\indexentry{LengthOneResolutionPrimePowerGroup@\texttt  {LengthOneResolutionPrimePowerGroup}|hyperpage}{10}
\indexentry{LengthZeroResolutionPrimePowerGroup@\texttt  {LengthZeroResolutionPrimePowerGroup}|hyperpage}{10}
\indexentry{ResolutionLength@\texttt  {ResolutionLength}|hyperpage}{11}
\indexentry{ResolutionGroup@\texttt  {ResolutionGroup}|hyperpage}{11}
\indexentry{ResolutionFpGModuleGF@\texttt  {ResolutionFpGModuleGF}|hyperpage}{11}
\indexentry{ResolutionModuleRank@\texttt  {ResolutionModuleRank}|hyperpage}{11}
\indexentry{ResolutionModuleRanks@\texttt  {ResolutionModuleRanks}|hyperpage}{11}
\indexentry{BoundaryFpGModuleHomomorphismGF@\texttt  {BoundaryFpGModuleHomomorphismGF}|hyperpage}{11}
\indexentry{ResolutionsAreEqual@\texttt  {ResolutionsAreEqual}|hyperpage}{11}
\indexentry{BestCentralSubgroupForResolutionFiniteExtension@\texttt  {Best}\discretionary {-}{}{}\texttt  {Central}\discretionary {-}{}{}\texttt  {Subgroup}\discretionary {-}{}{}\texttt  {For}\discretionary {-}{}{}\texttt  {Resolution}\discretionary {-}{}{}\texttt  {Finite}\discretionary {-}{}{}\texttt  {Extension}|hyperpage}{13}
\indexentry{ModPRingGeneratorDegrees@\texttt  {ModPRingGeneratorDegrees}|hyperpage}{14}
\indexentry{ModPRingNiceBasis@\texttt  {ModPRingNiceBasis}|hyperpage}{15}
\indexentry{ModPRingNiceBasisAsPolynomials@\texttt  {ModPRingNiceBasisAsPolynomials}|hyperpage}{15}
\indexentry{ModPRingBasisAsPolynomials@\texttt  {ModPRingBasisAsPolynomials}|hyperpage}{15}
\indexentry{PresentationOfGradedStructureConstantAlgebra@\texttt  {Presentation}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Graded}\discretionary {-}{}{}\texttt  {Structure}\discretionary {-}{}{}\texttt  {Constant}\discretionary {-}{}{}\texttt  {Algebra}|hyperpage}{15}
\indexentry{GradedAlgebraPresentation@\texttt  {GradedAlgebraPresentation}|hyperpage}{17}
\indexentry{GradedAlgebraPresentationNC@\texttt  {GradedAlgebraPresentationNC}|hyperpage}{17}
\indexentry{BaseRing@\texttt  {BaseRing}|hyperpage}{18}
\indexentry{CoefficientsRing@\texttt  {CoefficientsRing}|hyperpage}{18}
\indexentry{IndeterminatesOfGradedAlgebraPresentation@\texttt  {Indeterminates}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Graded}\discretionary {-}{}{}\texttt  {Algebra}\discretionary {-}{}{}\texttt  {Presentation}|hyperpage}{18}
\indexentry{GeneratorsOfPresentationIdeal@\texttt  {GeneratorsOfPresentationIdeal}|hyperpage}{18}
\indexentry{PresentationIdeal@\texttt  {PresentationIdeal}|hyperpage}{18}
\indexentry{IndeterminateDegrees@\texttt  {IndeterminateDegrees}|hyperpage}{18}
\indexentry{TensorProduct@\texttt  {TensorProduct}!for two algebra presentations|hyperpage}{19}
\indexentry{TensorProduct@\texttt  {TensorProduct}!for collection of algebra presentations|hyperpage}{19}
\indexentry{IsIsomorphicGradedAlgebra@\texttt  {IsIsomorphicGradedAlgebra}|hyperpage}{19}
\indexentry{IsAssociatedGradedRing@\texttt  {IsAssociatedGradedRing}|hyperpage}{19}
\indexentry{DegreeOfRepresentative@\texttt  {DegreeOfRepresentative}|hyperpage}{19}
\indexentry{MaximumDegreeForPresentation@\texttt  {MaximumDegreeForPresentation}|hyperpage}{20}
\indexentry{SubspaceDimensionDegree@\texttt  {SubspaceDimensionDegree}!for one degree|hyperpage}{20}
\indexentry{SubspaceDimensionDegree@\texttt  {SubspaceDimensionDegree}!for list of degrees|hyperpage}{20}
\indexentry{SubspaceBasisRepsByDegree@\texttt  {SubspaceBasisRepsByDegree}!for one degree|hyperpage}{20}
\indexentry{SubspaceBasisRepsByDegree@\texttt  {SubspaceBasisRepsByDegree}!for list of degrees|hyperpage}{20}
\indexentry{CoefficientsOfPoincareSeries@\texttt  {CoefficientsOfPoincareSeries}|hyperpage}{20}
\indexentry{HilbertPoincareSeries@\texttt  {HilbertPoincareSeries}|hyperpage}{20}
\indexentry{LHSSpectralSequence@\texttt  {LHSSpectralSequence}|hyperpage}{20}
\indexentry{LHSSpectralSequenceLastSheet@\texttt  {LHSSpectralSequenceLastSheet}|hyperpage}{20}
\indexentry{FpGModuleGF@\texttt  {FpGModuleGF}!construction from generators, group and action|hyperpage}{27}
\indexentry{FpGModuleGF@\texttt  {FpGModuleGF}!construction from generators and groupAndAction|hyperpage}{27}
\indexentry{FpGModuleGF@\texttt  {FpGModuleGF}!construction of empty module from group and action|hyperpage}{27}
\indexentry{FpGModuleGF@\texttt  {FpGModuleGF}!construction of empty module from groupAndAction|hyperpage}{27}
\indexentry{FpGModuleGF@\texttt  {FpGModuleGF}!construction of full canonical module|hyperpage}{27}
\indexentry{FpGModuleGF@\texttt  {FpGModuleGF}!construction of full canonical module from groupAndAction|hyperpage}{27}
\indexentry{FpGModuleGF@\texttt  {FpGModuleGF}!construction from FpGModule|hyperpage}{27}
\indexentry{FpGModuleGFNC@\texttt  {FpGModuleGFNC}!construction from generators, group and action|hyperpage}{27}
\indexentry{FpGModuleGFNC@\texttt  {FpGModuleGFNC}!construction for empty module with group and action|hyperpage}{27}
\indexentry{FpGModuleGFNC@\texttt  {FpGModuleGFNC}!construction from generators and groupAndAction|hyperpage}{27}
\indexentry{FpGModuleFromFpGModuleGF@\texttt  {FpGModuleFromFpGModuleGF}|hyperpage}{28}
\indexentry{MutableCopyModule@\texttt  {MutableCopyModule}|hyperpage}{28}
\indexentry{CanonicalAction@\texttt  {CanonicalAction}|hyperpage}{28}
\indexentry{CanonicalActionOnRight@\texttt  {CanonicalActionOnRight}|hyperpage}{28}
\indexentry{CanonicalGroupAndAction@\texttt  {CanonicalGroupAndAction}|hyperpage}{28}
\indexentry{ModuleGroup@\texttt  {ModuleGroup}|hyperpage}{30}
\indexentry{ModuleGroupOrder@\texttt  {ModuleGroupOrder}|hyperpage}{30}
\indexentry{ModuleAction@\texttt  {ModuleAction}|hyperpage}{30}
\indexentry{ModuleActionBlockSize@\texttt  {ModuleActionBlockSize}|hyperpage}{30}
\indexentry{ModuleGroupAndAction@\texttt  {ModuleGroupAndAction}|hyperpage}{30}
\indexentry{ModuleCharacteristic@\texttt  {ModuleCharacteristic}|hyperpage}{31}
\indexentry{ModuleField@\texttt  {ModuleField}|hyperpage}{31}
\indexentry{ModuleAmbientDimension@\texttt  {ModuleAmbientDimension}|hyperpage}{31}
\indexentry{AmbientModuleDimension@\texttt  {AmbientModuleDimension}|hyperpage}{31}
\indexentry{DisplayBlocks@\texttt  {DisplayBlocks}!for FpGModuleGF|hyperpage}{31}
\indexentry{ModuleGenerators@\texttt  {ModuleGenerators}|hyperpage}{33}
\indexentry{ModuleGeneratorsAreMinimal@\texttt  {ModuleGeneratorsAreMinimal}|hyperpage}{33}
\indexentry{ModuleGeneratorsAreEchelonForm@\texttt  {ModuleGeneratorsAreEchelonForm}|hyperpage}{33}
\indexentry{ModuleIsFullCanonical@\texttt  {ModuleIsFullCanonical}|hyperpage}{33}
\indexentry{ModuleGeneratorsForm@\texttt  {ModuleGeneratorsForm}|hyperpage}{33}
\indexentry{ModuleRank@\texttt  {ModuleRank}|hyperpage}{34}
\indexentry{ModuleRankDestructive@\texttt  {ModuleRankDestructive}|hyperpage}{34}
\indexentry{ModuleVectorSpaceBasis@\texttt  {ModuleVectorSpaceBasis}|hyperpage}{34}
\indexentry{ModuleVectorSpaceDimension@\texttt  {ModuleVectorSpaceDimension}|hyperpage}{34}
\indexentry{MinimalGeneratorsModuleGF@\texttt  {MinimalGeneratorsModuleGF}|hyperpage}{34}
\indexentry{MinimalGeneratorsModuleGFDestructive@\texttt  {MinimalGeneratorsModuleGFDestructive}|hyperpage}{34}
\indexentry{MinimalGeneratorsModuleRadical@\texttt  {MinimalGeneratorsModuleRadical}|hyperpage}{34}
\indexentry{RadicalOfModule@\texttt  {RadicalOfModule}|hyperpage}{35}
\indexentry{EchelonModuleGenerators@\texttt  {EchelonModuleGenerators}|hyperpage}{36}
\indexentry{EchelonModuleGeneratorsDestructive@\texttt  {EchelonModuleGeneratorsDestructive}|hyperpage}{36}
\indexentry{SemiEchelonModuleGenerators@\texttt  {SemiEchelonModuleGenerators}|hyperpage}{36}
\indexentry{SemiEchelonModuleGeneratorsDestructive@\texttt  {SemiEchelonModuleGeneratorsDestructive}|hyperpage}{36}
\indexentry{EchelonModuleGeneratorsMinMem@\texttt  {EchelonModuleGeneratorsMinMem}|hyperpage}{36}
\indexentry{EchelonModuleGeneratorsMinMemDestructive@\texttt  {EchelonModuleGeneratorsMinMemDestructive}|hyperpage}{36}
\indexentry{SemiEchelonModuleGeneratorsMinMem@\texttt  {SemiEchelonModuleGeneratorsMinMem}|hyperpage}{36}
\indexentry{SemiEchelonModuleGeneratorsMinMemDestructive@\texttt  {Semi}\discretionary {-}{}{}\texttt  {Echelon}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Generators}\discretionary {-}{}{}\texttt  {Min}\discretionary {-}{}{}\texttt  {Mem}\discretionary {-}{}{}\texttt  {Destructive}|hyperpage}{37}
\indexentry{ReverseEchelonModuleGenerators@\texttt  {ReverseEchelonModuleGenerators}|hyperpage}{37}
\indexentry{ReverseEchelonModuleGeneratorsDestructive@\texttt  {Reverse}\discretionary {-}{}{}\texttt  {Echelon}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Generators}\discretionary {-}{}{}\texttt  {Destructive}|hyperpage}{37}
\indexentry{DirectSumOfModules@\texttt  {DirectSumOfModules}!for two modules|hyperpage}{39}
\indexentry{DirectSumOfModules@\texttt  {DirectSumOfModules}!for collection of modules|hyperpage}{39}
\indexentry{DirectSumOfModules@\texttt  {DirectSumOfModules}!for n copies of the same module|hyperpage}{39}
\indexentry{DirectDecompositionOfModule@\texttt  {DirectDecompositionOfModule}|hyperpage}{39}
\indexentry{DirectDecompositionOfModuleDestructive@\texttt  {DirectDecompositionOfModuleDestructive}|hyperpage}{39}
\indexentry{IntersectionModules@\texttt  {IntersectionModules}|hyperpage}{40}
\indexentry{IntersectionModulesGF@\texttt  {IntersectionModulesGF}|hyperpage}{40}
\indexentry{IntersectionModulesGFDestructive@\texttt  {IntersectionModulesGFDestructive}|hyperpage}{40}
\indexentry{IntersectionModulesGF2@\texttt  {IntersectionModulesGF2}|hyperpage}{40}
\indexentry{SumModules@\texttt  {SumModules}|hyperpage}{40}
\indexentry{=@\texttt  {=}!for FpGModuleGF|hyperpage}{42}
\indexentry{IsModuleElement@\texttt  {IsModuleElement}!for element|hyperpage}{42}
\indexentry{IsModuleElement@\texttt  {IsModuleElement}!for collection of elements|hyperpage}{42}
\indexentry{IsSubModule@\texttt  {IsSubModule}|hyperpage}{42}
\indexentry{RandomElement@\texttt  {RandomElement}|hyperpage}{42}
\indexentry{RandomSubmodule@\texttt  {RandomSubmodule}|hyperpage}{43}
\indexentry{FpGModuleHomomorphismGF@\texttt  {FpGModuleHomomorphismGF}|hyperpage}{46}
\indexentry{FpGModuleHomomorphismGFNC@\texttt  {FpGModuleHomomorphismGFNC}|hyperpage}{46}
\indexentry{SourceModule@\texttt  {SourceModule}|hyperpage}{47}
\indexentry{TargetModule@\texttt  {TargetModule}|hyperpage}{47}
\indexentry{ModuleHomomorphismGeneratorMatrix@\texttt  {ModuleHomomorphismGeneratorMatrix}|hyperpage}{47}
\indexentry{DisplayBlocks@\texttt  {DisplayBlocks}!for FpGModuleHomomorphismGF|hyperpage}{47}
\indexentry{DisplayModuleHomomorphismGeneratorMatrix@\texttt  {DisplayModuleHomomorphismGeneratorMatrix}|hyperpage}{47}
\indexentry{DisplayModuleHomomorphismGeneratorMatrixBlocks@\texttt  {Display}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {Generator}\discretionary {-}{}{}\texttt  {Matrix}\discretionary {-}{}{}\texttt  {Blocks}|hyperpage}{47}
\indexentry{ImageOfModuleHomomorphism@\texttt  {ImageOfModuleHomomorphism}!image of homomorphism|hyperpage}{49}
\indexentry{ImageOfModuleHomomorphism@\texttt  {ImageOfModuleHomomorphism}!of module|hyperpage}{49}
\indexentry{ImageOfModuleHomomorphism@\texttt  {ImageOfModuleHomomorphism}!of element|hyperpage}{49}
\indexentry{ImageOfModuleHomomorphism@\texttt  {ImageOfModuleHomomorphism}!of collections of elements|hyperpage}{49}
\indexentry{ImageOfModuleHomomorphismDestructive@\texttt  {ImageOfModuleHomomorphismDestructive}!of element|hyperpage}{49}
\indexentry{ImageOfModuleHomomorphismDestructive@\texttt  {ImageOfModuleHomomorphismDestructive}!of collection of elements|hyperpage}{49}
\indexentry{PreImageRepresentativeOfModuleHomomorphism@\texttt  {Pre}\discretionary {-}{}{}\texttt  {Image}\discretionary {-}{}{}\texttt  {Representative}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Homomorphism}!for element|hyperpage}{49}
\indexentry{PreImageRepresentativeOfModuleHomomorphism@\texttt  {Pre}\discretionary {-}{}{}\texttt  {Image}\discretionary {-}{}{}\texttt  {Representative}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Homomorphism}!for collection of elements|hyperpage}{49}
\indexentry{PreImageRepresentativeOfModuleHomomorphism@\texttt  {Pre}\discretionary {-}{}{}\texttt  {Image}\discretionary {-}{}{}\texttt  {Representative}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Homomorphism}!for module|hyperpage}{49}
\indexentry{PreImageRepresentativeOfModuleHomomorphismGF@\texttt  {Pre}\discretionary {-}{}{}\texttt  {Image}\discretionary {-}{}{}\texttt  {Representative}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {HomomorphismGF}!for element|hyperpage}{49}
\indexentry{PreImageRepresentativeOfModuleHomomorphismGF@\texttt  {Pre}\discretionary {-}{}{}\texttt  {Image}\discretionary {-}{}{}\texttt  {Representative}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {HomomorphismGF}!for collection of elements|hyperpage}{49}
\indexentry{KernelOfModuleHomomorphism@\texttt  {KernelOfModuleHomomorphism}|hyperpage}{49}
\indexentry{KernelOfModuleHomomorphismSplit@\texttt  {KernelOfModuleHomomorphismSplit}|hyperpage}{49}
\indexentry{KernelOfModuleHomomorphismIndependentSplit@\texttt  {Kernel}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Homomorphism}\discretionary {-}{}{}\texttt  {Independent}\discretionary {-}{}{}\texttt  {Split}|hyperpage}{50}
\indexentry{KernelOfModuleHomomorphismGF@\texttt  {KernelOfModuleHomomorphismGF}|hyperpage}{50}
\indexentry{HAPRingToSubringHomomorphism@\texttt  {HAPRingToSubringHomomorphism}|hyperpage}{54}
\indexentry{HAPSubringToRingHomomorphism@\texttt  {HAPSubringToRingHomomorphism}!for relations defined at source|hyperpage}{54}
\indexentry{HAPSubringToRingHomomorphism@\texttt  {HAPSubringToRingHomomorphism}!for relations defined at image|hyperpage}{54}
\indexentry{HAPRingHomomorphismByIndeterminateMap@\texttt  {HAPRingHomomorphismByIndeterminateMap}|hyperpage}{54}
\indexentry{HAPRingReductionHomomorphism@\texttt  {HAPRingReductionHomomorphism}!for ring presentation|hyperpage}{54}
\indexentry{HAPRingReductionHomomorphism@\texttt  {HAPRingReductionHomomorphism}!for image of ring homomorphism|hyperpage}{54}
\indexentry{HAPZeroRingHomomorphism@\texttt  {HAPZeroRingHomomorphism}|hyperpage}{55}
\indexentry{InverseRingHomomorphism@\texttt  {InverseRingHomomorphism}|hyperpage}{55}
\indexentry{CompositionRingHomomorphism@\texttt  {CompositionRingHomomorphism}|hyperpage}{55}
\indexentry{SourceGenerators@\texttt  {SourceGenerators}|hyperpage}{55}
\indexentry{SourceRelations@\texttt  {SourceRelations}|hyperpage}{55}
\indexentry{SourcePolynomialRing@\texttt  {SourcePolynomialRing}|hyperpage}{55}
\indexentry{ImageGenerators@\texttt  {ImageGenerators}|hyperpage}{56}
\indexentry{ImageRelations@\texttt  {ImageRelations}|hyperpage}{56}
\indexentry{ImagePolynomialRing@\texttt  {ImagePolynomialRing}|hyperpage}{56}
\indexentry{ImageOfRingHomomorphism@\texttt  {ImageOfRingHomomorphism}!for one polynomial|hyperpage}{56}
\indexentry{ImageOfRingHomomorphism@\texttt  {ImageOfRingHomomorphism}!for collection of polynomials|hyperpage}{56}
\indexentry{PreimageOfRingHomomorphism@\texttt  {PreimageOfRingHomomorphism}!for one polynomial|hyperpage}{56}
\indexentry{PreimageOfRingHomomorphism@\texttt  {PreimageOfRingHomomorphism}!for collection of polynomials|hyperpage}{56}
\indexentry{HAPDerivation@\texttt  {HAPDerivation}|hyperpage}{60}
\indexentry{HAPDerivationNC@\texttt  {HAPDerivationNC}|hyperpage}{60}
\indexentry{DerivationRing@\texttt  {DerivationRing}|hyperpage}{60}
\indexentry{DerivationImages@\texttt  {DerivationImages}|hyperpage}{61}
\indexentry{DerivationRelations@\texttt  {DerivationRelations}|hyperpage}{61}
\indexentry{ImageOfDerivation@\texttt  {ImageOfDerivation}|hyperpage}{61}
\indexentry{KernelOfDerivation@\texttt  {KernelOfDerivation}|hyperpage}{61}
\indexentry{HomologyOfDerivation@\texttt  {HomologyOfDerivation}|hyperpage}{62}
\indexentry{PoincareSeriesAutoMem@\texttt  {PoincareSeriesAutoMem}|hyperpage}{65}
\indexentry{SumIntersectionMatDestructive@\texttt  {SumIntersectionMatDestructive}|hyperpage}{67}
\indexentry{SumIntersectionMatDestructiveSE@\texttt  {SumIntersectionMatDestructiveSE}|hyperpage}{67}
\indexentry{SolutionMat@\texttt  {SolutionMat}!for multiple vectors|hyperpage}{68}
\indexentry{SolutionMatDestructive@\texttt  {SolutionMatDestructive}!for multiple vectors|hyperpage}{68}
\indexentry{IsSameSubspace@\texttt  {IsSameSubspace}|hyperpage}{68}
\indexentry{PrintDimensionsMat@\texttt  {PrintDimensionsMat}|hyperpage}{68}
\indexentry{TermsOfPolynomial@\texttt  {TermsOfPolynomial}|hyperpage}{69}
\indexentry{IsMonomial@\texttt  {IsMonomial}!for polynomial|hyperpage}{69}
\indexentry{UnivariateMonomialsOfMonomial@\texttt  {UnivariateMonomialsOfMonomial}|hyperpage}{69}
\indexentry{IndeterminateAndExponentOfUnivariateMonomial@\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {And}\discretionary {-}{}{}\texttt  {Exponent}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Univariate}\discretionary {-}{}{}\texttt  {Monomial}|hyperpage}{69}
\indexentry{IndeterminatesOfPolynomial@\texttt  {IndeterminatesOfPolynomial}|hyperpage}{69}
\indexentry{ReduceIdeal@\texttt  {ReduceIdeal}!for Ideal|hyperpage}{69}
\indexentry{ReduceIdeal@\texttt  {ReduceIdeal}!for list of relations|hyperpage}{69}
\indexentry{ReducedPolynomialRingPresentation@\texttt  {ReducedPolynomialRingPresentation}|hyperpage}{70}
\indexentry{ReducedPolynomialRingPresentationMap@\texttt  {ReducedPolynomialRingPresentationMap}|hyperpage}{70}
\indexentry{SingularSetNormalFormIdeal@\texttt  {SingularSetNormalFormIdeal}|hyperpage}{71}
\indexentry{SingularSetNormalFormIdealNC@\texttt  {SingularSetNormalFormIdealNC}|hyperpage}{71}
\indexentry{SingularPolynomialNormalForm@\texttt  {SingularPolynomialNormalForm}|hyperpage}{71}
\indexentry{SingularGroebnerBasis@\texttt  {SingularGroebnerBasis}|hyperpage}{71}
\indexentry{SingularReducedGroebnerBasis@\texttt  {SingularReducedGroebnerBasis}|hyperpage}{72}
\indexentry{HallSeniorNumber@\texttt  {HallSeniorNumber}!for SmallGroup library ref|hyperpage}{72}
\indexentry{HallSeniorNumber@\texttt  {HallSeniorNumber}!for group|hyperpage}{72}
