","Tester(IsInverseSemigroup)","IsCompletelyRegularSemigroup","Tester(IsComplete\
lyRegularSemigroup)","IsGroupAsSemigroup","Tester(IsGroupAsSemigroup)","IsMonoidAsSemigroup","Tester(IsMonoidAsSemigroup)","IsOrthodo\
xSemigroup","Tester(IsOrthodoxSemigroup)","CanComputeSizeAnySubgroup","IsSolvableGroup","Tester(IsSolvableGroup)","CanEasilyComputePc\
gs","IsNormalizedUnitGroupOfGroupRing","Tester(IsNormalizedUnitGroupOfGroupRing)"]},"IsLieAlgebraOfGroupRing" : {"type" : "GAP_Proper\
ty","implied" : ["IsLieAlgebraOfGroupRing","Tester(IsLieAlgebraOfGroupRing)"]},"IsBasisOfLieAlgebraOfGroupRing" : {"type" : "GAP_Prop\
erty","implied" : ["IsBasisOfLieAlgebraOfGroupRing","Tester(IsBasisOfLieAlgebraOfGroupRing)"]},"IsLieMetabelian" : {"type" : "GAP_Pro\
perty","implied" : ["IsLieMetabelian","Tester(IsLieMetabelian)"]},"IsLieCentreByMetabelian" : {"type" : "GAP_Property","implied" : ["\
IsLieCentreByMetabelian","Tester(IsLieCentreByMetabelian)"]},"IsSolvablePolynomial" : {"type" : "GAP_Property","implied" : ["IsSolvab\
lePolynomial","Tester(IsSolvablePolynomial)"]},"IsSeparablePolynomial" : {"type" : "GAP_Property","implied" : ["IsSeparablePolynomial\
","Tester(IsSeparablePolynomial)"]},"IsAffineCrystGroupOnRight" : {"type" : "GAP_Property","implied" : ["CanComputeSize","CanEasilyTe\
stMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnRight","Tester(IsAffineCrystGroupOnRight)","IsAffineCrystGroupOnLeftOr\
Right","Tester(IsAffineCrystGroupOnLeftOrRight)"]},"IsAffineCrystGroupOnLeft" : {"type" : "GAP_Property","implied" : ["CanComputeSize\
","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnLeft","Tester(IsAffineCrystGroupOnLeft)","IsAffineCrystG\
roupOnLeftOrRight","Tester(IsAffineCrystGroupOnLeftOrRight)"]},"IsAffineCrystGroupOnLeftOrRight" : {"type" : "GAP_Property","implied"\
: ["CanComputeSize","CanEasilyTestMembership","CanComputeSizeAnySubgroup","IsAffineCrystGroupOnLeftOrRight","Tester(IsAffineCrystGro\
upOnLeftOrRight)"]},"IsSpaceGroup" : {"type" : "GAP_Property","implied" : ["IsSpaceGroup","Tester(IsSpaceGroup)"]},"IsStandardAffineC\
rystGroup" : {"type" : "GAP_Property","implied" : ["IsStandardAffineCrystGroup","Tester(IsStandardAffineCrystGroup)"]},"IsSymmorphicS\
paceGroup" : {"type" : "GAP_Property","implied" : ["IsSymmorphicSpaceGroup","Tester(IsSymmorphicSpaceGroup)"]},"IsPointGroup" : {"typ\
e" : "GAP_Property","implied" : ["IsPointGroup","Tester(IsPointGroup)"]},"IsPointHomomorphism" : {"type" : "GAP_Property","implied" :\
["IsPointHomomorphism","Tester(IsPointHomomorphism)"]},"IsFromAffineCrystGroupToFpGroup" : {"type" : "GAP_Property","implied" : ["Is\
FromAffineCrystGroupToFpGroup","Tester(IsFromAffineCrystGroupToFpGroup)"]},"IsFromAffineCrystGroupToPcpGroup" : {"type" : "GAP_Proper\
ty","implied" : ["IsFromAffineCrystGroupToPcpGroup","Tester(IsFromAffineCrystGroupToPcpGroup)"]},"IsColorGroup" : {"type" : "GAP_Prop\
erty","implied" : ["IsColorGroup","Tester(IsColorGroup)"]},"IsAlmostCrystallographic" : {"type" : "GAP_Property","implied" : ["IsAlmo\
stCrystallographic","Tester(IsAlmostCrystallographic)"]},"IsAlmostBieberbachGroup" : {"type" : "GAP_Property","implied" : ["IsAlmostB\
ieberbachGroup","Tester(IsAlmostBieberbachGroup)"]},"IsIsomorphismByFinitePolycyclicMatrixGroup" : {"type" : "GAP_Property","implied"\
: ["IsIsomorphismByFinitePolycyclicMatrixGroup","Tester(IsIsomorphismByFinitePolycyclicMatrixGroup)"]},"IsIsomorphismByPolycyclicMat\
rixGroup" : {"type" : "GAP_Property","implied" : ["IsIsomorphismByPolycyclicMatrixGroup","Tester(IsIsomorphismByPolycyclicMatrixGroup\
)"]},"IsTriangularizableMatGroup" : {"type" : "GAP_Property","implied" : ["IsTriangularizableMatGroup","Tester(IsTriangularizableMatG\
roup)"]},"IsZ_pi" : {"type" : "GAP_Property","implied" : ["IsZ_pi","Tester(IsZ_pi)"]},"IsResidueClass" : {"type" : "GAP_Property","im\
plied" : ["IsResidueClass","Tester(IsResidueClass)"]},"IsZxZ" : {"type" : "GAP_Property","implied" : ["IsZxZ","Tester(IsZxZ)"]},"IsRe\
sidueClassWithFixedRepresentative" : {"type" : "GAP_Property","implied" : ["IsResidueClassWithFixedRepresentative","Tester(IsResidueC\
lassWithFixedRepresentative)"]},"IsOverlappingFree" : {"type" : "GAP_Property","implied" : ["IsOverlappingFree","Tester(IsOverlapping\
Free)"]},"IsMutable" : {"type" : "GAP_Category","implied" : ["IsMutable","IsCopyable"]},"IsCopyable" : {"type" : "GAP_Category","impl\
ied" : ["IsCopyable"]},"IsFunction" : {"type" : "GAP_Category","implied" : ["IsFunction"]},"IsOperation" : {"type" : "GAP_Category","\
implied" : ["IsFunction","IsOperation"]},"IsInt" : {"type" : "GAP_Category","implied" : ["IsInt","IsRat","IsCyc","IsExtAElement","IsN\
earAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtREle\
ment","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement\
","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},"IsRat" : {"type" : "GAP_Category","implied" : ["IsRat","I\
sCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement",\
"IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZD\
FRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},"IsCyc" : {"type" : "GAP_Categor\
y","implied" : ["IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","I\
sAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElement\
WithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic"]},"Tester(CONDUC\
TOR)" : {"type" : "GAP_Attribute","implied" : ["Tester(CONDUCTOR)"]},"IsFFE" : {"type" : "GAP_Category","implied" : ["IsFFE","IsExtAE\
lement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement\
","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssoci\
ativeElement","IsAdditivelyCommutativeElement","IsCommutativeElement"]},"IsPerm" : {"type" : "GAP_Category","implied" : ["IsPerm","Is\
ExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssoc\
iativeElement","IsFiniteOrderElement"]},"IsTransformation" : {"type" : "GAP_Category","implied" : ["IsTransformation","IsExtLElement"\
,"IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsAssociativeElemen\
t"]},"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"]},"IsT\
able" : {"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","im\
plied" : ["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","IsHomogeneous\
List","IsRange","IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","IsNearAdditiveElement","Cat\
egoryCollections(IsNearAdditiveElement)","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","IsNear\
AdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","IsAdditiveElement","CategoryCollections(IsAdditi\
veElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollec\
tions(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWit\
hInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeEle\
ment)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsCyclotomic)","IsGeneratorsOfSemigroup","Tester(IsGenerators\
OfSemigroup)"]},"IsRangeRep" : {"type" : "GAP_Representation","implied" : ["IsRangeRep","IsInternalRep"]},"IsString" : {"type" : "GAP\
_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsString","IsListOrCollection"]},"IsStringRep" : {"type" : "GAP_R\
epresentation","implied" : ["IsStringRep","IsInternalRep"]},"IsWeakPointerObject" : {"type" : "GAP_Category","implied" : ["IsList","I\
sWeakPointerObject","IsListOrCollection","IsFinite","Tester(IsFinite)","IsSmallList","Tester(IsSmallList)"]},"IsNoImmediateMethodsObj\
ect" : {"type" : "GAP_Filter","implied" : ["IsNoImmediateMethodsObject"]},"IsInternalRep" : {"type" : "GAP_Representation","implied" \
: ["IsInternalRep"]},"IsPositionalObjectRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep"]},"IsComponentObje\
ctRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep"]},"IsDataObjectRep" : {"type" : "GAP_Representation","imp\
lied" : ["IsDataObjectRep"]},"IsNonAtomicComponentObjectRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","Is\
NonAtomicComponentObjectRep"]},"IsReadOnlyPositionalObjectRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep",\
"IsReadOnlyPositionalObjectRep"]},"IsAtomicPositionalObjectRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep"\
,"IsAtomicPositionalObjectRep"]},"IsAttributeStoringRep" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsAttr\
ibuteStoringRep"]},"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" : ["IsCo\
mponentObjectRep","IsFamilyDefaultRep"]},"IsTypeDefaultRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","Is\
TypeDefaultRep"]},"Tester(Name)" : {"type" : "GAP_Attribute","implied" : ["Tester(Name)"]},"Tester(InfoText)" : {"type" : "GAP_Attrib\
ute","implied" : ["Tester(InfoText)"]},"Tester(String)" : {"type" : "GAP_Attribute","implied" : ["Tester(String)"]},"Tester(IsImpossi\
ble)" : {"type" : "GAP_Attribute","implied" : ["Tester(IsImpossible)"]},"IsPackedElementDefaultRep" : {"type" : "GAP_Representation",\
"implied" : ["IsPositionalObjectRep","IsPackedElementDefaultRep"]},"IsToBeDefinedObj" : {"type" : "GAP_Category","implied" : ["IsToBe\
DefinedObj"]},"IsLVarsBag" : {"type" : "GAP_Category","implied" : ["IsLVarsBag"]},"IsListOrCollection" : {"type" : "GAP_Category","im\
plied" : ["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","impli\
ed" : ["Tester(ElementsFamily)"]},"IsStandardIterator" : {"type" : "GAP_Filter","implied" : ["IsStandardIterator"]},"IsIterator" : {"\
type" : "GAP_Category","implied" : ["IsIterator"]},"Tester(IsEmpty)" : {"type" : "GAP_Tester","implied" : ["Tester(IsEmpty)"]},"Teste\
r(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)","C\
anComputeSize"]},"Tester(Representative)" : {"type" : "GAP_Attribute","implied" : ["Tester(Representative)"]},"Tester(RepresentativeS\
mallest)" : {"type" : "GAP_Attribute","implied" : ["Tester(RepresentativeSmallest)"]},"Tester(PseudoRandomSeed)" : {"type" : "GAP_Att\
ribute","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" : ["Tes\
ter(AsList)"]},"Tester(AsSortedList)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsSortedList)"]},"Tester(AsSSortedList)" : {"t\
ype" : "GAP_Attribute","implied" : ["Tester(AsSSortedList)"]},"Tester(CanEasilyCompareElements)" : {"type" : "GAP_Tester","implied" :\
["Tester(CanEasilyCompareElements)"]},"Tester(CanEasilySortElements)" : {"type" : "GAP_Tester","implied" : ["Tester(CanEasilySortEle\
ments)"]},"CanComputeSize" : {"type" : "GAP_Filter","implied" : ["CanComputeSize"]},"Tester(RandomizerAttr)" : {"type" : "GAP_Attribu\
te","implied" : ["Tester(RandomizerAttr)"]},"Tester(CheapRandomizerAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(CheapRando\
mizerAttr)"]},"IsConstantTimeAccessList" : {"type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsConstantTimeAccessL\
ist"]},"Tester(IsSmallList)" : {"type" : "GAP_Tester","implied" : ["Tester(IsSmallList)"]},"Tester(ConstantTimeAccessList)" : {"type"\
: "GAP_Attribute","implied" : ["Tester(ConstantTimeAccessList)"]},"Tester(IsSortedList)" : {"type" : "GAP_Tester","implied" : ["Test\
er(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)"]},"IsExtAElemen\
t" : {"type" : "GAP_Category","implied" : ["IsExtAElement"]},"CategoryCollections(IsExtAElement)" : {"type" : "GAP_Category","implied\
" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)"]},"CategoryCollections(CategoryCollecti\
ons(IsExtAElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollect\
ions(IsExtAElement))"]},"IsNearAdditiveElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement"]},"Ca\
tegoryCollections(IsNearAdditiveElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement"\
,"CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)"]},"CategoryCollections(CategoryCollections(IsNearA\
dditiveElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(Is\
ExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElemen\
t))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))" : {"type" : "GAP_Category","implied" : \
["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(Is\
ExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))"]},"IsNearAdditiveElementWithZer\
o" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero"]},"CategoryCollect\
ions(IsNearAdditiveElementWithZero)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","Cat\
egoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)"]},\
"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection\
","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","Cate\
goryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))\
"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))" : {"type" : "GAP_Category","implie\
d" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollectio\
ns(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(Categ\
oryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))"]},"IsNearAdditiveElementWithInverse" : {"type" : "GAP_Category",\
"implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse"]},"CategoryCo\
llections(IsNearAdditiveElementWithInverse)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAEleme\
nt","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZ\
ero)","CategoryCollections(IsNearAdditiveElementWithInverse)"]},"CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInv\
erse))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElemen\
t)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","Cate\
goryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWi\
thInverse))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))" : {"type" : "GAP_Cat\
egory","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(Cat\
egoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCol\
lections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryC\
ollections(IsNearAdditiveElementWithInverse)))"]},"IsAdditiveElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNear\
AdditiveElement","IsAdditiveElement"]},"CategoryCollections(IsAdditiveElement)" : {"type" : "GAP_Category","implied" : ["IsListOrColl\
ection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCol\
lections(IsAdditiveElement)"]},"CategoryCollections(CategoryCollections(IsAdditiveElement))" : {"type" : "GAP_Category","implied" : [\
"IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsE\
xtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditiveEl\
ement))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))" : {"type" : "GAP_Category","implied" : \
["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(Is\
ExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCo\
llections(CategoryCollections(IsAdditiveElement)))"]},"IsExtLElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement"]},"Cate\
goryCollections(IsExtLElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","Category\
Collections(IsExtLElement)"]},"CategoryCollections(CategoryCollections(IsExtLElement))" : {"type" : "GAP_Category","implied" : ["IsLi\
stOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtLElement))"]},"IsExtRElement" : {"type" : "GAP_Category"\
,"implied" : ["IsExtRElement"]},"CategoryCollections(IsExtRElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","Is\
Collection","IsExtRElement","CategoryCollections(IsExtRElement)"]},"CategoryCollections(CategoryCollections(IsExtRElement))" : {"type\
" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsExtRElement))"]},"IsMu\
ltiplicativeElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement"]},"CategoryCol\
lections(IsMultiplicativeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","Categ\
oryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)"]},\
"CategoryCollections(CategoryCollections(IsMultiplicativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsC\
ollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElem\
ent","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryColl\
ections(IsMultiplicativeElement))"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))" : {"typ\
e" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCo\
llections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryColl\
ections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))"]},"IsMultiplicative\
ElementWithOne" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeEl\
ementWithOne"]},"CategoryCollections(IsMultiplicativeElementWithOne)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","I\
sCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryColle\
ctions(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)"]},"CategoryCollections(CategoryCollections(IsM\
ultiplicativeElementWithOne))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryC\
ollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtREleme\
nt)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","C\
ategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))"]},"CategoryCollections(CategoryCollections(CategoryCollectio\
ns(IsMultiplicativeElementWithOne)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","Ca\
tegoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsEx\
tRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(Is\
MultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))"]},"IsMultip\
licativeElementWithInverse" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMult\
iplicativeElementWithOne","IsMultiplicativeElementWithInverse"]},"CategoryCollections(IsMultiplicativeElementWithInverse)" : {"type" \
: "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement\
","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWit\
hOne)","CategoryCollections(IsMultiplicativeElementWithInverse)"]},"CategoryCollections(CategoryCollections(IsMultiplicativeElementWi\
thInverse))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLE\
lement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryColl\
ections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections\
(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))"\
]},"CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))" : {"type" : "GAP_Category","im\
plied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryColle\
ctions(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))\
","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(C\
ategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeEl\
ementWithInverse)))"]},"IsOddAdditiveNestingDepthFamily" : {"type" : "GAP_Filter","implied" : ["IsOddAdditiveNestingDepthFamily"]},"I\
sOddAdditiveNestingDepthObject" : {"type" : "GAP_Filter","implied" : ["IsOddAdditiveNestingDepthObject"]},"IsGeneralizedRowVector" : \
{"type" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWit\
hZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsGeneralizedRowVector"]},"IsMultiplicativeGeneralizedRowVector" : {"t\
ype" : "GAP_Category","implied" : ["IsList","IsListOrCollection","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZe\
ro","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))"]},"CategoryF\
amily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))" : {"type" : "GAP_Category","implied" :\
["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElement\
WithInverse and IsAdditiveElement) and IsMultiplicativeElement))"]},"IsZDFRE" : {"type" : "GAP_Category","implied" : ["IsExtAElement"\
,"IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsEx\
tRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE"]},"CategoryColle\
ctions(IsZDFRE)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsE\
xtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(I\
sNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsEx\
tRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeE\
lementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsZDFRE)"]},"CategoryCollections(Categ\
oryCollections(IsZDFRE))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollec\
tions(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditi\
veElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNea\
rAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsE\
xtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","Category\
Collections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollect\
ions(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInvers\
e))","CategoryCollections(CategoryCollections(IsZDFRE))"]},"CategoryCollections((((CategoryCollections(CategoryCollections(IsNearAddi\
tiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElement))) and IsTable) and (CategoryCollections(Categ\
oryCollections(IsMultiplicativeElement)) and IsTable)))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection",\
"IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(I\
sNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(Cat\
egoryCollections(IsNearAdditiveElement)))","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollecti\
ons(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","\
CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","\
CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(IsAdditiveEleme\
nt)","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdd\
itiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsEx\
tRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(IsMult\
iplicativeElement)","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollections((((\
CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAdditiveElem\
ent))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))"]},"IsOrdinaryMatrix" : {"t\
ype" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","IsListOrCollection","IsCollection","IsExtAEl\
ement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","IsNearAdditiveElement","Catego\
ryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","IsNearAdditiveElementWithZer\
o","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","Is\
NearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNe\
arAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)","CategoryCollections(CategoryCollections\
(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))",\
"IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","IsMultiplicativeEleme\
nt","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVecto\
r","IsOrdinaryMatrix"]},"CategoryCollections(IsOrdinaryMatrix)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsColle\
ction","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollec\
tions(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollecti\
ons(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryC\
ollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZer\
o)))","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInver\
se))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)))","CategoryCollections(IsAdditi\
veElement)","CategoryCollections(CategoryCollections(IsAdditiveElement))","CategoryCollections(CategoryCollections(CategoryCollection\
s(IsAdditiveElement)))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))\
","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections\
(IsMultiplicativeElement)","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElement)))","CategoryCollecti\
ons((((CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse)) and CategoryCollections(CategoryCollections(IsAddit\
iveElement))) and IsTable) and (CategoryCollections(CategoryCollections(IsMultiplicativeElement)) and IsTable)))","CategoryCollection\
s(IsOrdinaryMatrix)"]},"IsLieMatrix" : {"type" : "GAP_Category","implied" : ["IsList","IsDenseList","IsHomogeneousList","IsTable","Is\
ListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtA\
Element))","IsNearAdditiveElement","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(CategoryCollections(IsNearAdditi\
veElement))","IsNearAdditiveElementWithZero","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(CategoryCollec\
tions(IsNearAdditiveElementWithZero))","IsNearAdditiveElementWithInverse","CategoryCollections(IsNearAdditiveElementWithInverse)","Ca\
tegoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","IsAdditiveElement","CategoryCollections(IsAdditiveElement)\
","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollect\
ions(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollectio\
ns(IsExtRElement))","IsMultiplicativeElement","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","IsGeneralizedRowVe\
ctor","IsLieMatrix"]},"IsAssociativeElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativ\
eElement","IsAssociativeElement"]},"CategoryCollections(IsAssociativeElement)" : {"type" : "GAP_Category","implied" : ["IsListOrColle\
ction","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","Cate\
goryCollections(IsMultiplicativeElement)","CategoryCollections(IsAssociativeElement)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsO\
fSemigroup)"]},"CategoryCollections(CategoryCollections(IsAssociativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrColl\
ection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))"\
,"IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(\
CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsAssociativeElement))","IsGeneratorsOfSemigr\
oup","Tester(IsGeneratorsOfSemigroup)"]},"IsAdditivelyCommutativeElement" : {"type" : "GAP_Category","implied" : ["IsExtAElement","Is\
NearAdditiveElement","IsAdditiveElement","IsAdditivelyCommutativeElement"]},"CategoryCollections(IsAdditivelyCommutativeElement)" : {\
"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","Catego\
ryCollections(IsNearAdditiveElement)","CategoryCollections(IsAdditiveElement)","CategoryCollections(IsAdditivelyCommutativeElement)"]\
},"CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollect\
ion","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","C\
ategoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsAdditiveElement))","Catego\
ryCollections(CategoryCollections(IsAdditivelyCommutativeElement))"]},"CategoryFamily(IsAdditivelyCommutativeElement)" : {"type" : "G\
AP_Category","implied" : ["IsFamily","CategoryFamily(IsAdditivelyCommutativeElement)"]},"IsCommutativeElement" : {"type" : "GAP_Categ\
ory","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsCommutativeElement"]},"CategoryCollections(IsCommutati\
veElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLEl\
ement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsCo\
mmutativeElement)"]},"CategoryCollections(CategoryCollections(IsCommutativeElement))" : {"type" : "GAP_Category","implied" : ["IsList\
OrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElem\
ent))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollec\
tions(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsCommutativeElement))"]},"IsFiniteOrde\
rElement" : {"type" : "GAP_Category","implied" : ["IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementW\
ithOne","IsMultiplicativeElementWithInverse","IsFiniteOrderElement"]},"CategoryCollections(IsFiniteOrderElement)" : {"type" : "GAP_Ca\
tegory","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","Catego\
ryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","C\
ategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCollections(IsFiniteOrderElement)"]},"CategoryCollections(CategoryCo\
llections(IsFiniteOrderElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","Catego\
ryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtREl\
ement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))"\
,"CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicative\
ElementWithInverse))","CategoryCollections(CategoryCollections(IsFiniteOrderElement))"]},"IsJacobianElement" : {"type" : "GAP_Categor\
y","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiv\
eElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement"]},"CategoryCollections(IsJacobianElement)" : \
{"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","Categ\
oryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElemen\
tWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","Categor\
yCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJacobianElement)"]},"CategoryColle\
ctions(CategoryCollections(IsJacobianElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAEl\
ement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCo\
llections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(Cat\
egoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","C\
ategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsE\
xtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeEleme\
nt))","CategoryCollections(CategoryCollections(IsJacobianElement))"]},"IsRestrictedJacobianElement" : {"type" : "GAP_Category","impli\
ed" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement"\
,"IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsJacobianElement","IsRestrictedJacobianElement"]},"CategoryCollections(I\
sRestrictedJacobianElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCol\
lections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryC\
ollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLEle\
ment)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsJac\
obianElement)","CategoryCollections(IsRestrictedJacobianElement)"]},"CategoryCollections(CategoryCollections(IsRestrictedJacobianElem\
ent))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement\
)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElement))","Categ\
oryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWit\
hInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLElement","CategoryCollections(IsExtLElement)","Categ\
oryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(Categor\
yCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollec\
tions(IsJacobianElement))","CategoryCollections(CategoryCollections(IsRestrictedJacobianElement))"]},"IsZeroSquaredElement" : {"type"\
: "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInve\
rse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsZeroSquaredElement"]},"CategoryCollections(IsZe\
roSquaredElement)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(I\
sExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections\
(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","Is\
ExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsZeroSquaredEl\
ement)"]},"CategoryCollections(CategoryCollections(IsZeroSquaredElement))" : {"type" : "GAP_Category","implied" : ["IsListOrCollectio\
n","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","Cat\
egoryCollections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero)\
)","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveEl\
ement))","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElemen\
t","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollec\
tions(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsZeroSquaredElement))"]},"Tester(IsZero)" : {"type" : "GAP\
_Tester","implied" : ["Tester(IsZero)"]},"Tester(IsOne)" : {"type" : "GAP_Tester","implied" : ["Tester(IsOne)"]},"Tester(ZeroImmutabl\
e)" : {"type" : "GAP_Attribute","implied" : ["Tester(ZeroImmutable)"]},"Tester(AdditiveInverseImmutable)" : {"type" : "GAP_Attribute"\
,"implied" : ["Tester(AdditiveInverseImmutable)"]},"Tester(OneImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(OneImmutab\
le)"]},"Tester(InverseImmutable)" : {"type" : "GAP_Attribute","implied" : ["Tester(InverseImmutable)"]},"Tester(Int)" : {"type" : "GA\
P_Attribute","implied" : ["Tester(Int)"]},"Tester(Rat)" : {"type" : "GAP_Attribute","implied" : ["Tester(Rat)"]},"Tester(Characterist\
ic)" : {"type" : "GAP_Attribute","implied" : ["Tester(Characteristic)"]},"Tester(Order)" : {"type" : "GAP_Attribute","implied" : ["Te\
ster(Order)"]},"Tester(NormedRowVector)" : {"type" : "GAP_Attribute","implied" : ["Tester(NormedRowVector)"]},"Tester(IsCommutativeFa\
mily)" : {"type" : "GAP_Tester","implied" : ["Tester(IsCommutativeFamily)"]},"Tester(IsSkewFieldFamily)" : {"type" : "GAP_Tester","im\
plied" : ["Tester(IsSkewFieldFamily)"]},"Tester(IsUFDFamily)" : {"type" : "GAP_Tester","implied" : ["Tester(IsUFDFamily)"]},"IsAdditi\
veElementAsMultiplicativeElementRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsExtLElement","IsExtREle\
ment","IsMultiplicativeElement","IsAdditiveElementAsMultiplicativeElementRep"]},"Tester(AdditiveElementsAsMultiplicativeElementsFamil\
y)" : {"type" : "GAP_Attribute","implied" : ["Tester(AdditiveElementsAsMultiplicativeElementsFamily)"]},"Tester(AdditiveElementAsMult\
iplicativeElement)" : {"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(I\
sAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","Categor\
yCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeEle\
mentWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommuta\
tiveElement)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsFFE)","IsGeneratorsOfSemigroup","Tester(IsGenerators\
OfSemigroup)"]},"CategoryCollections(CategoryCollections(IsFFE))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCol\
lection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryColl\
ections(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","Categ\
oryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))",\
"IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","Categ\
oryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsM\
ultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryColle\
ctions(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollect\
ions(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(Category\
Collections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsFFE))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsO\
fSemigroup)"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsFFE)))" : {"type" : "GAP_Category","implied" : ["IsList\
OrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElem\
ent))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(CategoryCollection\
s(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveEl\
ementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement","CategoryColl\
ections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)\
","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplica\
tiveElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","CategoryCollections(\
CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryColle\
ctions(IsFFE)))"]},"IsLexOrderedFFE" : {"type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","IsNearAdditiveElement","IsNearA\
dditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeEleme\
nt","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeEl\
ement","IsCommutativeElement","IsLexOrderedFFE"]},"IsLogOrderedFFE" : {"type" : "GAP_Category","implied" : ["IsFFE","IsExtAElement","\
IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtR\
Element","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElem\
ent","IsAdditivelyCommutativeElement","IsCommutativeElement","IsLogOrderedFFE"]},"CategoryFamily(IsFFE)" : {"type" : "GAP_Category","\
implied" : ["IsFamily","CategoryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAddit\
iveElementWithInverse and IsAdditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsAdditivelyCommutativeElement)","Categor\
yFamily(IsFFE)"]},"Tester(DegreeFFE)" : {"type" : "GAP_Attribute","implied" : ["Tester(DegreeFFE)"]},"Tester(IntFFE)" : {"type" : "GA\
P_Attribute","implied" : ["Tester(IntFFE)"]},"Tester(IntFFESymm)" : {"type" : "GAP_Attribute","implied" : ["Tester(IntFFESymm)"]},"Te\
ster(AsInternalFFE)" : {"type" : "GAP_Attribute","implied" : ["Tester(AsInternalFFE)"]},"IsGeneralizedDomain" : {"type" : "GAP_Catego\
ry","implied" : ["IsGeneralizedDomain"]},"Tester(GeneratorsOfDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(GeneratorsOfDo\
main)"]},"Tester(ParentAttr)" : {"type" : "GAP_Attribute","implied" : ["Tester(ParentAttr)"]},"IsChar" : {"type" : "GAP_Category","im\
plied" : ["IsChar"]},"CategoryCollections(IsChar)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","Categ\
oryCollections(IsChar)"]},"IsCyclotomic" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAddit\
iveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement",\
"IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElemen\
t","IsCommutativeElement","IsCyclotomic"]},"CategoryCollections(IsCyclotomic)" : {"type" : "GAP_Category","implied" : ["IsListOrColle\
ction","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAdditiveElement)","CategoryColl\
ections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryCollections(IsAdditiveElemen\
t)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(Is\
MultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse\
)","CategoryCollections(IsZDFRE)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsAdditivelyCommutativeElement)","\
CategoryCollections(IsCommutativeElement)","CategoryCollections(IsCyclotomic)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigr\
oup)"]},"CategoryCollections(CategoryCollections(IsCyclotomic))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsColl\
ection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryColle\
ctions(CategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","Catego\
ryCollections(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","\
IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","Catego\
ryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMu\
ltiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollec\
tions(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollecti\
ons(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsAdditivelyCommutativeElement))","CategoryCollections(CategoryC\
ollections(IsCommutativeElement))","CategoryCollections(CategoryCollections(IsCyclotomic))","IsGeneratorsOfSemigroup","Tester(IsGener\
atorsOfSemigroup)"]},"CategoryCollections(CategoryCollections(CategoryCollections(IsCyclotomic)))" : {"type" : "GAP_Category","implie\
d" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollectio\
ns(IsExtAElement))","CategoryCollections(CategoryCollections(CategoryCollections(IsNearAdditiveElement)))","CategoryCollections(Categ\
oryCollections(CategoryCollections(IsNearAdditiveElementWithZero)))","CategoryCollections(CategoryCollections(CategoryCollections(IsN\
earAdditiveElementWithInverse)))","CategoryCollections(CategoryCollections(CategoryCollections(IsAdditiveElement)))","IsExtLElement",\
"CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(I\
sExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(CategoryCollections\
(IsMultiplicativeElement)))","CategoryCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne)))","Categor\
yCollections(CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse)))","CategoryCollections(CategoryCollections(\
CategoryCollections(IsCyclotomic)))"]},"IsPosRat" : {"type" : "GAP_Category","implied" : ["IsRat","IsCyc","IsExtAElement","IsNearAddi\
tiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","\
IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAd\
ditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsPosRat"]},"IsNegRat" : {"type" : "GAP_Category","implied" : ["Is\
Rat","IsCyc","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveEl\
ement","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","IsMultiplicativeEl\
ementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement","IsCommutativeEl\
ement","IsZero","Tester(IsZero)","IsCyclotomic","IsZeroCyc"]},"IsSmallIntRep" : {"type" : "GAP_Representation","implied" : ["IsIntern\
alRep","IsSmallIntRep"]},"IsInfinity" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditive\
ElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","Is\
MultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","IsAdditivelyCommutativeElement",\
"IsCommutativeElement","IsCyclotomic","IsInfinity"]},"IsNegInfinity" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearA\
dditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement\
","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsAssociativeElement","I\
sAdditivelyCommutativeElement","IsCommutativeElement","IsCyclotomic","IsNegInfinity"]},"Tester(IsIntegralCyclotomic)" : {"type" : "GA\
P_Tester","implied" : ["Tester(IsIntegralCyclotomic)"]},"CategoryCollections(IsRecord)" : {"type" : "GAP_Category","implied" : ["IsLi\
stOrCollection","IsCollection","CategoryCollections(IsRecord)"]},"CategoryCollections(CategoryCollections(IsRecord))" : {"type" : "GA\
P_Category","implied" : ["IsListOrCollection","IsCollection","CategoryCollections(CategoryCollections(IsRecord))"]},"Tester(RecNames)\
" : {"type" : "GAP_Attribute","implied" : ["Tester(RecNames)"]},"IsEnumeratorByFunctionsRep" : {"type" : "GAP_Representation","implie\
d" : ["IsComponentObjectRep","IsEnumeratorByFunctionsRep"]},"IsIteratorByFunctionsRep" : {"type" : "GAP_Representation","implied" : [\
"IsComponentObjectRep","IsIteratorByFunctionsRep"]},"IsListDefault" : {"type" : "GAP_Category","implied" : ["IsList","IsListOrCollect\
ion","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","\
IsGeneralizedRowVector","IsMultiplicativeGeneralizedRowVector","IsListDefault"]},"Tester(IsRectangularTable)" : {"type" : "GAP_Tester\
","implied" : ["Tester(IsRectangularTable)"]},"CategoryCollections(IsPerm)" : {"type" : "GAP_Category","implied" : ["IsListOrCollecti\
on","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","Categor\
yCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeEle\
mentWithInverse)","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsFiniteOrderElement)","CategoryCollections(IsPerm\
)","IsGeneratorsOfMagmaWithInverses","Tester(IsGeneratorsOfMagmaWithInverses)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigr\
oup)","IsSubsetLocallyFiniteGroup","Tester(IsSubsetLocallyFiniteGroup)"]},"CategoryCollections(CategoryCollections(IsPerm))" : {"type\
" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCol\
lections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(CategoryColle\
ctions(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(\
IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","CategoryCollections\
(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsFiniteOrderElement))","CategoryCollections(Ca\
tegoryCollections(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)"]},"T\
ester(NrMovedPoints)" : {"type" : "GAP_Attribute","implied" : ["Tester(NrMovedPoints)"]},"Tester(MovedPoints)" : {"type" : "GAP_Attri\
bute","implied" : ["Tester(MovedPoints)"]},"Tester(SignPerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(SignPerm)"]},"Tester(C\
ycleStructurePerm)" : {"type" : "GAP_Attribute","implied" : ["Tester(CycleStructurePerm)"]},"IsPerm2Rep" : {"type" : "GAP_Representat\
ion","implied" : ["IsInternalRep","IsPerm2Rep"]},"IsPerm4Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsPerm4R\
ep"]},"CategoryCollections(IsTransformation)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElem\
ent","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsMultiplicativeE\
lement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)","CategoryCol\
lections(IsAssociativeElement)","CategoryCollections(IsTransformation)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]}\
,"CategoryCollections(CategoryCollections(IsTransformation))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollect\
ion","IsExtLElement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","\
CategoryCollections(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollection\
s(IsMultiplicativeElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(Category\
Collections(IsMultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollectio\
ns(CategoryCollections(IsTransformation))","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsTrans2Rep" : {"type" : "G\
AP_Representation","implied" : ["IsInternalRep","IsTrans2Rep"]},"IsTrans4Rep" : {"type" : "GAP_Representation","implied" : ["IsIntern\
alRep","IsTrans4Rep"]},"CategoryCollections(IsPartialPerm)" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollectio\
n","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollections(IsM\
ultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMultiplicativeElementWithInverse)\
","CategoryCollections(IsAssociativeElement)","CategoryCollections(IsPartialPerm)","IsGeneratorsOfSemigroup","Tester(IsGeneratorsOfSe\
migroup)","IsGeneratorsOfInverseSemigroup","Tester(IsGeneratorsOfInverseSemigroup)"]},"CategoryCollections(CategoryCollections(IsPart\
ialPerm))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtLElement","CategoryCollections(IsExtLEle\
ment)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollections(IsExtRElement)","CategoryCollec\
tions(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElement))","CategoryCollections(C\
ategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithInverse))","\
CategoryCollections(CategoryCollections(IsAssociativeElement))","CategoryCollections(CategoryCollections(IsPartialPerm))","IsGenerato\
rsOfSemigroup","Tester(IsGeneratorsOfSemigroup)"]},"IsPPerm2Rep" : {"type" : "GAP_Representation","implied" : ["IsInternalRep","IsPPe\
rm2Rep"]},"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"]},"IsInputT\
extStringRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputTextStringRep"]},"IsClosedStream" : {"typ\
e" : "GAP_Category","implied" : ["IsClosedStream"]},"IsStream" : {"type" : "GAP_Category","implied" : ["IsStream"]},"IsInputStream" :\
{"type" : "GAP_Category","implied" : ["IsStream","IsInputStream"]},"IsInputTextStream" : {"type" : "GAP_Category","implied" : ["IsSt\
ream","IsInputStream","IsInputTextStream"]},"IsInputTextNone" : {"type" : "GAP_Category","implied" : ["IsStream","IsInputStream","IsI\
nputTextStream","IsInputTextNone"]},"IsOutputStream" : {"type" : "GAP_Category","implied" : ["IsStream","IsOutputStream"]},"IsOutputT\
extStream" : {"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_Cate\
gory","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInv\
erse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj"]},"IsMatrixObj" : {"type" : "GAP_Category","implied" : ["I\
sCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElem\
ent","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse",\
"IsMatrixObj"]},"IsRowListMatrix" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNea\
rAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeEle\
ment","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix"]},"IsFlatMatrix" : {"type\
" : "GAP_Category","implied" : ["IsCopyable","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveE\
lementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","Is\
MultiplicativeElementWithInverse","IsMatrixObj","IsFlatMatrix"]},"IsGF2VectorRep" : {"type" : "GAP_Representation","implied" : ["IsCo\
pyable","IsDataObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse",\
"IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","IsGF2VectorRep"]},"IsGF2MatrixRep" : {"type" : "GAP_Representat\
ion","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNea\
rAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWi\
thOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","IsGF2MatrixRep"]},"Is8BitVectorRep" : {"type" : "GAP_Rep\
resentation","implied" : ["IsCopyable","IsDataObjectRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsN\
earAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsRowVectorObj","Is8BitVectorRep"]},"Is8BitMatrix\
Rep" : {"type" : "GAP_Representation","implied" : ["IsCopyable","IsPositionalObjectRep","IsExtAElement","IsNearAdditiveElement","IsNe\
arAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeEl\
ement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsMatrixObj","IsRowListMatrix","Is8BitMatrixRep"]},"IsI\
nfoClassListRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInfoClassListRep"]},"IsRandomSource" : {"ty\
pe" : "GAP_Category","implied" : ["IsComponentObjectRep","IsRandomSource"]},"IsGlobalRandomSource" : {"type" : "GAP_Category","implie\
d" : ["IsComponentObjectRep","IsRandomSource","IsGlobalRandomSource"]},"IsGAPRandomSource" : {"type" : "GAP_Category","implied" : ["I\
sComponentObjectRep","IsRandomSource","IsGAPRandomSource"]},"IsMersenneTwister" : {"type" : "GAP_Category","implied" : ["IsComponentO\
bjectRep","IsRandomSource","IsMersenneTwister"]},"IsFloat" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveEle\
ment","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMulti\
plicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat"]},\
"IsFloatInterval" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","IsNearAdditiveElement"\
,"IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplica\
tiveElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsFloa\
tInterval"]},"IsComplexFloat" : {"type" : "GAP_Category","implied" : ["IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementW\
ithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultipli\
cativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsComplexFloat"]},"IsComplexFl\
oatInterval" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","IsNearAdditiveElement","IsN\
earAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeE\
lement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsFloatInte\
rval","IsComplexFloat","IsComplexFloatInterval"]},"CategoryFamily(IsFloat)" : {"type" : "GAP_Category","implied" : ["IsFamily","Categ\
oryFamily((IsNearAdditiveElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsA\
dditiveElement) and IsMultiplicativeElement))","CategoryFamily(IsFloat)"]},"CategoryCollections(IsFloat)" : {"type" : "GAP_Category",\
"implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNearAddi\
tiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","CategoryC\
ollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtRElemen\
t)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(IsMulti\
plicativeElementWithInverse)","CategoryCollections(IsZDFRE)","CategoryCollections(IsCommutativeElement)","CategoryCollections(IsFloat\
)"]},"CategoryCollections(CategoryCollections(IsFloat))" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection",\
"IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(CategoryCollections(IsExtAElement))","CategoryCollections(C\
ategoryCollections(IsNearAdditiveElement))","CategoryCollections(CategoryCollections(IsNearAdditiveElementWithZero))","CategoryCollec\
tions(CategoryCollections(IsNearAdditiveElementWithInverse))","CategoryCollections(CategoryCollections(IsAdditiveElement))","IsExtLEl\
ement","CategoryCollections(IsExtLElement)","CategoryCollections(CategoryCollections(IsExtLElement))","IsExtRElement","CategoryCollec\
tions(IsExtRElement)","CategoryCollections(CategoryCollections(IsExtRElement))","CategoryCollections(CategoryCollections(IsMultiplica\
tiveElement))","CategoryCollections(CategoryCollections(IsMultiplicativeElementWithOne))","CategoryCollections(CategoryCollections(Is\
MultiplicativeElementWithInverse))","CategoryCollections(CategoryCollections(IsZDFRE))","CategoryCollections(CategoryCollections(IsCo\
mmutativeElement))","CategoryCollections(CategoryCollections(IsFloat))"]},"Tester(Cos)" : {"type" : "GAP_Attribute","implied" : ["Tes\
ter(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)"]},"Teste\
r(Sinh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Sinh)"]},"Tester(Tanh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Ta\
nh)"]},"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_Attribu\
te","implied" : ["Tester(Asinh)"]},"Tester(Acosh)" : {"type" : "GAP_Attribute","implied" : ["Tester(Acosh)"]},"Tester(Atanh)" : {"typ\
e" : "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(L\
og1p)"]},"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_Attri\
bute","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_Attrib\
ute","implied" : ["Tester(FrExp)"]},"Tester(Argument)" : {"type" : "GAP_Attribute","implied" : ["Tester(Argument)"]},"Tester(Absolute\
Value)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbsoluteValue)"]},"Tester(Frac)" : {"type" : "GAP_Attribute","implied" : ["T\
ester(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" : "G\
AP_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(AbsoluteD\
iameter)" : {"type" : "GAP_Attribute","implied" : ["Tester(AbsoluteDiameter)"]},"Tester(RelativeDiameter)" : {"type" : "GAP_Attribute\
","implied" : ["Tester(RelativeDiameter)"]},"Tester(IsPInfinity)" : {"type" : "GAP_Tester","implied" : ["Tester(IsPInfinity)"]},"Test\
er(IsNInfinity)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNInfinity)"]},"Tester(IsXInfinity)" : {"type" : "GAP_Tester","implie\
d" : ["Tester(IsXInfinity)"]},"Tester(IsNaN)" : {"type" : "GAP_Tester","implied" : ["Tester(IsNaN)"]},"IsIEEE754FloatRep" : {"type" :\
"GAP_Representation","implied" : ["<<unknown>>","IsInternalRep","IsExtAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZe\
ro","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement","IsExtRElement","IsMultiplicativeElement","IsMultiplicativ\
eElementWithOne","IsMultiplicativeElementWithInverse","IsZDFRE","IsCommutativeElement","IsFloat","IsIEEE754FloatRep"]},"IsDirectoryRe\
p" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsDirectoryRep"]},"IsInputTextFileRep" : {"type" : "GAP_Rep\
resentation","implied" : ["IsPositionalObjectRep","IsInputTextFileRep"]},"IsInputTextNoneRep" : {"type" : "GAP_Representation","impli\
ed" : ["IsPositionalObjectRep","IsInputTextNoneRep"]},"IsOutputTextStringRep" : {"type" : "GAP_Representation","implied" : ["IsPositi\
onalObjectRep","IsOutputTextStringRep"]},"IsOutputTextFileRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep",\
"IsOutputTextFileRep"]},"IsOutputTextNoneRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsOutputTextNone\
Rep"]},"IsInputOutputStreamByPtyRep" : {"type" : "GAP_Representation","implied" : ["IsPositionalObjectRep","IsInputOutputStreamByPtyR\
ep"]},"IsDirectProductElement" : {"type" : "GAP_Category","implied" : ["IsCopyable","IsList","IsDenseList","IsListOrCollection","IsEx\
tAElement","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElem\
ent","IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsDirectProduct\
Element"]},"CategoryFamily(IsDirectProductElement)" : {"type" : "GAP_Category","implied" : ["IsFamily","CategoryFamily((IsNearAdditiv\
eElementWithInverse and IsMultiplicativeElement))","CategoryFamily(((IsNearAdditiveElementWithInverse and IsAdditiveElement) and IsMu\
ltiplicativeElement))","CategoryFamily(IsDirectProductElement)"]},"CategoryCollections(IsDirectProductElement)" : {"type" : "GAP_Cate\
gory","implied" : ["IsListOrCollection","IsCollection","IsExtAElement","CategoryCollections(IsExtAElement)","CategoryCollections(IsNe\
arAdditiveElement)","CategoryCollections(IsNearAdditiveElementWithZero)","CategoryCollections(IsNearAdditiveElementWithInverse)","Cat\
egoryCollections(IsAdditiveElement)","IsExtLElement","CategoryCollections(IsExtLElement)","IsExtRElement","CategoryCollections(IsExtR\
Element)","CategoryCollections(IsMultiplicativeElement)","CategoryCollections(IsMultiplicativeElementWithOne)","CategoryCollections(I\
sMultiplicativeElementWithInverse)","CategoryCollections(IsDirectProductElement)"]},"Tester(ComponentsOfDirectProductElementsFamily)"\
: {"type" : "GAP_Attribute","implied" : ["Tester(ComponentsOfDirectProductElementsFamily)"]},"IsDefaultDirectProductElementRep" : {"\
type" : "GAP_Representation","implied" : ["IsCopyable","IsList","IsDenseList","IsPositionalObjectRep","IsListOrCollection","IsExtAEle\
ment","IsNearAdditiveElement","IsNearAdditiveElementWithZero","IsNearAdditiveElementWithInverse","IsAdditiveElement","IsExtLElement",\
"IsExtRElement","IsMultiplicativeElement","IsMultiplicativeElementWithOne","IsMultiplicativeElementWithInverse","IsDirectProductEleme\
nt","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" : "G\
AP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAddi\
tiveElement","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpDSum"]},"IsAssociativeAOpESum" : {"type" : "GAP_C\
ategory","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditive\
Element","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsAssociativeAOpESum"]},"IsTrivialAOpEZero" : {"type" : "GAP_Category\
","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsExtAElement","IsNearAdditiveElement\
","IsAdditiveElement","IsGeneralizedDomain","IsExtASet","IsTrivialAOpEZero"]},"Tester(GeneratorsOfExtASet)" : {"type" : "GAP_Attribut\
e","implied" : ["Tester(GeneratorsOfExtASet)"]},"Tester(AdditivelyActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(Add\
itivelyActingDomain)"]},"IsExtLSet" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Te\
ster(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet"]},"IsAssociativeLOpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrC\
ollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpDProd"]},"Is\
AssociativeLOpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicat\
eFree)","IsGeneralizedDomain","IsExtLSet","IsAssociativeLOpEProd"]},"IsDistributiveLOpDProd" : {"type" : "GAP_Category","implied" : [\
"IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpD\
Prod"]},"IsDistributiveLOpDSum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester\
(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpDSum"]},"IsDistributiveLOpEProd" : {"type" : "GAP_Category","i\
mplied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistr\
ibutiveLOpEProd"]},"IsDistributiveLOpESum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFr\
ee","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsDistributiveLOpESum"]},"IsTrivialLOpEOne" : {"type" : "GAP_Categor\
y","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","Is\
TrivialLOpEOne"]},"IsTrivialLOpEZero" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","\
Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsTrivialLOpEZero"]},"IsLeftActedOnByRing" : {"type" : "GAP_Category","im\
plied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtLSet","IsLeftAc\
tedOnByRing"]},"Tester(IsLeftActedOnByDivisionRing)" : {"type" : "GAP_Tester","implied" : ["Tester(IsLeftActedOnByDivisionRing)"]},"I\
sLeftActedOnBySuperset" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDupli\
cateFree)","IsGeneralizedDomain","IsExtLSet","IsLeftActedOnBySuperset"]},"Tester(GeneratorsOfExtLSet)" : {"type" : "GAP_Attribute","i\
mplied" : ["Tester(GeneratorsOfExtLSet)"]},"Tester(LeftActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(LeftActingDoma\
in)"]},"IsExtRSet" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateF\
ree)","IsGeneralizedDomain","IsExtRSet"]},"IsAssociativeROpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCol\
lection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsAssociativeROpDProd"]},"IsAssociativeROpEPr\
od" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGenera\
lizedDomain","IsExtRSet","IsAssociativeROpEProd"]},"IsDistributiveROpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollecti\
on","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpDProd"]},"IsDistri\
butiveROpDSum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)\
","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpDSum"]},"IsDistributiveROpEProd" : {"type" : "GAP_Category","implied" : ["IsLis\
tOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtRSet","IsDistributiveROpEProd"]\
},"IsDistributiveROpESum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDup\
licateFree)","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(IsDuplicat\
eFree)","IsGeneralizedDomain","IsExtRSet","IsTrivialROpEZero"]},"IsRightActedOnByRing" : {"type" : "GAP_Category","implied" : ["IsLis\
tOrCollection","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)","IsGenerali\
zedDomain","IsExtRSet","IsRightActedOnBySuperset"]},"Tester(GeneratorsOfExtRSet)" : {"type" : "GAP_Attribute","implied" : ["Tester(Ge\
neratorsOfExtRSet)"]},"Tester(RightActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(RightActingDomain)"]},"IsExtUSet" \
: {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralize\
dDomain","IsExtUSet"]},"IsAssociativeUOpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplica\
teFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsAssociativeUOpDProd"]},"IsAssociativeUOpEProd" : {"type" : "GA\
P_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExt\
USet","IsAssociativeUOpEProd"]},"IsDistributiveUOpDProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection",\
"IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpDProd"]},"IsDistributiveUOpDSum" : {"\
type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDom\
ain","IsExtUSet","IsDistributiveUOpDSum"]},"IsDistributiveUOpEProd" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsC\
ollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsDistributiveUOpEProd"]},"IsDistributiveUO\
pESum" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGen\
eralizedDomain","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)","IsGenerali\
zedDomain","IsExtUSet","IsTrivialUOpEZero"]},"IsUpperActedOnByGroup" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","Is\
Collection","IsDuplicateFree","Tester(IsDuplicateFree)","IsGeneralizedDomain","IsExtUSet","IsUpperActedOnByGroup"]},"IsUpperActedOnBy\
Superset" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDuplicateFree","Tester(IsDuplicateFree)","Is\
GeneralizedDomain","IsExtUSet","IsUpperActedOnBySuperset"]},"Tester(GeneratorsOfExtUSet)" : {"type" : "GAP_Attribute","implied" : ["T\
ester(GeneratorsOfExtUSet)"]},"Tester(UpperActingDomain)" : {"type" : "GAP_Attribute","implied" : ["Tester(UpperActingDomain)"]},"IsD\
ictionary" : {"type" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary"]},"IsLookupDictionary" : {"type\
" : "GAP_Category","implied" : ["IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary"]},"IsHash" : {"type" : "GAP_C\
ategory","implied" : ["IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsHash"]},"IsDictionaryDefaultRep" : {\
"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsDictionaryDef\
aultRep"]},"IsListDictionary" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection\
","IsDictionary","IsDictionaryDefaultRep","IsListDictionary"]},"IsListLookupDictionary" : {"type" : "GAP_Representation","implied" : \
["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDictionary","IsDictionaryDefaultRep","IsListDicti\
onary","IsListLookupDictionary"]},"IsSortDictionary" : {"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCo\
llection","IsCollection","IsDictionary","IsDictionaryDefaultRep","IsListDictionary","IsSortDictionary"]},"IsSortLookupDictionary" : {\
"type" : "GAP_Representation","implied" : ["IsComponentObjectRep","IsListOrCollection","IsCollection","IsDictionary","IsLookupDiction\
ary","IsDictionaryDefaultRep","IsListDictionary","IsListLookupDictionary","IsSortDictionary","IsSortLookupDictionary"]},"IsPositionDi\