\indexentry{\textsf{Modules}|hyperpage}{6}
\indexentry{KernelSubobject@\texttt  {KernelSubobject}!for ring maps|hyperpage}{17}
\indexentry{KernelEmb@\texttt  {KernelEmb}!for ring maps|hyperpage}{17}
\indexentry{Kernel@\texttt  {Kernel}!for ring maps|hyperpage}{17}
\indexentry{IsHomalgRelations@\texttt  {IsHomalgRelations}|hyperpage}{18}
\indexentry{IsHomalgRelationsOfLeftModule@\texttt  {IsHomalgRelationsOfLeftModule}|hyperpage}{18}
\indexentry{IsHomalgRelationsOfRightModule@\texttt  {IsHomalgRelationsOfRightModule}|hyperpage}{18}
\indexentry{IsRelationsOfFinitelyPresentedModuleRep@\texttt  {IsRelations}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Finitely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {ModuleRep}|hyperpage}{19}
\indexentry{CanBeUsedToDecideZeroEffectively@\texttt  {CanBeUsedToDecideZeroEffectively}|hyperpage}{19}
\indexentry{IsInjectivePresentation@\texttt  {IsInjectivePresentation}|hyperpage}{19}
\indexentry{IsHomalgGenerators@\texttt  {IsHomalgGenerators}|hyperpage}{20}
\indexentry{IsHomalgGeneratorsOfLeftModule@\texttt  {IsHomalgGeneratorsOfLeftModule}|hyperpage}{20}
\indexentry{IsHomalgGeneratorsOfRightModule@\texttt  {IsHomalgGeneratorsOfRightModule}|hyperpage}{20}
\indexentry{IsGeneratorsOfModuleRep@\texttt  {IsGeneratorsOfModuleRep}|hyperpage}{21}
\indexentry{IsGeneratorsOfFinitelyGeneratedModuleRep@\texttt  {IsGenerators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Finitely}\discretionary {-}{}{}\texttt  {Generated}\discretionary {-}{}{}\texttt  {ModuleRep}|hyperpage}{21}
\indexentry{IsReduced@\texttt  {IsReduced}!for generators|hyperpage}{21}
\indexentry{ProcedureToReadjustGenerators@\texttt  {ProcedureToReadjustGenerators}|hyperpage}{21}
\indexentry{IsHomalgModule@\texttt  {IsHomalgModule}|hyperpage}{22}
\indexentry{IsFinitelyPresentedModuleOrSubmoduleRep@\texttt  {IsFinitely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Or}\discretionary {-}{}{}\texttt  {SubmoduleRep}|hyperpage}{23}
\indexentry{IsFinitelyPresentedModuleRep@\texttt  {IsFinitelyPresentedModuleRep}|hyperpage}{23}
\indexentry{IsFinitelyPresentedSubmoduleRep@\texttt  {IsFinitelyPresentedSubmoduleRep}|hyperpage}{23}
\indexentry{LeftPresentation@\texttt  {LeftPresentation}!constructor for left modules|hyperpage}{24}
\indexentry{RightPresentation@\texttt  {RightPresentation}!constructor for right modules|hyperpage}{24}
\indexentry{HomalgFreeLeftModule@\texttt  {HomalgFreeLeftModule}!constructor for free left modules|hyperpage}{25}
\indexentry{HomalgFreeRightModule@\texttt  {HomalgFreeRightModule}!constructor for free right modules|hyperpage}{25}
\indexentry{HomalgZeroLeftModule@\texttt  {HomalgZeroLeftModule}!constructor for zero left modules|hyperpage}{25}
\indexentry{HomalgZeroRightModule@\texttt  {HomalgZeroRightModule}!constructor for zero right modules|hyperpage}{25}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!transfer a module over a different ring|hyperpage}{26}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!transfer a module over a different ring (right)|hyperpage}{26}
\indexentry{Subobject@\texttt  {Subobject}!constructor for submodules using matrices|hyperpage}{28}
\indexentry{Subobject@\texttt  {Subobject}!constructor for submodules using a list of ring elements|hyperpage}{28}
\indexentry{LeftSubmodule@\texttt  {LeftSubmodule}!constructor for left submodules|hyperpage}{28}
\indexentry{RightSubmodule@\texttt  {RightSubmodule}!constructor for right submodules|hyperpage}{29}
\indexentry{IsCyclic@\texttt  {IsCyclic}|hyperpage}{29}
\indexentry{IsHolonomic@\texttt  {IsHolonomic}|hyperpage}{29}
\indexentry{IsReduced@\texttt  {IsReduced}!for modules|hyperpage}{29}
\indexentry{IsPrimeIdeal@\texttt  {IsPrimeIdeal}|hyperpage}{30}
\indexentry{IsPrimeModule@\texttt  {IsPrimeModule}!for modules|hyperpage}{30}
\indexentry{ResidueClassRing@\texttt  {ResidueClassRing}|hyperpage}{30}
\indexentry{PrimaryDecomposition@\texttt  {PrimaryDecomposition}|hyperpage}{30}
\indexentry{RadicalDecomposition@\texttt  {RadicalDecomposition}|hyperpage}{30}
\indexentry{ModuleOfKaehlerDifferentials@\texttt  {ModuleOfKaehlerDifferentials}|hyperpage}{30}
\indexentry{RadicalSubobject@\texttt  {RadicalSubobject}|hyperpage}{31}
\indexentry{SymmetricAlgebra@\texttt  {SymmetricAlgebra}|hyperpage}{31}
\indexentry{ExteriorAlgebra@\texttt  {ExteriorAlgebra}|hyperpage}{31}
\indexentry{ElementaryDivisors@\texttt  {ElementaryDivisors}|hyperpage}{31}
\indexentry{FittingIdeal@\texttt  {FittingIdeal}|hyperpage}{31}
\indexentry{NonFlatLocus@\texttt  {NonFlatLocus}|hyperpage}{31}
\indexentry{LargestMinimalNumberOfLocalGenerators@\texttt  {Largest}\discretionary {-}{}{}\texttt  {Minimal}\discretionary {-}{}{}\texttt  {Number}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Local}\discretionary {-}{}{}\texttt  {Generators}|hyperpage}{31}
\indexentry{CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries@\texttt  {Coefficients}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Unreduced}\discretionary {-}{}{}\texttt  {Numerator}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Poincare}\discretionary {-}{}{}\texttt  {Series}|hyperpage}{31}
\indexentry{CoefficientsOfNumeratorOfHilbertPoincareSeries@\texttt  {Coefficients}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerator}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Poincare}\discretionary {-}{}{}\texttt  {Series}|hyperpage}{32}
\indexentry{UnreducedNumeratorOfHilbertPoincareSeries@\texttt  {Unreduced}\discretionary {-}{}{}\texttt  {Numerator}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Poincare}\discretionary {-}{}{}\texttt  {Series}|hyperpage}{32}
\indexentry{NumeratorOfHilbertPoincareSeries@\texttt  {NumeratorOfHilbertPoincareSeries}|hyperpage}{32}
\indexentry{HilbertPoincareSeries@\texttt  {HilbertPoincareSeries}|hyperpage}{32}
\indexentry{AffineDegree@\texttt  {AffineDegree}|hyperpage}{32}
\indexentry{DataOfHilbertFunction@\texttt  {DataOfHilbertFunction}|hyperpage}{32}
\indexentry{HilbertFunction@\texttt  {HilbertFunction}|hyperpage}{32}
\indexentry{IndexOfRegularity@\texttt  {IndexOfRegularity}|hyperpage}{32}
\indexentry{HomalgRing@\texttt  {HomalgRing}!for modules|hyperpage}{33}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for modules|hyperpage}{33}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!constructor for ideal multiples|hyperpage}{34}
\indexentry{SubobjectQuotient@\texttt  {SubobjectQuotient}!for submodules|hyperpage}{34}
\indexentry{IsHomalgMap@\texttt  {IsHomalgMap}|hyperpage}{35}
\indexentry{IsHomalgSelfMap@\texttt  {IsHomalgSelfMap}|hyperpage}{35}
\indexentry{IsMapOfFinitelyGeneratedModulesRep@\texttt  {IsMapOfFinitelyGeneratedModulesRep}|hyperpage}{36}
\indexentry{HomalgMap@\texttt  {HomalgMap}!constructor for maps|hyperpage}{36}
\indexentry{HomalgMap@\texttt  {HomalgMap}!constructor for maps between free modules|hyperpage}{36}
\indexentry{HomalgZeroMap@\texttt  {HomalgZeroMap}!constructor for zero maps|hyperpage}{38}
\indexentry{HomalgIdentityMap@\texttt  {HomalgIdentityMap}!constructor for identity maps|hyperpage}{38}
\indexentry{HomalgRing@\texttt  {HomalgRing}|hyperpage}{39}
\indexentry{PreInverse@\texttt  {PreInverse}|hyperpage}{39}
\indexentry{IsHomalgElement@\texttt  {IsHomalgElement}|hyperpage}{40}
\indexentry{IsElementOfAModuleGivenByAMorphismRep@\texttt  {IsElement}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {Module}\discretionary {-}{}{}\texttt  {Given}\discretionary {-}{}{}\texttt  {By}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {MorphismRep}|hyperpage}{40}
\indexentry{IsElementOfIntegers@\texttt  {IsElementOfIntegers}|hyperpage}{40}
\indexentry{HomalgRing@\texttt  {HomalgRing}!for module elements|hyperpage}{41}
\indexentry{functorCokernel@\texttt  {functor{\textunderscore }Cokernel}|hyperpage}{42}
\indexentry{Cokernel@\texttt  {Cokernel}|hyperpage}{42}
\indexentry{functorImageObject@\texttt  {functor{\textunderscore }ImageObject}|hyperpage}{43}
\indexentry{ImageObject@\texttt  {ImageObject}|hyperpage}{44}
\indexentry{Kernel@\texttt  {Kernel}!for maps|hyperpage}{45}
\indexentry{DefectOfExactness@\texttt  {DefectOfExactness}|hyperpage}{46}
\indexentry{FunctorHom@\texttt  {Functor{\textunderscore }Hom}|hyperpage}{46}
\indexentry{Hom@\texttt  {Hom}|hyperpage}{47}
\indexentry{FunctorTensorProduct@\texttt  {Functor{\textunderscore }}\discretionary {-}{}{}\texttt  {Tensor}\discretionary {-}{}{}\texttt  {Product}|hyperpage}{51}
\indexentry{TensorProduct@\texttt  {TensorProduct}|hyperpage}{51}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!TensorProduct|hyperpage}{51}
\indexentry{FunctorExt@\texttt  {Functor{\textunderscore }Ext}|hyperpage}{54}
\indexentry{Ext@\texttt  {Ext}|hyperpage}{54}
\indexentry{FunctorTor@\texttt  {Functor{\textunderscore }Tor}|hyperpage}{55}
\indexentry{Tor@\texttt  {Tor}|hyperpage}{55}
\indexentry{FunctorRHom@\texttt  {Functor{\textunderscore }RHom}|hyperpage}{56}
\indexentry{RHom@\texttt  {RHom}|hyperpage}{57}
\indexentry{FunctorLTensorProduct@\texttt  {Functor{\textunderscore }}\discretionary {-}{}{}\texttt  {L}\discretionary {-}{}{}\texttt  {Tensor}\discretionary {-}{}{}\texttt  {Product}|hyperpage}{59}
\indexentry{LTensorProduct@\texttt  {LTensorProduct}|hyperpage}{59}
\indexentry{FunctorHomHom@\texttt  {Functor{\textunderscore }HomHom}|hyperpage}{62}
\indexentry{FunctorLHomHom@\texttt  {Functor{\textunderscore }LHomHom}|hyperpage}{62}
\indexentry{SymmetricPower@\texttt  {SymmetricPower}|hyperpage}{63}
\indexentry{IsSymmetricPower@\texttt  {IsSymmetricPower}|hyperpage}{63}
\indexentry{SymmetricPowerExponent@\texttt  {SymmetricPowerExponent}|hyperpage}{63}
\indexentry{SymmetricPowerBaseModule@\texttt  {SymmetricPowerBaseModule}|hyperpage}{63}
\indexentry{ExteriorPower@\texttt  {ExteriorPower}|hyperpage}{64}
\indexentry{IsExteriorPower@\texttt  {IsExteriorPower}|hyperpage}{64}
\indexentry{ExteriorPowerExponent@\texttt  {ExteriorPowerExponent}|hyperpage}{64}
\indexentry{ExteriorPowerBaseModule@\texttt  {ExteriorPowerBaseModule}|hyperpage}{65}
\indexentry{IsExteriorPowerElement@\texttt  {IsExteriorPowerElement}|hyperpage}{65}
\indexentry{Wedge@\texttt  {Wedge}!for elements of exterior powers of free modules|hyperpage}{65}
\indexentry{ExteriorPowerElementDual@\texttt  {ExteriorPowerElementDual}|hyperpage}{65}
\indexentry{SingleValueOfExteriorPowerElement@\texttt  {SingleValueOfExteriorPowerElement}|hyperpage}{65}
\indexentry{KoszulCocomplex@\texttt  {KoszulCocomplex}|hyperpage}{65}
\indexentry{CayleyDeterminant@\texttt  {CayleyDeterminant}|hyperpage}{66}
\indexentry{GcdUsingCayleyDeterminant@\texttt  {Gcd{\textunderscore }}\discretionary {-}{}{}\texttt  {Using}\discretionary {-}{}{}\texttt  {Cayley}\discretionary {-}{}{}\texttt  {Determinant}|hyperpage}{66}
