\indexentry{\textsf{homalg}|hyperpage}{19}
\indexentry{IsHomalgRing@\texttt  {IsHomalgRing}|hyperpage}{32}
\indexentry{IsPreHomalgRing@\texttt  {IsPreHomalgRing}|hyperpage}{32}
\indexentry{IsHomalgRingElement@\texttt  {IsHomalgRingElement}|hyperpage}{32}
\indexentry{IsHomalgInternalRingRep@\texttt  {IsHomalgInternalRingRep}|hyperpage}{32}
\indexentry{HomalgRingOfIntegers@\texttt  {HomalgRingOfIntegers}!constructor for the integers|hyperpage}{33}
\indexentry{HomalgRingOfIntegers@\texttt  {HomalgRingOfIntegers}!constructor for the residue class rings of the integers|hyperpage}{33}
\indexentry{HomalgFieldOfRationals@\texttt  {HomalgFieldOfRationals}!constructor for the field of rationals|hyperpage}{33}
\indexentry{/@\texttt  {\texttt  {\char 92\relax }/}!constructor for residue class rings|hyperpage}{33}
\indexentry{ContainsAField@\texttt  {ContainsAField}|hyperpage}{34}
\indexentry{IsRationalsForHomalg@\texttt  {IsRationalsForHomalg}|hyperpage}{34}
\indexentry{IsFieldForHomalg@\texttt  {IsFieldForHomalg}|hyperpage}{35}
\indexentry{IsDivisionRingForHomalg@\texttt  {IsDivisionRingForHomalg}|hyperpage}{35}
\indexentry{IsIntegersForHomalg@\texttt  {IsIntegersForHomalg}|hyperpage}{35}
\indexentry{IsResidueClassRingOfTheIntegers@\texttt  {IsResidueClassRingOfTheIntegers}|hyperpage}{35}
\indexentry{IsBezoutRing@\texttt  {IsBezoutRing}|hyperpage}{35}
\indexentry{IsIntegrallyClosedDomain@\texttt  {IsIntegrallyClosedDomain}|hyperpage}{35}
\indexentry{IsUniqueFactorizationDomain@\texttt  {IsUniqueFactorizationDomain}|hyperpage}{35}
\indexentry{IsKaplanskyHermite@\texttt  {IsKaplanskyHermite}|hyperpage}{35}
\indexentry{IsDedekindDomain@\texttt  {IsDedekindDomain}|hyperpage}{36}
\indexentry{IsDiscreteValuationRing@\texttt  {IsDiscreteValuationRing}|hyperpage}{36}
\indexentry{IsFreePolynomialRing@\texttt  {IsFreePolynomialRing}|hyperpage}{36}
\indexentry{IsWeylRing@\texttt  {IsWeylRing}|hyperpage}{36}
\indexentry{IsGlobalDimensionFinite@\texttt  {IsGlobalDimensionFinite}|hyperpage}{36}
\indexentry{IsLeftGlobalDimensionFinite@\texttt  {IsLeftGlobalDimensionFinite}|hyperpage}{36}
\indexentry{IsRightGlobalDimensionFinite@\texttt  {IsRightGlobalDimensionFinite}|hyperpage}{36}
\indexentry{HasInvariantBasisProperty@\texttt  {HasInvariantBasisProperty}|hyperpage}{36}
\indexentry{HasLeftInvariantBasisProperty@\texttt  {HasLeftInvariantBasisProperty}|hyperpage}{37}
\indexentry{HasRightInvariantBasisProperty@\texttt  {HasRightInvariantBasisProperty}|hyperpage}{37}
\indexentry{IsLocalRing@\texttt  {IsLocalRing}|hyperpage}{37}
\indexentry{IsSemiLocalRing@\texttt  {IsSemiLocalRing}|hyperpage}{37}
\indexentry{IsIntegralDomain@\texttt  {IsIntegralDomain}|hyperpage}{37}
\indexentry{IsHereditary@\texttt  {IsHereditary}|hyperpage}{37}
\indexentry{IsLeftHereditary@\texttt  {IsLeftHereditary}|hyperpage}{37}
\indexentry{IsRightHereditary@\texttt  {IsRightHereditary}|hyperpage}{37}
\indexentry{IsHermite@\texttt  {IsHermite}|hyperpage}{38}
\indexentry{IsLeftHermite@\texttt  {IsLeftHermite}|hyperpage}{38}
\indexentry{IsRightHermite@\texttt  {IsRightHermite}|hyperpage}{38}
\indexentry{IsNoetherian@\texttt  {IsNoetherian}|hyperpage}{38}
\indexentry{IsLeftNoetherian@\texttt  {IsLeftNoetherian}|hyperpage}{38}
\indexentry{IsRightNoetherian@\texttt  {IsRightNoetherian}|hyperpage}{38}
\indexentry{IsArtinian@\texttt  {IsArtinian}!for rings|hyperpage}{38}
\indexentry{IsLeftArtinian@\texttt  {IsLeftArtinian}|hyperpage}{38}
\indexentry{IsRightArtinian@\texttt  {IsRightArtinian}|hyperpage}{39}
\indexentry{IsOreDomain@\texttt  {IsOreDomain}|hyperpage}{39}
\indexentry{IsLeftOreDomain@\texttt  {IsLeftOreDomain}|hyperpage}{39}
\indexentry{IsRightOreDomain@\texttt  {IsRightOreDomain}|hyperpage}{39}
\indexentry{IsPrincipalIdealRing@\texttt  {IsPrincipalIdealRing}|hyperpage}{39}
\indexentry{IsLeftPrincipalIdealRing@\texttt  {IsLeftPrincipalIdealRing}|hyperpage}{39}
\indexentry{IsRightPrincipalIdealRing@\texttt  {IsRightPrincipalIdealRing}|hyperpage}{39}
\indexentry{IsRegular@\texttt  {IsRegular}|hyperpage}{39}
\indexentry{IsFiniteFreePresentationRing@\texttt  {IsFiniteFreePresentationRing}|hyperpage}{40}
\indexentry{IsLeftFiniteFreePresentationRing@\texttt  {IsLeftFiniteFreePresentationRing}|hyperpage}{40}
\indexentry{IsRightFiniteFreePresentationRing@\texttt  {IsRightFiniteFreePresentationRing}|hyperpage}{40}
\indexentry{IsSimpleRing@\texttt  {IsSimpleRing}|hyperpage}{40}
\indexentry{IsSemiSimpleRing@\texttt  {IsSemiSimpleRing}|hyperpage}{40}
\indexentry{BasisAlgorithmRespectsPrincipalIdeals@\texttt  {BasisAlgorithmRespectsPrincipalIdeals}|hyperpage}{40}
\indexentry{IsMinusOne@\texttt  {IsMinusOne}|hyperpage}{40}
\indexentry{Zero@\texttt  {Zero}!for homalg ring elements|hyperpage}{40}
\indexentry{One@\texttt  {One}!for homalg ring elements|hyperpage}{41}
\indexentry{homalgTable@\texttt  {homalgTable}|hyperpage}{41}
\indexentry{RingElementConstructor@\texttt  {RingElementConstructor}|hyperpage}{41}
\indexentry{TypeOfHomalgMatrix@\texttt  {TypeOfHomalgMatrix}|hyperpage}{41}
\indexentry{ConstructorForHomalgMatrices@\texttt  {ConstructorForHomalgMatrices}|hyperpage}{41}
\indexentry{Zero@\texttt  {Zero}!for homalg rings|hyperpage}{41}
\indexentry{One@\texttt  {One}!for homalg rings|hyperpage}{41}
\indexentry{MinusOne@\texttt  {MinusOne}|hyperpage}{41}
\indexentry{IndeterminatesOfPolynomialRing@\texttt  {IndeterminatesOfPolynomialRing}|hyperpage}{42}
\indexentry{IndeterminateCoordinatesOfRingOfDerivations@\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Coordinates}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Derivations}|hyperpage}{42}
\indexentry{IndeterminateDerivationsOfRingOfDerivations@\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Derivations}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Derivations}|hyperpage}{42}
\indexentry{IndeterminateAntiCommutingVariablesOfExteriorRing@\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Anti}\discretionary {-}{}{}\texttt  {Commuting}\discretionary {-}{}{}\texttt  {Variables}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Exterior}\discretionary {-}{}{}\texttt  {Ring}|hyperpage}{42}
\indexentry{IndeterminatesOfExteriorRing@\texttt  {IndeterminatesOfExteriorRing}|hyperpage}{42}
\indexentry{WeightsOfIndeterminates@\texttt  {WeightsOfIndeterminates}|hyperpage}{42}
\indexentry{MatrixOfWeightsOfIndeterminates@\texttt  {MatrixOfWeightsOfIndeterminates}|hyperpage}{42}
\indexentry{CoefficientsRing@\texttt  {CoefficientsRing}|hyperpage}{42}
\indexentry{KrullDimension@\texttt  {KrullDimension}|hyperpage}{43}
\indexentry{LeftGlobalDimension@\texttt  {LeftGlobalDimension}|hyperpage}{43}
\indexentry{RightGlobalDimension@\texttt  {RightGlobalDimension}|hyperpage}{43}
\indexentry{GlobalDimension@\texttt  {GlobalDimension}|hyperpage}{43}
\indexentry{GeneralLinearRank@\texttt  {GeneralLinearRank}|hyperpage}{43}
\indexentry{ElementaryRank@\texttt  {ElementaryRank}|hyperpage}{43}
\indexentry{StableRank@\texttt  {StableRank}|hyperpage}{43}
\indexentry{IsHomalgRingMap@\texttt  {IsHomalgRingMap}|hyperpage}{44}
\indexentry{IsHomalgRingSelfMap@\texttt  {IsHomalgRingSelfMap}|hyperpage}{44}
\indexentry{IsHomalgRingMapRep@\texttt  {IsHomalgRingMapRep}|hyperpage}{44}
\indexentry{RingMap@\texttt  {RingMap}!constructor for ring maps|hyperpage}{44}
\indexentry{IsMorphism@\texttt  {IsMorphism}!for ring maps|hyperpage}{45}
\indexentry{IsIdentityMorphism@\texttt  {IsIdentityMorphism}!for ring maps|hyperpage}{45}
\indexentry{IsMonomorphism@\texttt  {IsMonomorphism}!for ring maps|hyperpage}{45}
\indexentry{IsEpimorphism@\texttt  {IsEpimorphism}!for ring maps|hyperpage}{45}
\indexentry{IsIsomorphism@\texttt  {IsIsomorphism}!for ring maps|hyperpage}{45}
\indexentry{IsAutomorphism@\texttt  {IsAutomorphism}!for ring maps|hyperpage}{45}
\indexentry{Source@\texttt  {Source}!for ring maps|hyperpage}{46}
\indexentry{Range@\texttt  {Range}!for ring maps|hyperpage}{46}
\indexentry{DegreeOfMorphism@\texttt  {DegreeOfMorphism}!for ring maps|hyperpage}{46}
\indexentry{CoordinateRingOfGraph@\texttt  {CoordinateRingOfGraph}!for ring maps|hyperpage}{46}
\indexentry{KernelSubmodule@\texttt  {KernelSubmodule}!for ring maps|hyperpage}{46}
\indexentry{KernelEmb@\texttt  {KernelEmb}!for ring maps|hyperpage}{46}
\indexentry{Kernel@\texttt  {Kernel}!for ring maps|hyperpage}{46}
\indexentry{IsHomalgMatrix@\texttt  {IsHomalgMatrix}|hyperpage}{47}
\indexentry{IsHomalgInternalMatrixRep@\texttt  {IsHomalgInternalMatrixRep}|hyperpage}{47}
\indexentry{HomalgInitialMatrix@\texttt  {HomalgInitialMatrix}!constructor for initial matrices filled with zeros|hyperpage}{47}
\indexentry{HomalgInitialIdentityMatrix@\texttt  {HomalgInitialIdentityMatrix}!constructor for initial quadratic matrices with ones on the diagonal|hyperpage}{48}
\indexentry{HomalgZeroMatrix@\texttt  {HomalgZeroMatrix}!constructor for zero matrices|hyperpage}{49}
\indexentry{HomalgIdentityMatrix@\texttt  {HomalgIdentityMatrix}!constructor for identity matrices|hyperpage}{49}
\indexentry{HomalgVoidMatrix@\texttt  {HomalgVoidMatrix}!constructor for void matrices|hyperpage}{49}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a listlist|hyperpage}{49}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a list|hyperpage}{49}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a string of a listlist|hyperpage}{49}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a string of a list|hyperpage}{49}
\indexentry{HomalgDiagonalMatrix@\texttt  {HomalgDiagonalMatrix}!constructor for diagonal matrices|hyperpage}{51}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!copy a matrix over a different ring|hyperpage}{51}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!copy a matrix over a different ring (right)|hyperpage}{51}
\indexentry{IsZero@\texttt  {IsZero}!for matrices|hyperpage}{52}
\indexentry{IsIdentityMatrix@\texttt  {IsIdentityMatrix}|hyperpage}{52}
\indexentry{IsPermutationMatrix@\texttt  {IsPermutationMatrix}|hyperpage}{52}
\indexentry{IsSpecialSubidentityMatrix@\texttt  {IsSpecialSubidentityMatrix}|hyperpage}{52}
\indexentry{IsSubidentityMatrix@\texttt  {IsSubidentityMatrix}|hyperpage}{53}
\indexentry{IsLeftRegularMatrix@\texttt  {IsLeftRegularMatrix}|hyperpage}{53}
\indexentry{IsRightRegularMatrix@\texttt  {IsRightRegularMatrix}|hyperpage}{53}
\indexentry{IsInvertibleMatrix@\texttt  {IsInvertibleMatrix}|hyperpage}{53}
\indexentry{IsLeftInvertibleMatrix@\texttt  {IsLeftInvertibleMatrix}|hyperpage}{53}
\indexentry{IsRightInvertibleMatrix@\texttt  {IsRightInvertibleMatrix}|hyperpage}{53}
\indexentry{IsEmptyMatrix@\texttt  {IsEmptyMatrix}|hyperpage}{53}
\indexentry{IsDiagonalMatrix@\texttt  {IsDiagonalMatrix}|hyperpage}{53}
\indexentry{IsScalarlMatrix@\texttt  {IsScalarlMatrix}|hyperpage}{54}
\indexentry{IsUpperTriangularMatrix@\texttt  {IsUpperTriangularMatrix}|hyperpage}{54}
\indexentry{IsLowerTriangularMatrix@\texttt  {IsLowerTriangularMatrix}|hyperpage}{54}
\indexentry{IsStrictUpperTriangularMatrix@\texttt  {IsStrictUpperTriangularMatrix}|hyperpage}{54}
\indexentry{IsStrictLowerTriangularMatrix@\texttt  {IsStrictLowerTriangularMatrix}|hyperpage}{54}
\indexentry{IsUpperStairCaseMatrix@\texttt  {IsUpperStairCaseMatrix}|hyperpage}{54}
\indexentry{IsLowerStairCaseMatrix@\texttt  {IsLowerStairCaseMatrix}|hyperpage}{54}
\indexentry{IsTriangularMatrix@\texttt  {IsTriangularMatrix}|hyperpage}{54}
\indexentry{IsBasisOfRowsMatrix@\texttt  {IsBasisOfRowsMatrix}|hyperpage}{55}
\indexentry{IsBasisOfColumnsMatrix@\texttt  {IsBasisOfColumnsMatrix}|hyperpage}{55}
\indexentry{IsReducedBasisOfRowsMatrix@\texttt  {IsReducedBasisOfRowsMatrix}|hyperpage}{55}
\indexentry{IsReducedBasisOfColumnsMatrix@\texttt  {IsReducedBasisOfColumnsMatrix}|hyperpage}{55}
\indexentry{IsMutableMatrix@\texttt  {IsMutableMatrix}|hyperpage}{55}
\indexentry{IsInitialMatrix@\texttt  {IsInitialMatrix}|hyperpage}{55}
\indexentry{IsInitialIdentityMatrix@\texttt  {IsInitialIdentityMatrix}|hyperpage}{55}
\indexentry{IsVoidMatrix@\texttt  {IsVoidMatrix}|hyperpage}{55}
\indexentry{NrRows@\texttt  {NrRows}|hyperpage}{56}
\indexentry{NrColumns@\texttt  {NrColumns}|hyperpage}{56}
\indexentry{DeterminantMat@\texttt  {DeterminantMat}|hyperpage}{56}
\indexentry{ZeroRows@\texttt  {ZeroRows}|hyperpage}{56}
\indexentry{ZeroColumns@\texttt  {ZeroColumns}|hyperpage}{56}
\indexentry{NonZeroRows@\texttt  {NonZeroRows}|hyperpage}{56}
\indexentry{NonZeroColumns@\texttt  {NonZeroColumns}|hyperpage}{56}
\indexentry{PositionOfFirstNonZeroEntryPerRow@\texttt  {PositionOfFirstNonZeroEntryPerRow}|hyperpage}{57}
\indexentry{PositionOfFirstNonZeroEntryPerColumn@\texttt  {PositionOfFirstNonZeroEntryPerColumn}|hyperpage}{57}
\indexentry{DegreesOfEntries@\texttt  {DegreesOfEntries}|hyperpage}{57}
\indexentry{RowRankOfMatrix@\texttt  {RowRankOfMatrix}|hyperpage}{57}
\indexentry{ColumnRankOfMatrix@\texttt  {ColumnRankOfMatrix}|hyperpage}{57}
\indexentry{LeftInverse@\texttt  {LeftInverse}!for matrices|hyperpage}{57}
\indexentry{RightInverse@\texttt  {RightInverse}!for matrices|hyperpage}{57}
\indexentry{HomalgRing@\texttt  {HomalgRing}!for matrices|hyperpage}{58}
\indexentry{Involution@\texttt  {Involution}!for matrices|hyperpage}{58}
\indexentry{CertainRows@\texttt  {CertainRows}!for matrices|hyperpage}{58}
\indexentry{CertainColumns@\texttt  {CertainColumns}!for matrices|hyperpage}{58}
\indexentry{UnionOfRows@\texttt  {UnionOfRows}!for matrices|hyperpage}{58}
\indexentry{UnionOfColumns@\texttt  {UnionOfColumns}!for matrices|hyperpage}{59}
\indexentry{DiagMat@\texttt  {DiagMat}!for matrices|hyperpage}{59}
\indexentry{KroneckerMat@\texttt  {KroneckerMat}!for matrices|hyperpage}{59}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!for ring elements and matrices|hyperpage}{59}
\indexentry{+@\texttt  {\texttt  {\char 92\relax }+}!for matrices|hyperpage}{59}
\indexentry{-@\texttt  {\texttt  {\char 92\relax }-}!for matrices|hyperpage}{59}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!for composable matrices|hyperpage}{59}
\indexentry{=@\texttt  {\texttt  {\char 92\relax }=}!for matrices|hyperpage}{60}
\indexentry{GetColumnIndependentUnitPositions@\texttt  {GetColumnIndependentUnitPositions}!for matrices|hyperpage}{60}
\indexentry{GetRowIndependentUnitPositions@\texttt  {GetRowIndependentUnitPositions}!for matrices|hyperpage}{60}
\indexentry{GetUnitPosition@\texttt  {GetUnitPosition}!for matrices|hyperpage}{61}
\indexentry{BasisOfRowModule@\texttt  {BasisOfRowModule}!for matrices|hyperpage}{61}
\indexentry{BasisOfColumnModule@\texttt  {BasisOfColumnModule}!for matrices|hyperpage}{61}
\indexentry{DecideZeroRows@\texttt  {DecideZeroRows}!for pairs of matrices|hyperpage}{61}
\indexentry{DecideZeroColumns@\texttt  {DecideZeroColumns}!for pairs of matrices|hyperpage}{62}
\indexentry{SyzygiesGeneratorsOfRows@\texttt  {SyzygiesGeneratorsOfRows}!for matrices|hyperpage}{62}
\indexentry{SyzygiesGeneratorsOfColumns@\texttt  {SyzygiesGeneratorsOfColumns}!for matrices|hyperpage}{62}
\indexentry{SyzygiesGeneratorsOfRows@\texttt  {SyzygiesGeneratorsOfRows}!for pairs of matrices|hyperpage}{62}
\indexentry{SyzygiesGeneratorsOfColumns@\texttt  {SyzygiesGeneratorsOfColumns}!for pairs of matrices|hyperpage}{62}
\indexentry{ReducedBasisOfRowModule@\texttt  {ReducedBasisOfRowModule}!for matrices|hyperpage}{63}
\indexentry{ReducedBasisOfColumnModule@\texttt  {ReducedBasisOfColumnModule}!for matrices|hyperpage}{63}
\indexentry{ReducedSyzygiesGeneratorsOfRows@\texttt  {ReducedSyzygiesGeneratorsOfRows}!for matrices|hyperpage}{63}
\indexentry{ReducedSyzygiesGeneratorsOfColumns@\texttt  {ReducedSyzygiesGeneratorsOfColumns}!for matrices|hyperpage}{63}
\indexentry{BasisOfRowsCoeff@\texttt  {BasisOfRowsCoeff}!for matrices|hyperpage}{63}
\indexentry{BasisOfColumnsCoeff@\texttt  {BasisOfColumnsCoeff}!for matrices|hyperpage}{63}
\indexentry{DecideZeroRowsEffectively@\texttt  {DecideZeroRowsEffectively}!for pairs of matrices|hyperpage}{64}
\indexentry{DecideZeroColumnsEffectively@\texttt  {DecideZeroColumnsEffectively}!for pairs of matrices|hyperpage}{64}
\indexentry{BasisOfRows@\texttt  {BasisOfRows}!for matrices|hyperpage}{64}
\indexentry{BasisOfRows@\texttt  {BasisOfRows}!for pairs of matrices|hyperpage}{64}
\indexentry{BasisOfColumns@\texttt  {BasisOfColumns}!for matrices|hyperpage}{64}
\indexentry{BasisOfColumns@\texttt  {BasisOfColumns}!for pairs of matrices|hyperpage}{64}
\indexentry{DecideZero@\texttt  {DecideZero}!for matrices and relations|hyperpage}{64}
\indexentry{SyzygiesOfRows@\texttt  {SyzygiesOfRows}!for matrices|hyperpage}{65}
\indexentry{SyzygiesOfRows@\texttt  {SyzygiesOfRows}!for pairs of matrices|hyperpage}{65}
\indexentry{SyzygiesOfColumns@\texttt  {SyzygiesOfColumns}!for matrices|hyperpage}{65}
\indexentry{SyzygiesOfColumns@\texttt  {SyzygiesOfColumns}!for pairs of matrices|hyperpage}{65}
\indexentry{ReducedSyzygiesOfRows@\texttt  {ReducedSyzygiesOfRows}!for matrices|hyperpage}{65}
\indexentry{ReducedSyzygiesOfRows@\texttt  {ReducedSyzygiesOfRows}!for pairs of matrices|hyperpage}{65}
\indexentry{ReducedSyzygiesOfColumns@\texttt  {ReducedSyzygiesOfColumns}!for matrices|hyperpage}{65}
\indexentry{ReducedSyzygiesOfColumns@\texttt  {ReducedSyzygiesOfColumns}!for pairs of matrices|hyperpage}{65}
\indexentry{RightDivide@\texttt  {RightDivide}!for pairs of matrices|hyperpage}{65}
\indexentry{LeftDivide@\texttt  {LeftDivide}!for pairs of matrices|hyperpage}{66}
\indexentry{RightDivide@\texttt  {RightDivide}!for triples of matrices|hyperpage}{66}
\indexentry{RightDivide@\texttt  {RightDivide}!for pairs matrices and a set of relations|hyperpage}{66}
\indexentry{LeftDivide@\texttt  {LeftDivide}!for triples of matrices|hyperpage}{67}
\indexentry{LeftDivide@\texttt  {LeftDivide}!for pairs matrices and a set of relations|hyperpage}{67}
\indexentry{GenerateSameRowModule@\texttt  {GenerateSameRowModule}!for pairs of matrices|hyperpage}{69}
\indexentry{GenerateSameColumnModule@\texttt  {GenerateSameColumnModule}!for pairs of matrices|hyperpage}{69}
\indexentry{IsHomalgRelations@\texttt  {IsHomalgRelations}|hyperpage}{70}
\indexentry{IsHomalgRelationsOfLeftModule@\texttt  {IsHomalgRelationsOfLeftModule}|hyperpage}{70}
\indexentry{IsHomalgRelationsOfRightModule@\texttt  {IsHomalgRelationsOfRightModule}|hyperpage}{70}
\indexentry{IsRelationsOfFinitelyPresentedModuleRep@\texttt  {IsRelationsOfFinitelyPresentedModuleRep}|hyperpage}{71}
\indexentry{CanBeUsedToDecideZeroEffectively@\texttt  {CanBeUsedToDecideZeroEffectively}|hyperpage}{71}
\indexentry{IsInjectivePresentation@\texttt  {IsInjectivePresentation}|hyperpage}{71}
\indexentry{FreeResolution@\texttt  {FreeResolution}|hyperpage}{71}
\indexentry{IsHomalgGenerators@\texttt  {IsHomalgGenerators}|hyperpage}{72}
\indexentry{IsHomalgGeneratorsOfLeftModule@\texttt  {IsHomalgGeneratorsOfLeftModule}|hyperpage}{72}
\indexentry{IsHomalgGeneratorsOfRightModule@\texttt  {IsHomalgGeneratorsOfRightModule}|hyperpage}{72}
\indexentry{IsGeneratorsOfFinitelyGeneratedModuleRep@\texttt  {IsGeneratorsOfFinitelyGeneratedModuleRep}|hyperpage}{73}
\indexentry{IsReduced@\texttt  {IsReduced}|hyperpage}{73}
\indexentry{ProcedureToReadjustGenerators@\texttt  {ProcedureToReadjustGenerators}|hyperpage}{73}
\indexentry{IsHomalgModule@\texttt  {IsHomalgModule}|hyperpage}{74}
\indexentry{IsFinitelyPresentedModuleOrSubmoduleRep@\texttt  {IsFinitelyPresentedModuleOrSubmoduleRep}|hyperpage}{74}
\indexentry{IsFinitelyPresentedModuleRep@\texttt  {IsFinitelyPresentedModuleRep}|hyperpage}{75}
\indexentry{IsFinitelyPresentedSubmoduleRep@\texttt  {IsFinitelyPresentedSubmoduleRep}|hyperpage}{75}
\indexentry{LeftPresentation@\texttt  {LeftPresentation}!constructor for left modules|hyperpage}{75}
\indexentry{RightPresentation@\texttt  {RightPresentation}!constructor for right modules|hyperpage}{76}
\indexentry{HomalgFreeLeftModule@\texttt  {HomalgFreeLeftModule}!constructor for free left modules|hyperpage}{76}
\indexentry{HomalgFreeRightModule@\texttt  {HomalgFreeRightModule}!constructor for free right modules|hyperpage}{76}
\indexentry{HomalgZeroLeftModule@\texttt  {HomalgZeroLeftModule}!constructor for zero left modules|hyperpage}{77}
\indexentry{HomalgZeroRightModule@\texttt  {HomalgZeroRightModule}!constructor for zero right modules|hyperpage}{77}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!transfer a module over a different ring|hyperpage}{77}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!transfer a module over a different ring (right)|hyperpage}{77}
\indexentry{Subobject@\texttt  {Subobject}!constructor for submodules using maps|hyperpage}{79}
\indexentry{Subobject@\texttt  {Subobject}!constructor for submodules using matrices|hyperpage}{79}
\indexentry{Subobject@\texttt  {Subobject}!constructor for submodules using a list of ring elements|hyperpage}{79}
\indexentry{LeftSubmodule@\texttt  {LeftSubmodule}!constructor for left submodules|hyperpage}{79}
\indexentry{RightSubmodule@\texttt  {RightSubmodule}!constructor for right submodules|hyperpage}{80}
\indexentry{IsFree@\texttt  {IsFree}|hyperpage}{81}
\indexentry{IsStablyFree@\texttt  {IsStablyFree}|hyperpage}{81}
\indexentry{IsProjective@\texttt  {IsProjective}|hyperpage}{81}
\indexentry{FiniteFreeResolutionExists@\texttt  {FiniteFreeResolutionExists}|hyperpage}{81}
\indexentry{IsReflexive@\texttt  {IsReflexive}|hyperpage}{81}
\indexentry{IsTorsionFree@\texttt  {IsTorsionFree}|hyperpage}{81}
\indexentry{IsArtinian@\texttt  {IsArtinian}!for modules|hyperpage}{81}
\indexentry{IsCyclic@\texttt  {IsCyclic}|hyperpage}{82}
\indexentry{IsTorsion@\texttt  {IsTorsion}|hyperpage}{82}
\indexentry{IsHolonomic@\texttt  {IsHolonomic}|hyperpage}{82}
\indexentry{IsPure@\texttt  {IsPure}|hyperpage}{82}
\indexentry{HasConstantRank@\texttt  {HasConstantRank}|hyperpage}{82}
\indexentry{ConstructedAsAnIdeal@\texttt  {ConstructedAsAnIdeal}|hyperpage}{82}
\indexentry{IsPrimeIdeal@\texttt  {IsPrimeIdeal}|hyperpage}{82}
\indexentry{TheZeroMorphism@\texttt  {TheZeroMorphism}|hyperpage}{83}
\indexentry{TheIdentityMorphism@\texttt  {TheIdentityMorphism}|hyperpage}{83}
\indexentry{FullSubmodule@\texttt  {FullSubmodule}|hyperpage}{83}
\indexentry{EmbeddingInSuperObject@\texttt  {EmbeddingInSuperObject}|hyperpage}{83}
\indexentry{FactorObject@\texttt  {FactorObject}|hyperpage}{83}
\indexentry{ResidueClassRing@\texttt  {ResidueClassRing}|hyperpage}{83}
\indexentry{UnderlyingSubobject@\texttt  {UnderlyingSubobject}|hyperpage}{83}
\indexentry{NatTrIdToHomHomR@\texttt  {NatTrIdToHomHom{\textunderscore }R}!for maps|hyperpage}{84}
\indexentry{PrimaryDecomposition@\texttt  {PrimaryDecomposition}|hyperpage}{84}
\indexentry{ElementaryDivisors@\texttt  {ElementaryDivisors}|hyperpage}{84}
\indexentry{RankOfModule@\texttt  {RankOfModule}|hyperpage}{84}
\indexentry{ProjectiveDimension@\texttt  {ProjectiveDimension}|hyperpage}{84}
\indexentry{DegreeOfTorsionFreeness@\texttt  {DegreeOfTorsionFreeness}|hyperpage}{84}
\indexentry{Codim@\texttt  {Codim}|hyperpage}{84}
\indexentry{PurityFiltration@\texttt  {PurityFiltration}|hyperpage}{85}
\indexentry{CodegreeOfPurity@\texttt  {CodegreeOfPurity}|hyperpage}{85}
\indexentry{BettiDiagram@\texttt  {BettiDiagram}!for modules|hyperpage}{85}
\indexentry{CastelnuovoMumfordRegularity@\texttt  {CastelnuovoMumfordRegularity}|hyperpage}{85}
\indexentry{HomalgRing@\texttt  {HomalgRing}!for modules|hyperpage}{85}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for modules|hyperpage}{85}
\indexentry{UnderlyingObject@\texttt  {UnderlyingObject}!for submodules|hyperpage}{86}
\indexentry{SuperObject@\texttt  {SuperObject}!for submodules|hyperpage}{86}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!constructor for ideal multiples|hyperpage}{86}
\indexentry{SubmoduleQuotient@\texttt  {SubmoduleQuotient}!for submodules|hyperpage}{87}
\indexentry{Saturate@\texttt  {Saturate}!for ideals|hyperpage}{87}
\indexentry{IsHomalgMap@\texttt  {IsHomalgMap}|hyperpage}{89}
\indexentry{IsHomalgSelfMap@\texttt  {IsHomalgSelfMap}|hyperpage}{89}
\indexentry{IsMapOfFinitelyGeneratedModulesRep@\texttt  {IsMapOfFinitelyGeneratedModulesRep}|hyperpage}{89}
\indexentry{HomalgMap@\texttt  {HomalgMap}!constructor for maps|hyperpage}{90}
\indexentry{HomalgMap@\texttt  {HomalgMap}!constructor for maps between free modules|hyperpage}{90}
\indexentry{HomalgZeroMap@\texttt  {HomalgZeroMap}!constructor for zero maps|hyperpage}{91}
\indexentry{HomalgIdentityMap@\texttt  {HomalgIdentityMap}!constructor for identity maps|hyperpage}{92}
\indexentry{IsMorphism@\texttt  {IsMorphism}!for maps|hyperpage}{92}
\indexentry{IsGeneralizedMorphism@\texttt  {IsGeneralizedMorphism}!for maps|hyperpage}{92}
\indexentry{IsGeneralizedEpimorphism@\texttt  {IsGeneralizedEpimorphism}!for maps|hyperpage}{92}
\indexentry{IsGeneralizedMonomorphism@\texttt  {IsGeneralizedMonomorphism}!for maps|hyperpage}{93}
\indexentry{IsGeneralizedIsomorphism@\texttt  {IsGeneralizedIsomorphism}!for maps|hyperpage}{93}
\indexentry{IsIdentityMorphism@\texttt  {IsIdentityMorphism}!for maps|hyperpage}{93}
\indexentry{IsMonomorphism@\texttt  {IsMonomorphism}!for maps|hyperpage}{93}
\indexentry{IsEpimorphism@\texttt  {IsEpimorphism}!for maps|hyperpage}{93}
\indexentry{IsSplitMonomorphism@\texttt  {IsSplitMonomorphism}!for maps|hyperpage}{93}
\indexentry{IsSplitEpimorphism@\texttt  {IsSplitEpimorphism}!for maps|hyperpage}{93}
\indexentry{IsIsomorphism@\texttt  {IsIsomorphism}!for maps|hyperpage}{93}
\indexentry{IsAutomorphism@\texttt  {IsAutomorphism}!for maps|hyperpage}{94}
\indexentry{Source@\texttt  {Source}!for maps|hyperpage}{94}
\indexentry{Range@\texttt  {Range}!for maps|hyperpage}{94}
\indexentry{DegreeOfMorphism@\texttt  {DegreeOfMorphism}!for maps|hyperpage}{94}
\indexentry{CokernelEpi@\texttt  {CokernelEpi}!for maps|hyperpage}{94}
\indexentry{CokernelNaturalGeneralizedIsomorphism@\texttt  {CokernelNaturalGeneralizedIsomorphism}!for maps|hyperpage}{94}
\indexentry{KernelSubmodule@\texttt  {KernelSubmodule}!for maps|hyperpage}{94}
\indexentry{KernelEmb@\texttt  {KernelEmb}!for maps|hyperpage}{95}
\indexentry{ImageSubmodule@\texttt  {ImageSubmodule}!for maps|hyperpage}{95}
\indexentry{ImageModuleEmb@\texttt  {ImageModuleEmb}!for maps|hyperpage}{95}
\indexentry{ImageModuleEpi@\texttt  {ImageModuleEpi}!for maps|hyperpage}{95}
\indexentry{MorphismAidMap@\texttt  {MorphismAidMap}!for maps|hyperpage}{95}
\indexentry{HomalgRing@\texttt  {HomalgRing}!for maps|hyperpage}{95}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for maps|hyperpage}{96}
\indexentry{PreInverse@\texttt  {PreInverse}!for maps|hyperpage}{97}
\indexentry{IsHomalgComplex@\texttt  {IsHomalgComplex}|hyperpage}{98}
\indexentry{IsComplexOfFinitelyPresentedObjectsRep@\texttt  {IsComplexOfFinitelyPresentedObjectsRep}|hyperpage}{98}
\indexentry{IsCocomplexOfFinitelyPresentedObjectsRep@\texttt  {IsCocomplexOfFinitelyPresentedObjectsRep}|hyperpage}{98}
\indexentry{HomalgComplex@\texttt  {HomalgComplex}!constructor for complexes given a module|hyperpage}{98}
\indexentry{HomalgComplex@\texttt  {HomalgComplex}!constructor for complexes given a map|hyperpage}{98}
\indexentry{HomalgComplex@\texttt  {HomalgComplex}!constructor for complexes given a complex|hyperpage}{98}
\indexentry{HomalgComplex@\texttt  {HomalgComplex}!constructor for complexes given a chain map|hyperpage}{98}
\indexentry{HomalgCocomplex@\texttt  {HomalgCocomplex}!constructor for cocomplexes given a module|hyperpage}{100}
\indexentry{HomalgCocomplex@\texttt  {HomalgCocomplex}!constructor for cocomplexes given a map|hyperpage}{100}
\indexentry{HomalgCocomplex@\texttt  {HomalgCocomplex}!constructor for cocomplexes given a complex|hyperpage}{100}
\indexentry{HomalgCocomplex@\texttt  {HomalgCocomplex}!constructor for cocomplexes given a chain map|hyperpage}{100}
\indexentry{IsSequence@\texttt  {IsSequence}|hyperpage}{101}
\indexentry{IsComplex@\texttt  {IsComplex}|hyperpage}{101}
\indexentry{IsAcyclic@\texttt  {IsAcyclic}|hyperpage}{101}
\indexentry{IsRightAcyclic@\texttt  {IsRightAcyclic}|hyperpage}{101}
\indexentry{IsLeftAcyclic@\texttt  {IsLeftAcyclic}|hyperpage}{101}
\indexentry{IsGradedObject@\texttt  {IsGradedObject}|hyperpage}{101}
\indexentry{IsExactSequence@\texttt  {IsExactSequence}|hyperpage}{101}
\indexentry{IsShortExactSequence@\texttt  {IsShortExactSequence}|hyperpage}{102}
\indexentry{IsSplitShortExactSequence@\texttt  {IsSplitShortExactSequence}|hyperpage}{102}
\indexentry{IsTriangle@\texttt  {IsTriangle}|hyperpage}{102}
\indexentry{IsExactTriangle@\texttt  {IsExactTriangle}|hyperpage}{102}
\indexentry{BettiDiagram@\texttt  {BettiDiagram}!for complexes|hyperpage}{102}
\indexentry{Add@\texttt  {Add}!to complexes given a map|hyperpage}{102}
\indexentry{Add@\texttt  {Add}!to complexes given a matrix|hyperpage}{102}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for complexes|hyperpage}{103}
\indexentry{IsHomalgChainMap@\texttt  {IsHomalgChainMap}|hyperpage}{106}
\indexentry{IsHomalgChainSelfMap@\texttt  {IsHomalgChainSelfMap}|hyperpage}{106}
\indexentry{IsChainMapOfFinitelyPresentedObjectsRep@\texttt  {IsChainMapOfFinitelyPresentedObjectsRep}|hyperpage}{106}
\indexentry{IsCochainMapOfFinitelyPresentedObjectsRep@\texttt  {IsCochain}\discretionary {-}{}{}\texttt  {Map}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Finitely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {ObjectsRep}|hyperpage}{106}
\indexentry{HomalgChainMap@\texttt  {HomalgChainMap}!constructor for chain maps given a map|hyperpage}{107}
\indexentry{IsMorphism@\texttt  {IsMorphism}!for chain maps|hyperpage}{108}
\indexentry{IsGeneralizedMorphism@\texttt  {IsGeneralizedMorphism}!for chain maps|hyperpage}{108}
\indexentry{IsGeneralizedEpimorphism@\texttt  {IsGeneralizedEpimorphism}!for chain maps|hyperpage}{108}
\indexentry{IsGeneralizedMonomorphism@\texttt  {IsGeneralizedMonomorphism}!for chain maps|hyperpage}{108}
\indexentry{IsGeneralizedIsomorphism@\texttt  {IsGeneralizedIsomorphism}!for chain maps|hyperpage}{108}
\indexentry{IsIdentityMorphism@\texttt  {IsIdentityMorphism}!for chain maps|hyperpage}{108}
\indexentry{IsMonomorphism@\texttt  {IsMonomorphism}!for chain maps|hyperpage}{108}
\indexentry{IsEpimorphism@\texttt  {IsEpimorphism}!for chain maps|hyperpage}{109}
\indexentry{IsSplitMonomorphism@\texttt  {IsSplitMonomorphism}!for chain maps|hyperpage}{109}
\indexentry{IsSplitEpimorphism@\texttt  {IsSplitEpimorphism}!for chain maps|hyperpage}{109}
\indexentry{IsIsomorphism@\texttt  {IsIsomorphism}!for chain maps|hyperpage}{109}
\indexentry{IsAutomorphism@\texttt  {IsAutomorphism}!for chain maps|hyperpage}{109}
\indexentry{IsGradedMorphism@\texttt  {IsGradedMorphism}!for chain maps|hyperpage}{109}
\indexentry{IsQuasiIsomorphism@\texttt  {IsQuasiIsomorphism}!for chain maps|hyperpage}{109}
\indexentry{Source@\texttt  {Source}!for chain maps|hyperpage}{110}
\indexentry{Range@\texttt  {Range}!for chain maps|hyperpage}{110}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for chain maps|hyperpage}{110}
\indexentry{IsHomalgBicomplex@\texttt  {IsHomalgBicomplex}|hyperpage}{111}
\indexentry{IsBicomplexOfFinitelyPresentedObjectsRep@\texttt  {IsBicomplexOfFinitelyPresentedObjectsRep}|hyperpage}{111}
\indexentry{IsBicocomplexOfFinitelyPresentedObjectsRep@\texttt  {IsBicocomplex}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Finitely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {ObjectsRep}|hyperpage}{111}
\indexentry{HomalgBicomplex@\texttt  {HomalgBicomplex}!constructor for bicomplexes given a complex of complexes|hyperpage}{112}
\indexentry{IsBisequence@\texttt  {IsBisequence}|hyperpage}{113}
\indexentry{IsBicomplex@\texttt  {IsBicomplex}|hyperpage}{113}
\indexentry{IsTransposedWRTTheAssociatedComplex@\texttt  {IsTransposedWRTTheAssociatedComplex}|hyperpage}{113}
\indexentry{TotalComplex@\texttt  {TotalComplex}|hyperpage}{113}
\indexentry{SpectralSequence@\texttt  {SpectralSequence}!for bicomplexes|hyperpage}{113}
\indexentry{UnderlyingComplex@\texttt  {UnderlyingComplex}|hyperpage}{113}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for bicomplexes|hyperpage}{113}
\indexentry{IsHomalgBigradedObject@\texttt  {IsHomalgBigradedObject}|hyperpage}{115}
\indexentry{IsHomalgBigradedObjectAssociatedToAnExactCouple@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Bigraded}\discretionary {-}{}{}\texttt  {Object}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {An}\discretionary {-}{}{}\texttt  {Exact}\discretionary {-}{}{}\texttt  {Couple}|hyperpage}{115}
\indexentry{IsHomalgBigradedObjectAssociatedToAFilteredComplex@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Bigraded}\discretionary {-}{}{}\texttt  {Object}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {Filtered}\discretionary {-}{}{}\texttt  {Complex}|hyperpage}{115}
\indexentry{IsHomalgBigradedObjectAssociatedToABicomplex@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Bigraded}\discretionary {-}{}{}\texttt  {Object}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {Bicomplex}|hyperpage}{115}
\indexentry{IsBigradedObjectOfFinitelyPresentedObjectsRep@\texttt  {IsBigraded}\discretionary {-}{}{}\texttt  {Object}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Finitely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {ObjectsRep}|hyperpage}{116}
\indexentry{HomalgBigradedObject@\texttt  {HomalgBigradedObject}!constructor for bigraded objects given a bicomplex|hyperpage}{116}
\indexentry{AsDifferentialObject@\texttt  {AsDifferentialObject}!for homalg bigraded objects stemming from a bicomplex|hyperpage}{116}
\indexentry{DefectOfExactness@\texttt  {DefectOfExactness}!for homalg differential bigraded objects|hyperpage}{117}
\indexentry{IsEndowedWithDifferential@\texttt  {IsEndowedWithDifferential}|hyperpage}{119}
\indexentry{IsStableSheet@\texttt  {IsStableSheet}|hyperpage}{119}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for bigraded objects|hyperpage}{119}
\indexentry{IsHomalgSpectralSequence@\texttt  {IsHomalgSpectralSequence}|hyperpage}{120}
\indexentry{IsHomalgSpectralSequenceAssociatedToAnExactCouple@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Spectral}\discretionary {-}{}{}\texttt  {Sequence}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {An}\discretionary {-}{}{}\texttt  {Exact}\discretionary {-}{}{}\texttt  {Couple}|hyperpage}{120}
\indexentry{IsHomalgSpectralSequenceAssociatedToAFilteredComplex@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Spectral}\discretionary {-}{}{}\texttt  {Sequence}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {Filtered}\discretionary {-}{}{}\texttt  {Complex}|hyperpage}{120}
\indexentry{IsHomalgSpectralSequenceAssociatedToABicomplex@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Spectral}\discretionary {-}{}{}\texttt  {Sequence}\discretionary {-}{}{}\texttt  {Associated}\discretionary {-}{}{}\texttt  {To}\discretionary {-}{}{}\texttt  {A}\discretionary {-}{}{}\texttt  {Bicomplex}|hyperpage}{121}
\indexentry{IsSpectralSequenceOfFinitelyPresentedObjectsRep@\texttt  {IsSpectral}\discretionary {-}{}{}\texttt  {Sequence}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Finitely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {ObjectsRep}|hyperpage}{121}
\indexentry{IsSpectralCosequenceOfFinitelyPresentedObjectsRep@\texttt  {IsSpectral}\discretionary {-}{}{}\texttt  {Cosequence}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Finitely}\discretionary {-}{}{}\texttt  {Presented}\discretionary {-}{}{}\texttt  {ObjectsRep}|hyperpage}{121}
\indexentry{HomalgSpectralSequence@\texttt  {HomalgSpectralSequence}!constructor for spectral sequences given a bicomplex|hyperpage}{121}
\indexentry{HomalgSpectralSequence@\texttt  {HomalgSpectralSequence}!constructor for spectral sequences without a special sheet given a bicomplex|hyperpage}{121}
\indexentry{HomalgSpectralSequence@\texttt  {HomalgSpectralSequence}!constructor for spectral sequences without bound given a bicomplex|hyperpage}{121}
\indexentry{HomalgSpectralSequence@\texttt  {HomalgSpectralSequence}!constructor for spectral sequences without bound and without a special sheet given a bicomplex|hyperpage}{121}
\indexentry{GeneralizedEmbeddingsInTotalObjects@\texttt  {GeneralizedEmbeddingsInTotalObjects}|hyperpage}{123}
\indexentry{GeneralizedEmbeddingsInTotalDefects@\texttt  {GeneralizedEmbeddingsInTotalDefects}|hyperpage}{123}
\indexentry{ByASmallerPresentation@\texttt  {ByASmallerPresentation}!for spectral sequences|hyperpage}{123}
\indexentry{IsHomalgFunctor@\texttt  {IsHomalgFunctor}|hyperpage}{126}
\indexentry{IsHomalgFunctorRep@\texttt  {IsHomalgFunctorRep}|hyperpage}{126}
\indexentry{CreateHomalgFunctor@\texttt  {CreateHomalgFunctor}!constructor for functors|hyperpage}{126}
\indexentry{InsertObjectInMultiFunctor@\texttt  {InsertObjectInMultiFunctor}!constructor for functors given a multi-functor and an object|hyperpage}{126}
\indexentry{RightSatelliteOfCofunctor@\texttt  {RightSatelliteOfCofunctor}!constructor of the right satellite of a contravariant functor|hyperpage}{127}
\indexentry{LeftSatelliteOfFunctor@\texttt  {LeftSatelliteOfFunctor}!constructor of the left satellite of a covariant functor|hyperpage}{127}
\indexentry{RightDerivedCofunctor@\texttt  {RightDerivedCofunctor}!constructor of the right derived functor of a contravariant functor|hyperpage}{128}
\indexentry{LeftDerivedFunctor@\texttt  {LeftDerivedFunctor}!constructor of the left derived functor of a covariant functor|hyperpage}{128}
\indexentry{ComposeFunctors@\texttt  {ComposeFunctors}!constructor for functors given two functors|hyperpage}{128}
\indexentry{Genesis@\texttt  {Genesis}|hyperpage}{129}
\indexentry{functorCokernel@\texttt  {functor{\textunderscore }Cokernel}|hyperpage}{130}
\indexentry{Cokernel@\texttt  {Cokernel}|hyperpage}{131}
\indexentry{functorImageModule@\texttt  {functor{\textunderscore }ImageModule}|hyperpage}{132}
\indexentry{ImageModule@\texttt  {ImageModule}|hyperpage}{132}
\indexentry{functorKernel@\texttt  {functor{\textunderscore }Kernel}|hyperpage}{133}
\indexentry{Kernel@\texttt  {Kernel}!for maps|hyperpage}{133}
\indexentry{functorDefectOfExactness@\texttt  {functor{\textunderscore }}\discretionary {-}{}{}\texttt  {Defect}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Exactness}|hyperpage}{134}
\indexentry{DefectOfExactness@\texttt  {DefectOfExactness}|hyperpage}{134}
\indexentry{FunctorHom@\texttt  {Functor{\textunderscore }Hom}|hyperpage}{135}
\indexentry{Hom@\texttt  {Hom}|hyperpage}{136}
\indexentry{FunctorTensorProduct@\texttt  {Functor{\textunderscore }TensorProduct}|hyperpage}{139}
\indexentry{TensorProduct@\texttt  {TensorProduct}|hyperpage}{140}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!TensorProduct|hyperpage}{140}
\indexentry{FunctorExt@\texttt  {Functor{\textunderscore }Ext}|hyperpage}{142}
\indexentry{Ext@\texttt  {Ext}|hyperpage}{142}
\indexentry{FunctorTor@\texttt  {Functor{\textunderscore }Tor}|hyperpage}{143}
\indexentry{Tor@\texttt  {Tor}|hyperpage}{143}
\indexentry{FunctorRHom@\texttt  {Functor{\textunderscore }RHom}|hyperpage}{144}
\indexentry{RHom@\texttt  {RHom}|hyperpage}{144}
\indexentry{FunctorLTensorProduct@\texttt  {Functor{\textunderscore }LTensorProduct}|hyperpage}{147}
\indexentry{LTensorProduct@\texttt  {LTensorProduct}|hyperpage}{147}
\indexentry{FunctorHomHom@\texttt  {Functor{\textunderscore }HomHom}|hyperpage}{150}
\indexentry{FunctorLHomHom@\texttt  {Functor{\textunderscore }LHomHom}|hyperpage}{150}
\indexentry{NameOfFunctor@\texttt  {NameOfFunctor}|hyperpage}{150}
\indexentry{InstallFunctor@\texttt  {InstallFunctor}|hyperpage}{151}
\indexentry{InstallDeltaFunctor@\texttt  {InstallDeltaFunctor}|hyperpage}{151}
\indexentry{ZeroMatrix@\texttt  {ZeroMatrix}!homalgTable entry for initial matrices|hyperpage}{167}
\indexentry{IdentityMatrix@\texttt  {IdentityMatrix}!homalgTable entry for initial identity matrices|hyperpage}{167}
\indexentry{ZeroMatrix@\texttt  {ZeroMatrix}!homalgTable entry|hyperpage}{167}
\indexentry{IdentityMatrix@\texttt  {IdentityMatrix}!homalgTable entry|hyperpage}{168}
\indexentry{Involution@\texttt  {Involution}!homalgTable entry|hyperpage}{168}
\indexentry{CertainRows@\texttt  {CertainRows}!homalgTable entry|hyperpage}{168}
\indexentry{CertainColumns@\texttt  {CertainColumns}!homalgTable entry|hyperpage}{168}
\indexentry{UnionOfRows@\texttt  {UnionOfRows}!homalgTable entry|hyperpage}{168}
\indexentry{UnionOfColumns@\texttt  {UnionOfColumns}!homalgTable entry|hyperpage}{168}
\indexentry{DiagMat@\texttt  {DiagMat}!homalgTable entry|hyperpage}{169}
\indexentry{KroneckerMat@\texttt  {KroneckerMat}!homalgTable entry|hyperpage}{169}
\indexentry{MulMat@\texttt  {MulMat}!homalgTable entry|hyperpage}{169}
\indexentry{AddMat@\texttt  {AddMat}!homalgTable entry|hyperpage}{169}
\indexentry{SubMat@\texttt  {SubMat}!homalgTable entry|hyperpage}{169}
\indexentry{Compose@\texttt  {Compose}!homalgTable entry|hyperpage}{169}
\indexentry{IsZeroMatrix@\texttt  {IsZeroMatrix}!homalgTable entry|hyperpage}{170}
\indexentry{NrRows@\texttt  {NrRows}!homalgTable entry|hyperpage}{170}
\indexentry{NrColumns@\texttt  {NrColumns}!homalgTable entry|hyperpage}{171}
\indexentry{Determinant@\texttt  {Determinant}!homalgTable entry|hyperpage}{172}
\indexentry{AreEqualMatrices@\texttt  {AreEqualMatrices}!homalgTable entry|hyperpage}{173}
\indexentry{IsIdentityMatrix@\texttt  {IsIdentityMatrix}!homalgTable entry|hyperpage}{173}
\indexentry{IsDiagonalMatrix@\texttt  {IsDiagonalMatrix}!homalgTable entry|hyperpage}{174}
\indexentry{ZeroRows@\texttt  {ZeroRows}!homalgTable entry|hyperpage}{175}
\indexentry{ZeroColumns@\texttt  {ZeroColumns}!homalgTable entry|hyperpage}{175}
\indexentry{GetColumnIndependentUnitPositions@\texttt  {GetColumnIndependentUnitPositions}!homalgTable entry|hyperpage}{176}
\indexentry{GetRowIndependentUnitPositions@\texttt  {GetRowIndependentUnitPositions}!homalgTable entry|hyperpage}{177}
\indexentry{GetUnitPosition@\texttt  {GetUnitPosition}!homalgTable entry|hyperpage}{178}
\indexentry{DegreesOfEntries@\texttt  {DegreesOfEntries}!homalgTable entry|hyperpage}{179}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgInitialMatrix|hyperpage}{181}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgInitialIdentityMatrix|hyperpage}{182}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgZeroMatrix|hyperpage}{183}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgIdentityMatrix|hyperpage}{184}
\indexentry{Eval@\texttt  {Eval}!for matrices created with Involution|hyperpage}{185}
\indexentry{Eval@\texttt  {Eval}!for matrices created with CertainRows|hyperpage}{185}
\indexentry{Eval@\texttt  {Eval}!for matrices created with CertainColumns|hyperpage}{186}
\indexentry{Eval@\texttt  {Eval}!for matrices created with UnionOfRows|hyperpage}{187}
\indexentry{Eval@\texttt  {Eval}!for matrices created with UnionOfColumns|hyperpage}{188}
\indexentry{Eval@\texttt  {Eval}!for matrices created with DiagMat|hyperpage}{189}
\indexentry{Eval@\texttt  {Eval}!for matrices created with KroneckerMat|hyperpage}{190}
\indexentry{Eval@\texttt  {Eval}!for matrices created with MulMat|hyperpage}{191}
\indexentry{Eval@\texttt  {Eval}!for matrices created with AddMat|hyperpage}{191}
\indexentry{Eval@\texttt  {Eval}!for matrices created with SubMat|hyperpage}{192}
\indexentry{Eval@\texttt  {Eval}!for matrices created with Compose|hyperpage}{193}
\indexentry{Eval@\texttt  {Eval}!for matrices created with LeftInverse|hyperpage}{194}
\indexentry{Eval@\texttt  {Eval}!for matrices created with RightInverse|hyperpage}{194}
\indexentry{BasisOfRowModule@\texttt  {BasisOfRowModule}!ResidueClassRing|hyperpage}{196}
\indexentry{BasisOfColumnModule@\texttt  {BasisOfColumnModule}!ResidueClassRing|hyperpage}{196}
\indexentry{DecideZeroRows@\texttt  {DecideZeroRows}!ResidueClassRing|hyperpage}{197}
\indexentry{DecideZeroColumns@\texttt  {DecideZeroColumns}!ResidueClassRing|hyperpage}{197}
\indexentry{SyzygiesGeneratorsOfRows@\texttt  {SyzygiesGeneratorsOfRows}!ResidueClassRing|hyperpage}{197}
\indexentry{SyzygiesGeneratorsOfColumns@\texttt  {SyzygiesGeneratorsOfColumns}!ResidueClassRing|hyperpage}{198}
\indexentry{BasisOfRowsCoeff@\texttt  {BasisOfRowsCoeff}!ResidueClassRing|hyperpage}{199}
\indexentry{BasisOfColumnsCoeff@\texttt  {BasisOfColumnsCoeff}!ResidueClassRing|hyperpage}{199}
\indexentry{DecideZeroRowsEffectively@\texttt  {DecideZeroRowsEffectively}!ResidueClassRing|hyperpage}{200}
\indexentry{DecideZeroColumnsEffectively@\texttt  {DecideZeroColumnsEffectively}!ResidueClassRing|hyperpage}{200}
\indexentry{RelativeSyzygiesGeneratorsOfRows@\texttt  {RelativeSyzygiesGeneratorsOfRows}!ResidueClassRing|hyperpage}{201}
\indexentry{RelativeSyzygiesGeneratorsOfColumns@\texttt  {RelativeSyzygiesGeneratorsOfColumns}!ResidueClassRing|hyperpage}{201}
\indexentry{ZeroMatrix@\texttt  {ZeroMatrix}!ResidueClassRing|hyperpage}{202}
\indexentry{IdentityMatrix@\texttt  {IdentityMatrix}!ResidueClassRing|hyperpage}{202}
\indexentry{Involution@\texttt  {Involution}!ResidueClassRing|hyperpage}{202}
\indexentry{CertainRows@\texttt  {CertainRows}!ResidueClassRing|hyperpage}{203}
\indexentry{CertainColumns@\texttt  {CertainColumns}!ResidueClassRing|hyperpage}{203}
\indexentry{UnionOfRows@\texttt  {UnionOfRows}!ResidueClassRing|hyperpage}{204}
\indexentry{UnionOfColumns@\texttt  {UnionOfColumns}!ResidueClassRing|hyperpage}{204}
\indexentry{DiagMat@\texttt  {DiagMat}!ResidueClassRing|hyperpage}{205}
\indexentry{KroneckerMat@\texttt  {KroneckerMat}!ResidueClassRing|hyperpage}{205}
\indexentry{MulMat@\texttt  {MulMat}!ResidueClassRing|hyperpage}{206}
\indexentry{AddMat@\texttt  {AddMat}!ResidueClassRing|hyperpage}{206}
\indexentry{SubMat@\texttt  {SubMat}!ResidueClassRing|hyperpage}{206}
\indexentry{Compose@\texttt  {Compose}!ResidueClassRing|hyperpage}{206}
\indexentry{IsZeroMatrix@\texttt  {IsZeroMatrix}!ResidueClassRing|hyperpage}{207}
\indexentry{NrRows@\texttt  {NrRows}!ResidueClassRing|hyperpage}{207}
\indexentry{NrColumns@\texttt  {NrColumns}!ResidueClassRing|hyperpage}{207}
\indexentry{Determinant@\texttt  {Determinant}!ResidueClassRing|hyperpage}{207}
\indexentry{AreEqualMatrices@\texttt  {AreEqualMatrices}!ResidueClassRing|hyperpage}{207}
\indexentry{IsIdentityMatrix@\texttt  {IsIdentityMatrix}!ResidueClassRing|hyperpage}{208}
\indexentry{IsDiagonalMatrix@\texttt  {IsDiagonalMatrix}!ResidueClassRing|hyperpage}{208}
\indexentry{ZeroRows@\texttt  {ZeroRows}!ResidueClassRing|hyperpage}{208}
\indexentry{ZeroColumns@\texttt  {ZeroColumns}!ResidueClassRing|hyperpage}{208}
\indexentry{homalgMode@\texttt  {homalgMode}|hyperpage}{211}
