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"Gap functions"
############################################################################### # Copyright (C) 2009, William Stein <wstein@gmail.com> # Copyright (C) 2012, Volker Braun <vbraun.name@gmail.com> # # Distributed under the terms of the GNU General Public License (GPL) # as published by the Free Software Foundation; either version 2 of # the License, or (at your option) any later version. # http://www.gnu.org/licenses/ ###############################################################################
# selected gap functions to use in tab completion 'AbelianGroup', 'AbelianInvariants', 'AbelianInvariantsMultiplier', 'AbelianInvariantsOfList', 'AbelianNumberField', 'AbsInt', 'AbsoluteValue', 'Action', 'ActionHomomorphism', 'Add', 'AddCoeffs', 'AddGenerator', 'AddRelator', 'AddRowVector', 'AddRule', 'AddSet', 'AdjointMatrix', 'Algebra', 'AlternatingGroup', 'AntiSymmetricParts', 'Append', 'AppendTo', 'Apply', 'AsGroup', 'Assert', 'AtlasGroup', 'AutomorphismGroup', 'BaseOfGroup', 'Basis', 'BasisVectors', 'Bell', 'Binomial', 'BlockMatrix', 'Blocks', 'CartanMatrix', 'CartanSubalgebra', 'Cartesian', 'Center', 'CentralCharacter', 'Centralizer', 'CentralizerInGLnZ', 'CentralizerModulo', 'Centre', 'CentreOfCharacter', 'Character', 'CharacterDegrees', 'CharacterNames', 'CharacterTable', 'Characteristic', 'CharacteristicPolynomial', 'CheckFixedPoints', 'ChevalleyBasis', 'ChiefNormalSeriesByPcgs', 'ChiefSeries', 'ChineseRem', 'Chomp', 'ClassElementLattice', 'ClassFunction', 'ClassFunctionSameType', 'ClassOrbit', 'ClassPermutation', 'ClassRoots', 'ClassesSolvableGroup', 'CoKernel', 'Coefficients', 'CoefficientsRing', 'CoeffsCyc', 'CoeffsMod', 'CollapsedMat', 'Collected', 'Combinations', 'CombinatorialCollector', 'CommutatorFactorGroup', 'CommutatorLength', 'CommutatorSubgroup', 'Compacted', 'CompanionMat', 'ComplexConjugate', 'ComplexificationQuat', 'CompositionMapping', 'CompositionMapping2', 'CompositionMaps', 'Concatenation', 'Conductor', 'ConjugacyClass', 'ConjugacyClassSubgroups', 'ConjugacyClasses', 'ConjugateGroup', 'ConjugateSubgroup', 'ConjugateSubgroups', 'ConstituentsCompositionMapping', 'ContainedMaps', 'ContinuedFractionApproximationOfRoot', 'ContinuedFractionExpansionOfRoot', 'ConvertToCharacterTable', 'ConvertToMatrixRep', 'ConvertToRangeRep', 'ConvertToStringRep', 'ConvertToTableOfMarks', 'ConvertToVectorRep', 'ConwayPolynomial', 'CosetTable', 'CosetTableInWholeGroup', 'Cycle', 'CycleLength', 'CycleLengths', 'CycleStructureClass', 'CycleStructurePerm', 'Cycles', 'CyclicGroup', 'CyclotomicField', 'CyclotomicPolynomial', 'Cyclotomics', 'DefiningPolynomial', 'Degree', 'DegreeFFE', 'DenominatorCyc', 'DenominatorOfRationalFunction', 'DenominatorRat', 'Derivations', 'Derivative', 'DerivedLength', 'DerivedSeries', 'DerivedSeriesOfGroup', 'DerivedSubgroup', 'Determinant', 'DeterminantIntMat', 'DeterminantMat', 'DeterminantMatDivFree', 'DeterminantOfCharacter', 'DiagonalMat', 'DihedralGroup', 'Dimension', 'DimensionOfMatrixGroup', 'DimensionsMat', 'DirectProduct', 'Discriminant', 'Display', 'DivisorsInt', 'DnLattice', 'DominantCharacter', 'DominantWeights', 'DoubleCoset', 'DoubleCosetRepsAndSizes', 'DoubleCosets', 'DoubleHashArraySize', 'DuplicateFreeList', 'E', 'Eigenspaces', 'Eigenvalues', 'Eigenvectors', 'ElementOfFpGroup', 'ElementOfFpSemigroup', 'ElementOrdersPowerMap', 'Elements', 'ElementsStabChain', 'EpimorphismFromFreeGroup', 'EpimorphismNilpotentQuotient', 'EpimorphismPGroup', 'EpimorphismQuotientSystem', 'EpimorphismSchurCover', 'EuclideanQuotient', 'EuclideanRemainder', 'EulerianFunction', 'Exponent', 'Extension', 'ExteriorCentre', 'ExteriorPower', 'Extract', 'FactorGroup', 'Factorial', 'Factorization', 'Factors', 'FactorsInt', 'Fibonacci', 'Field', 'FieldExtension', 'FieldOfMatrixGroup', 'Filtered', 'First', 'FittingSubgroup', 'Flat', 'ForAll', 'ForAny', 'FreeGroup', 'FreeProduct', 'FreeSemigroup', 'FrobeniusAutomorphism', 'FullRowSpace', 'GF', 'GL', 'GQuotients', 'GaloisCyc', 'GaloisField', 'GaloisGroup', 'GaloisMat', 'GaloisStabilizer', 'GaussianIntegers', 'GaussianRationals', 'Gcd', 'GcdInt', 'GcdOp', 'GeneralLinearGroup', 'GeneralOrthogonalGroup', 'GeneralUnitaryGroup', 'GeneralisedEigenspaces', 'GeneralisedEigenvalues', 'GeneralizedEigenspaces', 'GeneralizedEigenvalues', 'GeneratorsOfField', 'GeneratorsOfGroup', 'GeneratorsOfIdeal', 'GlobalMersenneTwister', 'GroebnerBasis', 'Group', 'GroupHomomorphismByFunction', 'GroupHomomorphismByImages', 'GroupRing', 'HermiteNormalFormIntegerMat', 'HermiteNormalFormIntegerMatTransform', 'Hom', 'IdGroup', 'Ideal', 'IdealByGenerators', 'Idempotents', 'Identifier', 'Identity', 'Image', 'Images', 'Index', 'InfoAlgebra', 'InfoAttributes', 'InfoBckt', 'InfoCharacterTable', 'InfoCoh', 'InfoComplement', 'InfoCoset', 'InfoFpGroup', 'InfoGroebner', 'InfoGroup', 'InfoLattice', 'InfoLevel', 'InfoMatrix', 'InfoMonomial', 'InfoNumtheor', 'InfoOptions', 'InfoPcSubgroup', 'InfoText', 'InnerAutomorphism', 'InnerAutomorphismsAutomorphismGroup', 'Int', 'IntFFE', 'IntFFESymm', 'IntHexString', 'IntScalarProducts', 'IntVecFFE', 'Integers', 'IntersectSet', 'Intersection', 'InvariantBilinearForm', 'InvariantElementaryAbelianSeries', 'InvariantLattice', 'InvariantQuadraticForm', 'InvariantSesquilinearForm', 'Inverse', 'InverseMap', 'Irr', 'IrrBaumClausen', 'IrrConlon', 'IrrDixonSchneider', 'IrreducibleModules', 'IrreducibleRepresentations', 'IrreducibleRepresentationsDixon', 'IsAbelian', 'IsAbelianNumberField', 'IsAbelianNumberFieldPolynomialRing', 'IsAdditiveElement', 'IsAdditiveElementWithInverse', 'IsAdditiveElementWithZero', 'IsAdditiveGroup', 'IsAdditiveGroupGeneralMapping', 'IsAdditiveGroupHomomorphism', 'IsAdditivelyCommutative', 'IsAdditivelyCommutativeElement', 'IsAlgebra', 'IsAlgebraGeneralMapping', 'IsAlgebraHomomorphism', 'IsAlgebraModule', 'IsAlgebraWithOne', 'IsAlgebraWithOneHomomorphism', 'IsAlgebraicElement', 'IsAlgebraicExtension', 'IsAlternatingGroup', 'IsAnticommutative', 'IsAntisymmetricBinaryRelation', 'IsAssocWord', 'IsAssocWordWithInverse', 'IsAssocWordWithOne', 'IsAssociated', 'IsAssociative', 'IsAutomorphismGroup', 'IsBasis', 'IsBijective', 'IsBinaryRelation', 'IsBlockMatrixRep', 'IsBool', 'IsBound', 'IsBoundGlobal', 'IsBrauerTable', 'IsBravaisGroup', 'IsBuiltFromGroup', 'IsBuiltFromSemigroup', 'IsCanonicalBasis', 'IsCanonicalBasisFullMatrixModule', 'IsCanonicalBasisFullRowModule', 'IsCanonicalNiceMonomorphism', 'IsCentral', 'IsCentralFactor', 'IsChar', 'IsCharacter', 'IsCharacterTable', 'IsCharacterTableInProgress', 'IsCharacteristicSubgroup', 'IsClosedStream', 'IsCochain', 'IsCochainCollection', 'IsCommutative', 'IsComponentObjectRep', 'IsCompositionMappingRep', 'IsConfluent', 'IsConjugate', 'IsCopyable', 'IsCyc', 'IsCyclic', 'IsCyclotomic', 'IsCyclotomicField', 'IsCyclotomicMatrixGroup', 'IsDenseList', 'IsDiagonalMat', 'IsDictionary', 'IsDigitChar', 'IsDivisionRing', 'IsDomain', 'IsDoneIterator', 'IsDoubleCoset', 'IsDuplicateFree', 'IsDuplicateFreeList', 'IsElementaryAbelian', 'IsEmpty', 'IsEmptyString', 'IsEuclideanRing', 'IsFFE', 'IsField', 'IsFinite', 'IsFiniteDimensional', 'IsFinitelyGeneratedGroup', 'IsFixedStabilizer', 'IsFpGroup', 'IsFpMonoid', 'IsFpSemigroup', 'IsFreeGroup', 'IsFreeLeftModule', 'IsFullHomModule', 'IsFullMatrixModule', 'IsFullRowModule', 'IsFunction', 'IsGL', 'IsGaussInt', 'IsGaussRat', 'IsGaussianIntegers', 'IsGaussianRationals', 'IsGaussianSpace', 'IsGeneralLinearGroup', 'IsGroup', 'IsGroupHomomorphism', 'IsGroupOfAutomorphisms', 'IsGroupRing', 'IsHasseDiagram', 'IsHomogeneousList', 'IsIdempotent', 'IsInfinity', 'IsInjective', 'IsInnerAutomorphism', 'IsInt', 'IsIntegerMatrixGroup', 'IsIntegers', 'IsIntegralBasis', 'IsIntegralCyclotomic', 'IsIntegralRing', 'IsIrreducible', 'IsIrreducibleCharacter', 'IsIrreducibleRingElement', 'IsIterator', 'IsJacobianRing', 'IsLaurentPolynomial', 'IsLaurentPolynomialDefaultRep', 'IsLexicographicallyLess', 'IsLieAbelian', 'IsLieAlgebra', 'IsLieMatrix', 'IsLieObject', 'IsLieObjectCollection', 'IsLieSolvable', 'IsLinearMapping', 'IsLinearMappingsModule', 'IsList', 'IsMapping', 'IsMatchingSublist', 'IsMatrix', 'IsMatrixGroup', 'IsMatrixModule', 'IsMatrixSpace', 'IsMonomial', 'IsMonomialGroup', 'IsMonomialMatrix', 'IsMonomialOrdering', 'IsMultiplicativeZero', 'IsMutable', 'IsMutableBasis', 'IsNilpotent', 'IsNilpotentElement', 'IsNilpotentGroup', 'IsNormal', 'IsNormalBasis', 'IsNotIdenticalObj', 'IsNumberField', 'IsObject', 'IsOddInt', 'IsOne', 'IsOrdering', 'IsOrdinaryMatrix', 'IsOrdinaryTable', 'IsPGroup', 'IsPSolvable', 'IsPcGroup', 'IsPcgs', 'IsPerfect', 'IsPerfectGroup', 'IsPerm', 'IsPermGroup', 'IsPolycyclicGroup', 'IsPolynomial', 'IsPolynomialRing', 'IsPosInt', 'IsPosRat', 'IsPositiveIntegers', 'IsPrime', 'IsPrimeField', 'IsPrimeInt', 'IsPrimePowerInt', 'IsPrimitive', 'IsPrimitiveCharacter', 'IsPrimitivePolynomial', 'IsProbablyPrimeInt', 'IsPurePadicNumber', 'IsQuaternion', 'IsQuickPositionList', 'IsQuotientSemigroup', 'IsRandomSource', 'IsRange', 'IsRat', 'IsRationalFunction', 'IsRationalMatrixGroup', 'IsRationals', 'IsRecord', 'IsReduced', 'IsReductionOrdering', 'IsReflexiveBinaryRelation', 'IsRegular', 'IsRegularSemigroup', 'IsRegularSemigroupElement', 'IsRing', 'IsRingElement', 'IsRingGeneralMapping', 'IsRingWithOne', 'IsRingWithOneGeneralMapping', 'IsRingWithOneHomomorphism', 'IsRowModule', 'IsRowSpace', 'IsRowVector', 'IsSL', 'IsSSortedList', 'IsScalar', 'IsSet', 'IsSimple', 'IsSimpleAlgebra', 'IsSimpleGroup', 'IsSimpleSemigroup', 'IsSingleValued', 'IsSolvable', 'IsSolvableGroup', 'IsSortedList', 'IsSpecialLinearGroup', 'IsSporadicSimple', 'IsStandardIterator', 'IsString', 'IsStringRep', 'IsSubgroup', 'IsSubgroupFpGroup', 'IsSubgroupOfWholeGroupByQuotientRep', 'IsSubgroupSL', 'IsSubset', 'IsSubsetSet', 'IsSubspace', 'IsSupersolvable', 'IsSupersolvableGroup', 'IsSurjective', 'IsSymmetricGroup', 'IsTable', 'IsTotal', 'IsTotalOrdering', 'IsTransformation', 'IsTransitive', 'IsTransitiveBinaryRelation', 'IsTrivial', 'IsTuple', 'IsUniqueFactorizationRing', 'IsUnit', 'IsUnivariatePolynomial', 'IsUnivariatePolynomialRing', 'IsUnivariateRationalFunction', 'IsUpperAlphaChar', 'IsUpperTriangularMat', 'IsValidIdentifier', 'IsVector', 'IsVectorSpace', 'IsVirtualCharacter', 'IsWeylGroup', 'IsWord', 'IsZero', 'IsZeroGroup', 'IsZeroSimpleSemigroup', 'IsZeroSquaredRing', 'IsZmodnZObj', 'IsZmodnZObjNonprime', 'IsZmodpZObj', 'IsZmodpZObjLarge', 'IsZmodpZObjSmall', 'IsomorphicSubgroups', 'IsomorphismFpAlgebra', 'IsomorphismFpGroup', 'IsomorphismFpGroupByGenerators', 'IsomorphismFpGroupByPcgs', 'IsomorphismFpSemigroup', 'IsomorphismGroups', 'IsomorphismMatrixAlgebra', 'IsomorphismPcGroup', 'IsomorphismPermGroup', 'IsomorphismPermGroupImfGroup', 'IsomorphismReesMatrixSemigroup', 'IsomorphismRefinedPcGroup', 'IsomorphismSimplifiedFpGroup', 'IsomorphismSpecialPcGroup', 'IsomorphismTransformationSemigroup', 'IsomorphismTypeInfoFiniteSimpleGroup', 'Iterated', 'Iterator', 'IteratorByBasis', 'IteratorByFunctions', 'IteratorList', 'IteratorSorted', 'Jacobi', 'JenningsLieAlgebra', 'JenningsSeries', 'JordanDecomposition', 'Kernel', 'KernelOfAdditiveGeneralMapping', 'KernelOfCharacter', 'KernelOfMultiplicativeGeneralMapping', 'KernelOfTransformation', 'KillingMatrix', 'KnuthBendixRewritingSystem', 'KroneckerProduct', 'KuKGenerators', 'LLL', 'LLLReducedBasis', 'LLLReducedGramMat', 'Lambda', 'LargestElementGroup', 'LargestElementStabChain', 'LargestMovedPoint', 'LastSystemError', 'LatticeByCyclicExtension', 'LatticeSubgroups', 'Lcm', 'LcmInt', 'LcmOp', 'LeadingCoefficient', 'LeadingCoefficientOfPolynomial', 'LeadingExponentOfPcElement', 'LeadingMonomial', 'LeadingMonomialOfPolynomial', 'LeadingTermOfPolynomial', 'Legendre', 'Length', 'LenstraBase', 'LessThanFunction', 'LessThanOrEqualFunction', 'LetterRepAssocWord', 'LevelsOfGenerators', 'LeviMalcevDecomposition', 'LexicographicOrdering', 'LieAlgebra', 'LieAlgebraByStructureConstants', 'LieBracket', 'LieCenter', 'LieCentralizer', 'LieCentre', 'LieCoboundaryOperator', 'LieDerivedSeries', 'LieDerivedSubalgebra', 'LieLowerCentralSeries', 'LieNilRadical', 'LieNormalizer', 'LieObject', 'LieSolvableRadical', 'LieUpperCentralSeries', 'LiftedInducedPcgs', 'LiftedPcElement', 'LinearAction', 'LinearActionLayer', 'LinearCharacters', 'LinearCombination', 'LinearCombinationPcgs', 'LinearIndependentColumns', 'LinearOperation', 'LinearOperationLayer', 'LinesOfStraightLineProgram', 'List', 'ListN', 'ListPerm', 'ListStabChain', 'ListWithIdenticalEntries', 'ListX', 'LoadDynamicModule', 'LoadPackage', 'Log', 'LogFFE', 'LogInt', 'LogMod', 'LogModShanks', 'LogTo', 'LongestWeylWordPerm', 'LookupDictionary', 'LowIndexSubgroupsFpGroup', 'LowIndexSubgroupsFpGroupIterator', 'LowerCentralSeries', 'LowerCentralSeriesOfGroup', 'LowercaseString', 'Lucas', 'MakeConfluent', 'MakeImmutable', 'MakeReadOnlyGlobal', 'MakeReadWriteGlobal', 'MappedWord', 'MappingByFunction', 'MappingPermListList', 'MatAlgebra', 'MatClassMultCoeffsCharTable', 'MatLieAlgebra', 'MatScalarProducts', 'MathieuGroup', 'MatrixAlgebra', 'MatrixAutomorphisms', 'MatrixByBlockMatrix', 'MatrixLieAlgebra', 'MatrixOfAction', 'MaximalAbelianQuotient', 'MaximalBlocks', 'MaximalNormalSubgroups', 'MaximalSubgroupClassReps', 'MaximalSubgroups', 'MaximalSubgroupsLattice', 'Maximum', 'MaximumList', 'MeetEquivalenceRelations', 'MeetMaps', 'MinimalElementCosetStabChain', 'MinimalGeneratingSet', 'MinimalNonmonomialGroup', 'MinimalNormalSubgroups', 'MinimalPolynomial', 'MinimalStabChain', 'MinimalSupergroupsLattice', 'MinimizedBombieriNorm', 'Minimum', 'MinimumList', 'MinusCharacter', 'ModuleByRestriction', 'ModuleOfExtension', 'ModuloPcgs', 'MoebiusMu', 'MolienSeries', 'MolienSeriesInfo', 'MolienSeriesWithGivenDenominator', 'Monoid', 'MonoidByGenerators', 'MonoidByMultiplicationTable', 'MonoidOfRewritingSystem', 'MonomialComparisonFunction', 'MonomialExtGrlexLess', 'MonomialExtrepComparisonFun', 'MonomialGrevlexOrdering', 'MonomialGrlexOrdering', 'MonomialLexOrdering', 'MonomialTotalDegreeLess', 'MostFrequentGeneratorFpGroup', 'MovedPoints', 'MultRowVector', 'MultiplicationTable', 'MultiplicativeNeutralElement', 'MultiplicativeZero', 'MultiplicativeZeroOp', 'NF', 'NK', 'NameFunction', 'NaturalCharacter', 'NaturalHomomorphismByGenerators', 'NaturalHomomorphismByIdeal', 'NaturalHomomorphismByNormalSubgroup', 'NaturalHomomorphismBySubAlgebraModule', 'NaturalHomomorphismBySubspace', 'NearAdditiveGroup', 'NearAdditiveGroupByGenerators', 'NegativeRootVectors', 'NegativeRoots', 'NextIterator', 'NextPrimeInt', 'NiceBasis', 'NiceBasisFiltersInfo', 'NiceFreeLeftModule', 'NiceFreeLeftModuleInfo', 'NiceMonomorphism', 'NiceMonomorphismAutomGroup', 'NiceObject', 'NiceVector', 'NilpotencyClassOfGroup', 'NonabelianExteriorSquare', 'Norm', 'NormalBase', 'NormalClosure', 'NormalFormIntMat', 'NormalIntersection', 'NormalSeriesByPcgs', 'NormalSubgroups', 'NormalizeWhitespace', 'NormalizedWhitespace', 'Normalizer', 'NormalizerInGLnZ', 'NormalizerInGLnZBravaisGroup', 'NormedRowVector', 'NrArrangements', 'NrBasisVectors', 'NrCombinations', 'NrConjugacyClasses', 'NrConjugacyClassesGL', 'NrConjugacyClassesGU', 'NrConjugacyClassesPGL', 'NrConjugacyClassesPGU', 'NrConjugacyClassesPSL', 'NrConjugacyClassesPSU', 'NrConjugacyClassesSL', 'NrConjugacyClassesSLIsogeneous', 'NrConjugacyClassesSU', 'NrConjugacyClassesSUIsogeneous', 'NrDerangements', 'NrInputsOfStraightLineProgram', 'NrMovedPoints', 'NrOrderedPartitions', 'NrPartitionTuples', 'NrPartitions', 'NrPartitionsSet', 'NrPermutationsList', 'NrPolyhedralSubgroups', 'NrRestrictedPartitions', 'NrTuples', 'NrUnorderedTuples', 'NullAlgebra', 'NullMat', 'NullspaceIntMat', 'NullspaceMat', 'NullspaceMatDestructive', 'NullspaceModQ', 'Number', 'NumberArgumentsFunction', 'NumberFFVector', 'NumberPerfectGroups', 'NumberPerfectLibraryGroups', 'NumberSmallGroups', 'NumberSyllables', 'NumeratorOfModuloPcgs', 'NumeratorOfRationalFunction', 'NumeratorRat', 'Objectify', 'ObjectifyWithAttributes', 'OctaveAlgebra', 'OldGeneratorsOfPresentation', 'Omega', 'OnBreak', 'OnBreakMessage', 'OnIndeterminates', 'OnLeftInverse', 'OnLines', 'OnPairs', 'OnPoints', 'OnRight', 'OnSets', 'OnSetsDisjointSets', 'OnSetsSets', 'OnSetsTuples', 'OnSubspacesByCanonicalBasis', 'OnTuples', 'OnTuplesSets', 'OnTuplesTuples', 'One', 'OneAttr', 'OneCoboundaries', 'OneCocycles', 'OneFactorBound', 'OneImmutable', 'OneMutable', 'OneOfPcgs', 'OneOp', 'OneSM', 'OneSameMutability', 'OperationAlgebraHomomorphism', 'Orbit', 'OrbitFusions', 'OrbitLength', 'OrbitLengths', 'OrbitLengthsDomain', 'OrbitPerms', 'OrbitPowerMaps', 'OrbitStabChain', 'OrbitStabilizer', 'OrbitStabilizerAlgorithm', 'Orbits', 'OrbitsDomain', 'OrbitsPerms', 'Order', 'OrderMod', 'OrderingOnGenerators', 'Ordinal', 'OrdinaryCharacterTable', 'OrthogonalComponents', 'OrthogonalEmbeddings', 'OrthogonalEmbeddingsSpecialDimension', 'PCentralLieAlgebra', 'PCentralNormalSeriesByPcgsPGroup', 'PCentralSeries', 'PClassPGroup', 'PCore', 'PGL', 'PGU', 'POW', 'PQuotient', 'PROD', 'PSL', 'PSP', 'PSU', 'PSp', 'PadicCoefficients', 'PadicNumber', 'PadicValuation', 'Parametrized', 'Parent', 'ParentPcgs', 'PartialFactorization', 'PartialOrderByOrderingFunction', 'PartialOrderOfHasseDiagram', 'Partition', 'PartitionTuples', 'Partitions', 'PartitionsGreatestEQ', 'PartitionsGreatestLE', 'PartitionsSet', 'PcGroupCode', 'PcGroupCodeRec', 'PcGroupFpGroup', 'PcGroupWithPcgs', 'PcSeries', 'Pcgs', 'PcgsCentralSeries', 'PcgsChiefSeries', 'PcgsElementaryAbelianSeries', 'PcgsPCentralSeriesPGroup', 'Pcgs_OrbitStabilizer', 'PerfectGroup', 'PerfectIdentification', 'PerfectResiduum', 'Perform', 'PermBounds', 'PermCharInfo', 'PermCharInfoRelative', 'PermChars', 'PermComb', 'PermLeftQuoTransformation', 'PermList', 'PermListList', 'Permanent', 'Permutation', 'PermutationCharacter', 'PermutationCycle', 'PermutationCycleOp', 'PermutationGModule', 'PermutationMat', 'PermutationsList', 'Permuted', 'Phi', 'PolynomialByExtRep', 'PolynomialCoefficientsOfPolynomial', 'PolynomialDivisionAlgorithm', 'PolynomialModP', 'PolynomialReducedRemainder', 'PolynomialReduction', 'PolynomialRing', 'PopOptions', 'Position', 'PositionBound', 'PositionCanonical', 'PositionFirstComponent', 'PositionNonZero', 'PositionNot', 'PositionNthOccurrence', 'PositionProperty', 'PositionSet', 'PositionSorted', 'PositionStream', 'PositionSublist', 'PositionWord', 'PositionsOp', 'PositiveRoots', 'PossibleClassFusions', 'PossiblePowerMaps', 'PowerMap', 'PowerMapOp', 'PowerModCoeffs', 'PowerModInt', 'PowerPartition', 'PreImage', 'PreImageElm', 'PreImages', 'PreImagesElm', 'PreImagesRange', 'PreImagesRepresentative', 'PreImagesSet', 'PrefrattiniSubgroup', 'PreimagesOfTransformation', 'PresentationFpGroup', 'PresentationNormalClosure', 'PresentationNormalClosureRrs', 'PresentationSubgroup', 'PresentationSubgroupMtc', 'PresentationSubgroupRrs', 'PresentationViaCosetTable', 'PrevPrimeInt', 'PrimaryGeneratorWords', 'PrimeBlocks', 'PrimeBlocksOp', 'PrimeField', 'PrimePGroup', 'PrimePowersInt', 'PrimeResidues', 'Primes', 'PrimitiveElement', 'PrimitiveGroup', 'PrimitiveIdentification', 'PrimitivePolynomial', 'PrimitiveRoot', 'PrimitiveRootMod', 'Print', 'PrintAmbiguity', 'PrintArray', 'PrintCharacterTable', 'PrintFactorsInt', 'PrintFormattingStatus', 'PrintHashWithNames', 'PrintObj', 'PrintTo', 'Process', 'Product', 'ProductCoeffs', 'ProductSpace', 'ProductX', 'ProjectedInducedPcgs', 'ProjectedPcElement', 'Projection', 'ProjectionMap', 'ProjectiveActionHomomorphismMatrixGroup', 'ProjectiveActionOnFullSpace', 'ProjectiveGeneralLinearGroup', 'ProjectiveGeneralUnitaryGroup', 'ProjectiveOrder', 'ProjectiveSpecialLinearGroup', 'ProjectiveSpecialUnitaryGroup', 'ProjectiveSymplecticGroup', 'PseudoRandom', 'PthPowerImage', 'PthPowerImages', 'PushOptions', 'QUO', 'Quadratic', 'QuaternionAlgebra', 'QuoInt', 'QuotRemLaurpols', 'Quotient', 'QuotientMod', 'QuotientPolynomialsExtRep', 'QuotientRemainder', 'READ', 'RadicalGroup', 'RadicalOfAlgebra', 'Random', 'RandomBinaryRelationOnPoints', 'RandomHashKey', 'RandomInvertibleMat', 'RandomIsomorphismTest', 'RandomList', 'RandomMat', 'RandomPrimitivePolynomial', 'RandomSource', 'RandomTransformation', 'RandomUnimodularMat', 'Range', 'Rank', 'RankAction', 'RankFilter', 'RankMat', 'RankOfTransformation', 'RankPGroup', 'Rat', 'RationalClass', 'RationalClasses', 'RationalizedMat', 'Rationals', 'Read', 'ReadAll', 'ReadAllLine', 'ReadAsFunction', 'ReadByte', 'ReadLine', 'ReadPackage', 'ReadPkg', 'ReadTest', 'RealClasses', 'RealPart', 'RealizableBrauerCharacters', 'RecFields', 'RecNames', 'RedispatchOnCondition', 'ReduceCoeffs', 'ReduceCoeffsMod', 'ReduceRules', 'ReduceStabChain', 'Reduced', 'ReducedAdditiveInverse', 'ReducedCharacters', 'ReducedClassFunctions', 'ReducedComm', 'ReducedConfluentRewritingSystem', 'ReducedConjugate', 'ReducedDifference', 'ReducedForm', 'ReducedGroebnerBasis', 'ReducedInverse', 'ReducedLeftQuotient', 'ReducedOne', 'ReducedPcElement', 'ReducedPower', 'ReducedProduct', 'ReducedQuotient', 'ReducedScalarProduct', 'ReducedSum', 'ReducedZero', 'Ree', 'ReeGroup', 'ReesCongruenceOfSemigroupIdeal', 'ReesMatrixSemigroup', 'ReesMatrixSemigroupElement', 'ReesZeroMatrixSemigroup', 'ReesZeroMatrixSemigroupElement', 'ReesZeroMatrixSemigroupElementIsZero', 'RefinedPcGroup', 'RegularActionHomomorphism', 'RegularModule', 'RelationsOfFpSemigroup', 'RelativeBasis', 'RelativeOrders', 'RelatorsOfFpGroup', 'RemInt', 'Remove', 'RemoveCharacters', 'RemoveFile', 'RemoveOuterCoeffs', 'RemoveRelator', 'RemoveSet', 'RemoveStabChain', 'ReplacedString', 'Representative', 'RepresentativeAction', 'RepresentativeLinearOperation', 'RepresentativeSmallest', 'RepresentativesContainedRightCosets', 'RepresentativesFusions', 'RepresentativesMinimalBlocks', 'RepresentativesPerfectSubgroups', 'RepresentativesPowerMaps', 'RepresentativesSimpleSubgroups', 'Reread', 'RereadPackage', 'Reset', 'RestoreStateRandom', 'RestrictOutputsOfSLP', 'Restricted', 'RestrictedClassFunction', 'RestrictedClassFunctions', 'RestrictedMapping', 'RestrictedPartitions', 'RestrictedPerm', 'RestrictedTransformation', 'ResultOfStraightLineProgram', 'Resultant', 'Reversed', 'RewriteWord', 'RightCoset', 'RightCosets', 'RightDerivations', 'Ring', 'RingWithOne', 'Root', 'RootInt', 'RootMod', 'RootOfDefiningPolynomial', 'RootSystem', 'RootsMod', 'RoundCyc', 'Rules', 'SL', 'SO', 'SP', 'SQ', 'SSortedList', 'SU', 'SameBlock', 'SandwichMatrixOfReesMatrixSemigroup', 'SandwichMatrixOfReesZeroMatrixSemigroup', 'SaveWorkspace', 'ScalarProduct', 'SchurCover', 'SemiSimpleType', 'SemidirectProduct', 'Semigroup', 'Set', 'SetAssertionLevel', 'SetCommutator', 'SetConjugate', 'SetCrystGroupDefaultAction', 'SetEntrySCTable', 'SetFilterObj', 'SetHashEntry', 'SetHashEntryAtLastIndex', 'SetHelpViewer', 'SetIndeterminateName', 'SetInfoLevel', 'SetName', 'SetParent', 'SetPower', 'ShallowCopy', 'ShiftedCoeffs', 'ShiftedPadicNumber', 'ShortLexOrdering', 'ShortestVectors', 'Sigma', 'SignInt', 'SignPartition', 'SignPerm', 'SimpleLieAlgebra', 'SimpleSystem', 'SimplifiedFpGroup', 'SimplifyPresentation', 'SimultaneousEigenvalues', 'SingleCollector', 'Size', 'SizeConsiderFunction', 'SizeNumbersPerfectGroups', 'SizeOfFieldOfDefinition', 'SizeScreen', 'SizeStabChain', 'SizesCentralizers', 'SizesConjugacyClasses', 'SizesPerfectGroups', 'SmallGeneratingSet', 'SmallGroup', 'SmallerDegreePermutationRepresentation', 'SmallestGeneratorPerm', 'SmallestMovedPoint', 'SmallestRootInt', 'SmithNormalFormIntegerMat', 'Socle', 'SocleTypePrimitiveGroup', 'SolutionIntMat', 'SolutionMat', 'SolutionMatDestructive', 'SolutionNullspaceIntMat', 'Sort', 'SortParallel', 'SortedCharacterTable', 'SortedCharacters', 'SortedList', 'SortedSparseActionHomomorphism', 'SortingPerm', 'Sp', 'SparseActionHomomorphism', 'SparseCartanMatrix', 'SparseHashTable', 'SparseIntKey', 'SpecialLinearGroup', 'SpecialOrthogonalGroup', 'SpecialPcgs', 'SpecialUnitaryGroup', 'SplitCharacters', 'SplitExtension', 'SplitString', 'SplittingField', 'Sqrt', 'SquareRoots', 'StabChain', 'StabChainBaseStrongGenerators', 'StabChainImmutable', 'StabChainMutable', 'StabChainOp', 'StabChainOptions', 'Stabilizer', 'StabilizerOfExternalSet', 'StabilizerPcgs', 'StandardAssociate', 'StandardGeneratorsInfo', 'StandardizeTable', 'StarCyc', 'Stirling1', 'Stirling2', 'StratMeetPartition', 'StretchImportantSLPElement', 'String', 'StringDate', 'StringOfResultOfStraightLineProgram', 'StringPP', 'StringTime', 'StructuralCopy', 'StructureConstantsTable', 'StructureDescription', 'SubAlgebraModule', 'Subalgebra', 'SubdirectProduct', 'SubdirectProducts', 'Subfield', 'Subfields', 'Subgroup', 'SubgroupByPcgs', 'SubgroupByProperty', 'SubgroupOfWholeGroupByCosetTable', 'SubgroupOfWholeGroupByQuotientSubgroup', 'SubgroupProperty', 'SubgroupShell', 'SubgroupsSolvableGroup', 'Submodule', 'Submonoid', 'SubnearAdditiveGroup', 'SubnormalSeries', 'Subring', 'SubringWithOne', 'Subsemigroup', 'Subspace', 'Subspaces', 'SubstitutedWord', 'SubtractSet', 'Subword', 'Successors', 'Sum', 'SumFactorizationFunctionPcgs', 'SumIntersectionMat', 'SumX', 'SupersolvableResiduum', 'SupportedCharacterTableInfo', 'SurjectiveActionHomomorphismAttr', 'SuzukiGroup', 'SylowComplement', 'SylowSubgroup', 'SylowSystem', 'SymmetricClosureBinaryRelation', 'SymmetricGroup', 'SymmetricParentGroup', 'SymmetricParts', 'SymmetricPower', 'SymmetricPowerOfAlgebraModule', 'Symmetrizations', 'SymplecticComponents', 'SymplecticGroup', 'TableAutomorphisms', 'TableOfMarks', 'TableOfMarksByLattice', 'TableOfMarksComponents', 'TableOfMarksCyclic', 'TableOfMarksDihedral', 'TableOfMarksFrobenius', 'Tau', 'TensorProduct', 'TensorProductGModule', 'TensorProductOfAlgebraModules', 'Tensored', 'TietzeWordAbstractWord', 'Trace', 'TraceImmediateMethods', 'TraceMat', 'TraceMethods', 'TracePolynomial', 'TracedCosetFpGroup', 'TransferDiagram', 'Transformation', 'TransformationData', 'TransformationRelation', 'TransformationType', 'TransformingPermutations', 'TransformingPermutationsCharacterTables', 'TransitiveClosureBinaryRelation', 'TransitiveIdentification', 'Transitivity', 'TranslatorSubalgebra', 'TransposedMat', 'TransposedMatAttr', 'TransposedMatDestructive', 'TransposedMatImmutable', 'TransposedMatMutable', 'TransposedMatOp', 'TransposedMatrixGroup', 'TriangulizeIntegerMat', 'TriangulizeMat', 'TriangulizedIntegerMat', 'TriangulizedIntegerMatTransform', 'TriangulizedNullspaceMat', 'TriangulizedNullspaceMatDestructive', 'TrivialCharacter', 'TrivialGroup', 'TrivialIterator', 'TrivialSubalgebra', 'TrivialSubgroup', 'TrivialSubmagmaWithOne', 'TrivialSubmodule', 'TrivialSubmonoid', 'TrivialSubspace', 'Tuple', 'Tuples', 'Unbind', 'UnbindElmWPObj', 'UnbindGlobal', 'UnderlyingCharacterTable', 'UnderlyingCharacteristic', 'UnderlyingElement', 'UnderlyingElementOfReesMatrixSemigroupElement', 'UnderlyingElementOfReesZeroMatrixSemigroupElement', 'UnderlyingExternalSet', 'UnderlyingGeneralMapping', 'UnderlyingGroup', 'UnderlyingLeftModule', 'UnderlyingLieAlgebra', 'UnderlyingRelation', 'Union', 'Union2', 'Unique', 'UniteSet', 'Units', 'UnivariatePolynomial', 'UnivariatePolynomialByCoefficients', 'UnivariatePolynomialRing', 'UnivariateRationalFunctionByCoefficients', 'UnivariatenessTestRationalFunction', 'UniversalEnvelopingAlgebra', 'Unknown', 'UnorderedTuples', 'UnprofileFunctions', 'UnprofileMethods', 'UntraceMethods', 'UpdateMap', 'UpperCentralSeries', 'UpperCentralSeriesOfGroup', 'UpperSubdiagonal', 'UseBasis', 'UseFactorRelation', 'UseIsomorphismRelation', 'UseSubsetRelation', 'Valuation', 'Value', 'ValueCochain', 'ValueGlobal', 'ValueMolienSeries', 'ValueOption', 'ValuePol', 'ValuesOfClassFunction', 'VectorSpace', 'VectorSpaceByPcgsOfElementaryAbelianGroup', 'View', 'VirtualCharacter', 'WeakPointerObj', 'WedgeGModule', 'WeekDay', 'WeightLexOrdering', 'WeightOfGenerators', 'WeightVecFFE', 'WeylGroup', 'WeylOrbitIterator', 'Where', 'WreathProduct', 'WreathProductImprimitiveAction', 'WreathProductOrdering', 'WreathProductProductAction', 'WriteAll', 'WriteByte', 'WriteLine', 'ZClassRepsQClass', 'Zero', 'ZeroAttr', 'ZeroCoefficient', 'ZeroCoefficientRatFun', 'ZeroMapping', 'ZeroMutable', 'ZeroOp', 'ZeroSM', 'ZeroSameMutability', ] |