\indexentry{\textsf{MatricesForHomalg}|hyperpage}{5}
\indexentry{IsHomalgRing@\texttt  {IsHomalgRing}|hyperpage}{8}
\indexentry{IsPreHomalgRing@\texttt  {IsPreHomalgRing}|hyperpage}{8}
\indexentry{IsHomalgRingElement@\texttt  {IsHomalgRingElement}|hyperpage}{8}
\indexentry{IsHomalgInternalRingRep@\texttt  {IsHomalgInternalRingRep}|hyperpage}{9}
\indexentry{HomalgRingOfIntegers@\texttt  {HomalgRingOfIntegers}!constructor for the integers|hyperpage}{9}
\indexentry{HomalgRingOfIntegers@\texttt  {HomalgRingOfIntegers}!constructor for the residue class rings of the integers|hyperpage}{9}
\indexentry{HomalgFieldOfRationals@\texttt  {HomalgFieldOfRationals}!constructor for the field of rationals|hyperpage}{10}
\indexentry{/@\texttt  {\texttt  {\char 92\relax }/}!constructor for residue class rings|hyperpage}{10}
\indexentry{IsZero@\texttt  {IsZero}!for rings|hyperpage}{11}
\indexentry{ContainsAField@\texttt  {ContainsAField}|hyperpage}{11}
\indexentry{IsRationalsForHomalg@\texttt  {IsRationalsForHomalg}|hyperpage}{11}
\indexentry{IsFieldForHomalg@\texttt  {IsFieldForHomalg}|hyperpage}{11}
\indexentry{IsDivisionRingForHomalg@\texttt  {IsDivisionRingForHomalg}|hyperpage}{11}
\indexentry{IsIntegersForHomalg@\texttt  {IsIntegersForHomalg}|hyperpage}{12}
\indexentry{IsResidueClassRingOfTheIntegers@\texttt  {IsResidueClassRingOfTheIntegers}|hyperpage}{12}
\indexentry{IsBezoutRing@\texttt  {IsBezoutRing}|hyperpage}{12}
\indexentry{IsIntegrallyClosedDomain@\texttt  {IsIntegrallyClosedDomain}|hyperpage}{12}
\indexentry{IsUniqueFactorizationDomain@\texttt  {IsUniqueFactorizationDomain}|hyperpage}{12}
\indexentry{IsKaplanskyHermite@\texttt  {IsKaplanskyHermite}|hyperpage}{12}
\indexentry{IsDedekindDomain@\texttt  {IsDedekindDomain}|hyperpage}{12}
\indexentry{IsDiscreteValuationRing@\texttt  {IsDiscreteValuationRing}|hyperpage}{12}
\indexentry{IsFreePolynomialRing@\texttt  {IsFreePolynomialRing}|hyperpage}{13}
\indexentry{IsWeylRing@\texttt  {IsWeylRing}|hyperpage}{13}
\indexentry{IsLocalizedWeylRing@\texttt  {IsLocalizedWeylRing}|hyperpage}{13}
\indexentry{IsGlobalDimensionFinite@\texttt  {IsGlobalDimensionFinite}|hyperpage}{13}
\indexentry{IsLeftGlobalDimensionFinite@\texttt  {IsLeftGlobalDimensionFinite}|hyperpage}{13}
\indexentry{IsRightGlobalDimensionFinite@\texttt  {IsRightGlobalDimensionFinite}|hyperpage}{13}
\indexentry{HasInvariantBasisProperty@\texttt  {HasInvariantBasisProperty}|hyperpage}{13}
\indexentry{HasLeftInvariantBasisProperty@\texttt  {HasLeftInvariantBasisProperty}|hyperpage}{13}
\indexentry{HasRightInvariantBasisProperty@\texttt  {HasRightInvariantBasisProperty}|hyperpage}{14}
\indexentry{IsLocal@\texttt  {IsLocal}|hyperpage}{14}
\indexentry{IsSemiLocalRing@\texttt  {IsSemiLocalRing}|hyperpage}{14}
\indexentry{IsIntegralDomain@\texttt  {IsIntegralDomain}|hyperpage}{14}
\indexentry{IsHereditary@\texttt  {IsHereditary}|hyperpage}{14}
\indexentry{IsLeftHereditary@\texttt  {IsLeftHereditary}|hyperpage}{14}
\indexentry{IsRightHereditary@\texttt  {IsRightHereditary}|hyperpage}{14}
\indexentry{IsHermite@\texttt  {IsHermite}|hyperpage}{14}
\indexentry{IsLeftHermite@\texttt  {IsLeftHermite}|hyperpage}{15}
\indexentry{IsRightHermite@\texttt  {IsRightHermite}|hyperpage}{15}
\indexentry{IsNoetherian@\texttt  {IsNoetherian}|hyperpage}{15}
\indexentry{IsLeftNoetherian@\texttt  {IsLeftNoetherian}|hyperpage}{15}
\indexentry{IsRightNoetherian@\texttt  {IsRightNoetherian}|hyperpage}{15}
\indexentry{IsCohenMacaulay@\texttt  {IsCohenMacaulay}|hyperpage}{15}
\indexentry{IsGorenstein@\texttt  {IsGorenstein}|hyperpage}{15}
\indexentry{IsKoszul@\texttt  {IsKoszul}|hyperpage}{15}
\indexentry{IsArtinian@\texttt  {IsArtinian}!for rings|hyperpage}{16}
\indexentry{IsLeftArtinian@\texttt  {IsLeftArtinian}|hyperpage}{16}
\indexentry{IsRightArtinian@\texttt  {IsRightArtinian}|hyperpage}{16}
\indexentry{IsOreDomain@\texttt  {IsOreDomain}|hyperpage}{16}
\indexentry{IsLeftOreDomain@\texttt  {IsLeftOreDomain}|hyperpage}{16}
\indexentry{IsRightOreDomain@\texttt  {IsRightOreDomain}|hyperpage}{16}
\indexentry{IsPrincipalIdealRing@\texttt  {IsPrincipalIdealRing}|hyperpage}{16}
\indexentry{IsLeftPrincipalIdealRing@\texttt  {IsLeftPrincipalIdealRing}|hyperpage}{16}
\indexentry{IsRightPrincipalIdealRing@\texttt  {IsRightPrincipalIdealRing}|hyperpage}{17}
\indexentry{IsRegular@\texttt  {IsRegular}|hyperpage}{17}
\indexentry{IsFiniteFreePresentationRing@\texttt  {IsFiniteFreePresentationRing}|hyperpage}{17}
\indexentry{IsLeftFiniteFreePresentationRing@\texttt  {IsLeftFiniteFreePresentationRing}|hyperpage}{17}
\indexentry{IsRightFiniteFreePresentationRing@\texttt  {IsRightFiniteFreePresentationRing}|hyperpage}{17}
\indexentry{IsSimpleRing@\texttt  {IsSimpleRing}|hyperpage}{17}
\indexentry{IsSemiSimpleRing@\texttt  {IsSemiSimpleRing}|hyperpage}{17}
\indexentry{IsSuperCommutative@\texttt  {IsSuperCommutative}|hyperpage}{17}
\indexentry{BasisAlgorithmRespectsPrincipalIdeals@\texttt  {Basis}\discretionary {-}{}{}\texttt  {Algorithm}\discretionary {-}{}{}\texttt  {Respects}\discretionary {-}{}{}\texttt  {Principal}\discretionary {-}{}{}\texttt  {Ideals}|hyperpage}{18}
\indexentry{AreUnitsCentral@\texttt  {AreUnitsCentral}|hyperpage}{18}
\indexentry{IsMinusOne@\texttt  {IsMinusOne}|hyperpage}{18}
\indexentry{IsMonic@\texttt  {IsMonic}!for homalg ring elements|hyperpage}{18}
\indexentry{IsMonicUptoUnit@\texttt  {IsMonicUptoUnit}!for homalg ring elements|hyperpage}{18}
\indexentry{IsLeftRegular@\texttt  {IsLeftRegular}!for homalg ring elements|hyperpage}{18}
\indexentry{IsRightRegular@\texttt  {IsRightRegular}!for homalg ring elements|hyperpage}{18}
\indexentry{IsRegular@\texttt  {IsRegular}!for homalg ring elements|hyperpage}{18}
\indexentry{Inverse@\texttt  {Inverse}!for homalg ring elements|hyperpage}{19}
\indexentry{homalgTable@\texttt  {homalgTable}|hyperpage}{19}
\indexentry{RingElementConstructor@\texttt  {RingElementConstructor}|hyperpage}{19}
\indexentry{TypeOfHomalgMatrix@\texttt  {TypeOfHomalgMatrix}|hyperpage}{19}
\indexentry{ConstructorForHomalgMatrices@\texttt  {ConstructorForHomalgMatrices}|hyperpage}{19}
\indexentry{Zero@\texttt  {Zero}!for homalg rings|hyperpage}{20}
\indexentry{One@\texttt  {One}!for homalg rings|hyperpage}{20}
\indexentry{MinusOne@\texttt  {MinusOne}|hyperpage}{20}
\indexentry{ProductOfIndeterminates@\texttt  {ProductOfIndeterminates}|hyperpage}{20}
\indexentry{RationalParameters@\texttt  {RationalParameters}|hyperpage}{20}
\indexentry{IndeterminatesOfPolynomialRing@\texttt  {IndeterminatesOfPolynomialRing}|hyperpage}{20}
\indexentry{RelativeIndeterminatesOfPolynomialRing@\texttt  {Relative}\discretionary {-}{}{}\texttt  {Indeterminates}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Polynomial}\discretionary {-}{}{}\texttt  {Ring}|hyperpage}{20}
\indexentry{IndeterminateCoordinatesOfRingOfDerivations@\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Coordinates}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Derivations}|hyperpage}{20}
\indexentry{RelativeIndeterminateCoordinatesOfRingOfDerivations@\texttt  {Relative}\discretionary {-}{}{}\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Coordinates}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Derivations}|hyperpage}{21}
\indexentry{IndeterminateDerivationsOfRingOfDerivations@\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Derivations}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Derivations}|hyperpage}{21}
\indexentry{RelativeIndeterminateDerivationsOfRingOfDerivations@\texttt  {Relative}\discretionary {-}{}{}\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Derivations}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Derivations}|hyperpage}{21}
\indexentry{IndeterminateAntiCommutingVariablesOfExteriorRing@\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Anti}\discretionary {-}{}{}\texttt  {Commuting}\discretionary {-}{}{}\texttt  {Variables}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Exterior}\discretionary {-}{}{}\texttt  {Ring}|hyperpage}{21}
\indexentry{RelativeIndeterminateAntiCommutingVariablesOfExteriorRing@\texttt  {Relative}\discretionary {-}{}{}\texttt  {Indeterminate}\discretionary {-}{}{}\texttt  {Anti}\discretionary {-}{}{}\texttt  {Commuting}\discretionary {-}{}{}\texttt  {Variables}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Exterior}\discretionary {-}{}{}\texttt  {Ring}|hyperpage}{21}
\indexentry{IndeterminatesOfExteriorRing@\texttt  {IndeterminatesOfExteriorRing}|hyperpage}{21}
\indexentry{CoefficientsRing@\texttt  {CoefficientsRing}|hyperpage}{21}
\indexentry{KrullDimension@\texttt  {KrullDimension}|hyperpage}{21}
\indexentry{LeftGlobalDimension@\texttt  {LeftGlobalDimension}|hyperpage}{22}
\indexentry{RightGlobalDimension@\texttt  {RightGlobalDimension}|hyperpage}{22}
\indexentry{GlobalDimension@\texttt  {GlobalDimension}|hyperpage}{22}
\indexentry{GeneralLinearRank@\texttt  {GeneralLinearRank}|hyperpage}{22}
\indexentry{ElementaryRank@\texttt  {ElementaryRank}|hyperpage}{22}
\indexentry{StableRank@\texttt  {StableRank}|hyperpage}{22}
\indexentry{AssociatedGradedRing@\texttt  {AssociatedGradedRing}|hyperpage}{22}
\indexentry{IsHomalgRingMap@\texttt  {IsHomalgRingMap}|hyperpage}{23}
\indexentry{IsHomalgRingSelfMap@\texttt  {IsHomalgRingSelfMap}|hyperpage}{23}
\indexentry{IsHomalgRingMapRep@\texttt  {IsHomalgRingMapRep}|hyperpage}{23}
\indexentry{RingMap@\texttt  {RingMap}!constructor for ring maps|hyperpage}{23}
\indexentry{IsMorphism@\texttt  {IsMorphism}!for ring maps|hyperpage}{24}
\indexentry{IsIdentityMorphism@\texttt  {IsIdentityMorphism}!for ring maps|hyperpage}{24}
\indexentry{IsMonomorphism@\texttt  {IsMonomorphism}!for ring maps|hyperpage}{24}
\indexentry{IsEpimorphism@\texttt  {IsEpimorphism}!for ring maps|hyperpage}{24}
\indexentry{IsIsomorphism@\texttt  {IsIsomorphism}!for ring maps|hyperpage}{24}
\indexentry{IsAutomorphism@\texttt  {IsAutomorphism}!for ring maps|hyperpage}{24}
\indexentry{Source@\texttt  {Source}!for ring maps|hyperpage}{25}
\indexentry{Range@\texttt  {Range}!for ring maps|hyperpage}{25}
\indexentry{DegreeOfMorphism@\texttt  {DegreeOfMorphism}!for ring maps|hyperpage}{25}
\indexentry{CoordinateRingOfGraph@\texttt  {CoordinateRingOfGraph}!for ring maps|hyperpage}{25}
\indexentry{IsHomalgMatrix@\texttt  {IsHomalgMatrix}|hyperpage}{26}
\indexentry{IsHomalgInternalMatrixRep@\texttt  {IsHomalgInternalMatrixRep}|hyperpage}{26}
\indexentry{HomalgInitialMatrix@\texttt  {HomalgInitialMatrix}!constructor for initial matrices filled with zeros|hyperpage}{26}
\indexentry{HomalgInitialIdentityMatrix@\texttt  {HomalgInitialIdentityMatrix}!constructor for initial quadratic matrices with ones on the diagonal|hyperpage}{27}
\indexentry{HomalgZeroMatrix@\texttt  {HomalgZeroMatrix}!constructor for zero matrices|hyperpage}{28}
\indexentry{HomalgIdentityMatrix@\texttt  {HomalgIdentityMatrix}!constructor for identity matrices|hyperpage}{28}
\indexentry{HomalgVoidMatrix@\texttt  {HomalgVoidMatrix}!constructor for void matrices|hyperpage}{28}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a listlist|hyperpage}{29}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a list|hyperpage}{29}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a string of a listlist|hyperpage}{29}
\indexentry{HomalgMatrix@\texttt  {HomalgMatrix}!constructor for matrices using a string of a list|hyperpage}{29}
\indexentry{HomalgDiagonalMatrix@\texttt  {HomalgDiagonalMatrix}!constructor for diagonal matrices|hyperpage}{30}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!copy a matrix over a different ring|hyperpage}{30}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!copy a matrix over a different ring (right)|hyperpage}{30}
\indexentry{IsZero@\texttt  {IsZero}!for matrices|hyperpage}{31}
\indexentry{IsOne@\texttt  {IsOne}|hyperpage}{31}
\indexentry{IsUnitFree@\texttt  {IsUnitFree}|hyperpage}{31}
\indexentry{IsPermutationMatrix@\texttt  {IsPermutationMatrix}|hyperpage}{32}
\indexentry{IsSpecialSubidentityMatrix@\texttt  {IsSpecialSubidentityMatrix}|hyperpage}{32}
\indexentry{IsSubidentityMatrix@\texttt  {IsSubidentityMatrix}|hyperpage}{32}
\indexentry{IsLeftRegular@\texttt  {IsLeftRegular}|hyperpage}{32}
\indexentry{IsRightRegular@\texttt  {IsRightRegular}|hyperpage}{32}
\indexentry{IsInvertibleMatrix@\texttt  {IsInvertibleMatrix}|hyperpage}{32}
\indexentry{IsLeftInvertibleMatrix@\texttt  {IsLeftInvertibleMatrix}|hyperpage}{32}
\indexentry{IsRightInvertibleMatrix@\texttt  {IsRightInvertibleMatrix}|hyperpage}{32}
\indexentry{IsEmptyMatrix@\texttt  {IsEmptyMatrix}|hyperpage}{33}
\indexentry{IsDiagonalMatrix@\texttt  {IsDiagonalMatrix}|hyperpage}{33}
\indexentry{IsScalarlMatrix@\texttt  {IsScalarlMatrix}|hyperpage}{33}
\indexentry{IsUpperTriangularMatrix@\texttt  {IsUpperTriangularMatrix}|hyperpage}{33}
\indexentry{IsLowerTriangularMatrix@\texttt  {IsLowerTriangularMatrix}|hyperpage}{33}
\indexentry{IsStrictUpperTriangularMatrix@\texttt  {IsStrictUpperTriangularMatrix}|hyperpage}{33}
\indexentry{IsStrictLowerTriangularMatrix@\texttt  {IsStrictLowerTriangularMatrix}|hyperpage}{33}
\indexentry{IsUpperStairCaseMatrix@\texttt  {IsUpperStairCaseMatrix}|hyperpage}{33}
\indexentry{IsLowerStairCaseMatrix@\texttt  {IsLowerStairCaseMatrix}|hyperpage}{34}
\indexentry{IsTriangularMatrix@\texttt  {IsTriangularMatrix}|hyperpage}{34}
\indexentry{IsBasisOfRowsMatrix@\texttt  {IsBasisOfRowsMatrix}|hyperpage}{34}
\indexentry{IsBasisOfColumnsMatrix@\texttt  {IsBasisOfColumnsMatrix}|hyperpage}{34}
\indexentry{IsReducedBasisOfRowsMatrix@\texttt  {IsReducedBasisOfRowsMatrix}|hyperpage}{34}
\indexentry{IsReducedBasisOfColumnsMatrix@\texttt  {IsReducedBasisOfColumnsMatrix}|hyperpage}{34}
\indexentry{IsInitialMatrix@\texttt  {IsInitialMatrix}|hyperpage}{34}
\indexentry{IsInitialIdentityMatrix@\texttt  {IsInitialIdentityMatrix}|hyperpage}{34}
\indexentry{IsVoidMatrix@\texttt  {IsVoidMatrix}|hyperpage}{35}
\indexentry{NrRows@\texttt  {NrRows}|hyperpage}{35}
\indexentry{NrColumns@\texttt  {NrColumns}|hyperpage}{35}
\indexentry{DeterminantMat@\texttt  {DeterminantMat}|hyperpage}{35}
\indexentry{ZeroRows@\texttt  {ZeroRows}|hyperpage}{35}
\indexentry{ZeroColumns@\texttt  {ZeroColumns}|hyperpage}{35}
\indexentry{NonZeroRows@\texttt  {NonZeroRows}|hyperpage}{35}
\indexentry{NonZeroColumns@\texttt  {NonZeroColumns}|hyperpage}{36}
\indexentry{PositionOfFirstNonZeroEntryPerRow@\texttt  {PositionOfFirstNonZeroEntryPerRow}|hyperpage}{36}
\indexentry{PositionOfFirstNonZeroEntryPerColumn@\texttt  {Position}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {First}\discretionary {-}{}{}\texttt  {Non}\discretionary {-}{}{}\texttt  {Zero}\discretionary {-}{}{}\texttt  {Entry}\discretionary {-}{}{}\texttt  {Per}\discretionary {-}{}{}\texttt  {Column}|hyperpage}{36}
\indexentry{RowRankOfMatrix@\texttt  {RowRankOfMatrix}|hyperpage}{36}
\indexentry{ColumnRankOfMatrix@\texttt  {ColumnRankOfMatrix}|hyperpage}{36}
\indexentry{LeftInverse@\texttt  {LeftInverse}|hyperpage}{36}
\indexentry{RightInverse@\texttt  {RightInverse}|hyperpage}{36}
\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}{37}
\indexentry{CoefficientsOfNumeratorOfHilbertPoincareSeries@\texttt  {Coefficients}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Numerator}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Poincare}\discretionary {-}{}{}\texttt  {Series}|hyperpage}{37}
\indexentry{UnreducedNumeratorOfHilbertPoincareSeries@\texttt  {Unreduced}\discretionary {-}{}{}\texttt  {Numerator}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Hilbert}\discretionary {-}{}{}\texttt  {Poincare}\discretionary {-}{}{}\texttt  {Series}|hyperpage}{37}
\indexentry{NumeratorOfHilbertPoincareSeries@\texttt  {NumeratorOfHilbertPoincareSeries}|hyperpage}{37}
\indexentry{HilbertPoincareSeries@\texttt  {HilbertPoincareSeries}|hyperpage}{37}
\indexentry{HilbertPolynomial@\texttt  {HilbertPolynomial}|hyperpage}{37}
\indexentry{AffineDimension@\texttt  {AffineDimension}|hyperpage}{37}
\indexentry{AffineDegree@\texttt  {AffineDegree}|hyperpage}{37}
\indexentry{ProjectiveDegree@\texttt  {ProjectiveDegree}|hyperpage}{38}
\indexentry{ConstantTermOfHilbertPolynomialn@\texttt  {ConstantTermOfHilbertPolynomialn}|hyperpage}{38}
\indexentry{MatrixOfSymbols@\texttt  {MatrixOfSymbols}|hyperpage}{38}
\indexentry{HomalgRing@\texttt  {HomalgRing}!for matrices|hyperpage}{38}
\indexentry{LeftInverse@\texttt  {LeftInverse}!for matrices|hyperpage}{38}
\indexentry{RightInverse@\texttt  {RightInverse}!for matrices|hyperpage}{39}
\indexentry{LeftInverseLazy@\texttt  {LeftInverseLazy}!for matrices|hyperpage}{40}
\indexentry{RightInverseLazy@\texttt  {RightInverseLazy}!for matrices|hyperpage}{40}
\indexentry{Involution@\texttt  {Involution}!for matrices|hyperpage}{40}
\indexentry{CertainRows@\texttt  {CertainRows}!for matrices|hyperpage}{41}
\indexentry{CertainColumns@\texttt  {CertainColumns}!for matrices|hyperpage}{41}
\indexentry{UnionOfRows@\texttt  {UnionOfRows}!for matrices|hyperpage}{41}
\indexentry{UnionOfColumns@\texttt  {UnionOfColumns}!for matrices|hyperpage}{41}
\indexentry{DiagMat@\texttt  {DiagMat}!for matrices|hyperpage}{41}
\indexentry{KroneckerMat@\texttt  {KroneckerMat}!for matrices|hyperpage}{41}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!for ring elements and matrices|hyperpage}{42}
\indexentry{+@\texttt  {\texttt  {\char 92\relax }+}!for matrices|hyperpage}{42}
\indexentry{-@\texttt  {\texttt  {\char 92\relax }-}!for matrices|hyperpage}{42}
\indexentry{*@\texttt  {\texttt  {\char 92\relax }*}!for composable matrices|hyperpage}{42}
\indexentry{=@\texttt  {\texttt  {\char 92\relax }=}!for matrices|hyperpage}{42}
\indexentry{GetColumnIndependentUnitPositions@\texttt  {GetColumnIndependentUnitPositions}!for matrices|hyperpage}{43}
\indexentry{GetRowIndependentUnitPositions@\texttt  {GetRowIndependentUnitPositions}!for matrices|hyperpage}{43}
\indexentry{GetUnitPosition@\texttt  {GetUnitPosition}!for matrices|hyperpage}{43}
\indexentry{Eliminate@\texttt  {Eliminate}|hyperpage}{43}
\indexentry{BasisOfRowModule@\texttt  {BasisOfRowModule}!for matrices|hyperpage}{44}
\indexentry{BasisOfColumnModule@\texttt  {BasisOfColumnModule}!for matrices|hyperpage}{44}
\indexentry{DecideZeroRows@\texttt  {DecideZeroRows}!for pairs of matrices|hyperpage}{44}
\indexentry{DecideZeroColumns@\texttt  {DecideZeroColumns}!for pairs of matrices|hyperpage}{44}
\indexentry{SyzygiesGeneratorsOfRows@\texttt  {SyzygiesGeneratorsOfRows}!for matrices|hyperpage}{45}
\indexentry{SyzygiesGeneratorsOfColumns@\texttt  {SyzygiesGeneratorsOfColumns}!for matrices|hyperpage}{45}
\indexentry{SyzygiesGeneratorsOfRows@\texttt  {SyzygiesGeneratorsOfRows}!for pairs of matrices|hyperpage}{45}
\indexentry{SyzygiesGeneratorsOfColumns@\texttt  {SyzygiesGeneratorsOfColumns}!for pairs of matrices|hyperpage}{45}
\indexentry{ReducedBasisOfRowModule@\texttt  {ReducedBasisOfRowModule}!for matrices|hyperpage}{45}
\indexentry{ReducedBasisOfColumnModule@\texttt  {ReducedBasisOfColumnModule}!for matrices|hyperpage}{45}
\indexentry{ReducedSyzygiesGeneratorsOfRows@\texttt  {ReducedSyzygiesGeneratorsOfRows}!for matrices|hyperpage}{46}
\indexentry{ReducedSyzygiesGeneratorsOfColumns@\texttt  {ReducedSyzygiesGeneratorsOfColumns}!for matrices|hyperpage}{46}
\indexentry{BasisOfRowsCoeff@\texttt  {BasisOfRowsCoeff}!for matrices|hyperpage}{46}
\indexentry{BasisOfColumnsCoeff@\texttt  {BasisOfColumnsCoeff}!for matrices|hyperpage}{46}
\indexentry{DecideZeroRowsEffectively@\texttt  {DecideZeroRowsEffectively}!for pairs of matrices|hyperpage}{46}
\indexentry{DecideZeroColumnsEffectively@\texttt  {DecideZeroColumnsEffectively}!for pairs of matrices|hyperpage}{47}
\indexentry{BasisOfRows@\texttt  {BasisOfRows}!for matrices|hyperpage}{47}
\indexentry{BasisOfRows@\texttt  {BasisOfRows}!for pairs of matrices|hyperpage}{47}
\indexentry{BasisOfColumns@\texttt  {BasisOfColumns}!for matrices|hyperpage}{47}
\indexentry{BasisOfColumns@\texttt  {BasisOfColumns}!for pairs of matrices|hyperpage}{47}
\indexentry{DecideZero@\texttt  {DecideZero}!for matrices and relations|hyperpage}{47}
\indexentry{SyzygiesOfRows@\texttt  {SyzygiesOfRows}!for matrices|hyperpage}{47}
\indexentry{SyzygiesOfRows@\texttt  {SyzygiesOfRows}!for pairs of matrices|hyperpage}{47}
\indexentry{SyzygiesOfColumns@\texttt  {SyzygiesOfColumns}!for matrices|hyperpage}{48}
\indexentry{SyzygiesOfColumns@\texttt  {SyzygiesOfColumns}!for pairs of matrices|hyperpage}{48}
\indexentry{ReducedSyzygiesOfRows@\texttt  {ReducedSyzygiesOfRows}!for matrices|hyperpage}{48}
\indexentry{ReducedSyzygiesOfRows@\texttt  {ReducedSyzygiesOfRows}!for pairs of matrices|hyperpage}{48}
\indexentry{ReducedSyzygiesOfColumns@\texttt  {ReducedSyzygiesOfColumns}!for matrices|hyperpage}{48}
\indexentry{ReducedSyzygiesOfColumns@\texttt  {ReducedSyzygiesOfColumns}!for pairs of matrices|hyperpage}{48}
\indexentry{RightDivide@\texttt  {RightDivide}!for pairs of matrices|hyperpage}{48}
\indexentry{LeftDivide@\texttt  {LeftDivide}!for pairs of matrices|hyperpage}{48}
\indexentry{RightDivide@\texttt  {RightDivide}!for triples of matrices|hyperpage}{49}
\indexentry{LeftDivide@\texttt  {LeftDivide}!for triples of matrices|hyperpage}{50}
\indexentry{GenerateSameRowModule@\texttt  {GenerateSameRowModule}!for pairs of matrices|hyperpage}{51}
\indexentry{GenerateSameColumnModule@\texttt  {GenerateSameColumnModule}!for pairs of matrices|hyperpage}{51}
\indexentry{IsHomalgRingRelations@\texttt  {IsHomalgRingRelations}|hyperpage}{52}
\indexentry{IsHomalgRingRelationsAsGeneratorsOfLeftIdeal@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Relations}\discretionary {-}{}{}\texttt  {As}\discretionary {-}{}{}\texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Left}\discretionary {-}{}{}\texttt  {Ideal}|hyperpage}{52}
\indexentry{IsHomalgRingRelationsAsGeneratorsOfRightIdeal@\texttt  {IsHomalg}\discretionary {-}{}{}\texttt  {Ring}\discretionary {-}{}{}\texttt  {Relations}\discretionary {-}{}{}\texttt  {As}\discretionary {-}{}{}\texttt  {Generators}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {Right}\discretionary {-}{}{}\texttt  {Ideal}|hyperpage}{52}
\indexentry{IsRingRelationsRep@\texttt  {IsRingRelationsRep}|hyperpage}{52}
\indexentry{CanBeUsedToDecideZero@\texttt  {CanBeUsedToDecideZero}|hyperpage}{53}
\indexentry{IsInjectivePresentation@\texttt  {IsInjectivePresentation}|hyperpage}{53}
\indexentry{InitialMatrix@\texttt  {InitialMatrix}!homalgTable entry for initial matrices|hyperpage}{56}
\indexentry{InitialIdentityMatrix@\texttt  {InitialIdentityMatrix}!homalgTable entry for initial identity matrices|hyperpage}{56}
\indexentry{ZeroMatrix@\texttt  {ZeroMatrix}!homalgTable entry|hyperpage}{56}
\indexentry{IdentityMatrix@\texttt  {IdentityMatrix}!homalgTable entry|hyperpage}{57}
\indexentry{Involution@\texttt  {Involution}!homalgTable entry|hyperpage}{57}
\indexentry{CertainRows@\texttt  {CertainRows}!homalgTable entry|hyperpage}{57}
\indexentry{CertainColumns@\texttt  {CertainColumns}!homalgTable entry|hyperpage}{57}
\indexentry{UnionOfRows@\texttt  {UnionOfRows}!homalgTable entry|hyperpage}{57}
\indexentry{UnionOfColumns@\texttt  {UnionOfColumns}!homalgTable entry|hyperpage}{57}
\indexentry{DiagMat@\texttt  {DiagMat}!homalgTable entry|hyperpage}{58}
\indexentry{KroneckerMat@\texttt  {KroneckerMat}!homalgTable entry|hyperpage}{58}
\indexentry{MulMat@\texttt  {MulMat}!homalgTable entry|hyperpage}{58}
\indexentry{AddMat@\texttt  {AddMat}!homalgTable entry|hyperpage}{58}
\indexentry{SubMat@\texttt  {SubMat}!homalgTable entry|hyperpage}{58}
\indexentry{Compose@\texttt  {Compose}!homalgTable entry|hyperpage}{58}
\indexentry{IsZeroMatrix@\texttt  {IsZeroMatrix}!homalgTable entry|hyperpage}{59}
\indexentry{NrRows@\texttt  {NrRows}!homalgTable entry|hyperpage}{59}
\indexentry{NrColumns@\texttt  {NrColumns}!homalgTable entry|hyperpage}{60}
\indexentry{Determinant@\texttt  {Determinant}!homalgTable entry|hyperpage}{61}
\indexentry{AreEqualMatrices@\texttt  {AreEqualMatrices}!homalgTable entry|hyperpage}{62}
\indexentry{IsIdentityMatrix@\texttt  {IsIdentityMatrix}!homalgTable entry|hyperpage}{63}
\indexentry{IsDiagonalMatrix@\texttt  {IsDiagonalMatrix}!homalgTable entry|hyperpage}{64}
\indexentry{ZeroRows@\texttt  {ZeroRows}!homalgTable entry|hyperpage}{65}
\indexentry{ZeroColumns@\texttt  {ZeroColumns}!homalgTable entry|hyperpage}{65}
\indexentry{GetColumnIndependentUnitPositions@\texttt  {GetColumnIndependentUnitPositions}!homalgTable entry|hyperpage}{66}
\indexentry{GetRowIndependentUnitPositions@\texttt  {GetRowIndependentUnitPositions}!homalgTable entry|hyperpage}{67}
\indexentry{GetUnitPosition@\texttt  {GetUnitPosition}!homalgTable entry|hyperpage}{68}
\indexentry{PositionOfFirstNonZeroEntryPerRow@\texttt  {PositionOfFirstNonZeroEntryPerRow}!homalgTable entry|hyperpage}{69}
\indexentry{PositionOfFirstNonZeroEntryPerColumn@\texttt  {Position}\discretionary {-}{}{}\texttt  {Of}\discretionary {-}{}{}\texttt  {First}\discretionary {-}{}{}\texttt  {Non}\discretionary {-}{}{}\texttt  {Zero}\discretionary {-}{}{}\texttt  {Entry}\discretionary {-}{}{}\texttt  {Per}\discretionary {-}{}{}\texttt  {Column}!homalgTable entry|hyperpage}{70}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgInitialMatrix|hyperpage}{72}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgInitialIdentityMatrix|hyperpage}{73}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgZeroMatrix|hyperpage}{74}
\indexentry{Eval@\texttt  {Eval}!for matrices created with HomalgIdentityMatrix|hyperpage}{75}
\indexentry{Eval@\texttt  {Eval}!for matrices created with LeftInverseLazy|hyperpage}{76}
\indexentry{Eval@\texttt  {Eval}!for matrices created with RightInverseLazy|hyperpage}{77}
\indexentry{Eval@\texttt  {Eval}!for matrices created with Involution|hyperpage}{77}
\indexentry{Eval@\texttt  {Eval}!for matrices created with CertainRows|hyperpage}{78}
\indexentry{Eval@\texttt  {Eval}!for matrices created with CertainColumns|hyperpage}{79}
\indexentry{Eval@\texttt  {Eval}!for matrices created with UnionOfRows|hyperpage}{79}
\indexentry{Eval@\texttt  {Eval}!for matrices created with UnionOfColumns|hyperpage}{80}
\indexentry{Eval@\texttt  {Eval}!for matrices created with DiagMat|hyperpage}{81}
\indexentry{Eval@\texttt  {Eval}!for matrices created with KroneckerMat|hyperpage}{82}
\indexentry{Eval@\texttt  {Eval}!for matrices created with MulMat|hyperpage}{83}
\indexentry{Eval@\texttt  {Eval}!for matrices created with AddMat|hyperpage}{84}
\indexentry{Eval@\texttt  {Eval}!for matrices created with SubMat|hyperpage}{84}
\indexentry{Eval@\texttt  {Eval}!for matrices created with Compose|hyperpage}{85}
\indexentry{BasisOfRowModule@\texttt  {BasisOfRowModule}!ResidueClassRing|hyperpage}{87}
\indexentry{BasisOfColumnModule@\texttt  {BasisOfColumnModule}!ResidueClassRing|hyperpage}{87}
\indexentry{DecideZeroRows@\texttt  {DecideZeroRows}!ResidueClassRing|hyperpage}{88}
\indexentry{DecideZeroColumns@\texttt  {DecideZeroColumns}!ResidueClassRing|hyperpage}{88}
\indexentry{SyzygiesGeneratorsOfRows@\texttt  {SyzygiesGeneratorsOfRows}!ResidueClassRing|hyperpage}{88}
\indexentry{SyzygiesGeneratorsOfColumns@\texttt  {SyzygiesGeneratorsOfColumns}!ResidueClassRing|hyperpage}{89}
\indexentry{BasisOfRowsCoeff@\texttt  {BasisOfRowsCoeff}!ResidueClassRing|hyperpage}{90}
\indexentry{BasisOfColumnsCoeff@\texttt  {BasisOfColumnsCoeff}!ResidueClassRing|hyperpage}{90}
\indexentry{DecideZeroRowsEffectively@\texttt  {DecideZeroRowsEffectively}!ResidueClassRing|hyperpage}{91}
\indexentry{DecideZeroColumnsEffectively@\texttt  {DecideZeroColumnsEffectively}!ResidueClassRing|hyperpage}{91}
\indexentry{RelativeSyzygiesGeneratorsOfRows@\texttt  {RelativeSyzygiesGeneratorsOfRows}!ResidueClassRing|hyperpage}{92}
\indexentry{RelativeSyzygiesGeneratorsOfColumns@\texttt  {RelativeSyzygiesGeneratorsOfColumns}!ResidueClassRing|hyperpage}{92}
\indexentry{InitialMatrix@\texttt  {InitialMatrix}!ResidueClassRing|hyperpage}{93}
\indexentry{InitialIdentityMatrix@\texttt  {InitialIdentityMatrix}!ResidueClassRing|hyperpage}{93}
\indexentry{ZeroMatrix@\texttt  {ZeroMatrix}!ResidueClassRing|hyperpage}{93}
\indexentry{IdentityMatrix@\texttt  {IdentityMatrix}!ResidueClassRing|hyperpage}{94}
\indexentry{Involution@\texttt  {Involution}!ResidueClassRing|hyperpage}{94}
\indexentry{CertainRows@\texttt  {CertainRows}!ResidueClassRing|hyperpage}{94}
\indexentry{CertainColumns@\texttt  {CertainColumns}!ResidueClassRing|hyperpage}{95}
\indexentry{UnionOfRows@\texttt  {UnionOfRows}!ResidueClassRing|hyperpage}{95}
\indexentry{UnionOfColumns@\texttt  {UnionOfColumns}!ResidueClassRing|hyperpage}{96}
\indexentry{DiagMat@\texttt  {DiagMat}!ResidueClassRing|hyperpage}{96}
\indexentry{KroneckerMat@\texttt  {KroneckerMat}!ResidueClassRing|hyperpage}{97}
\indexentry{MulMat@\texttt  {MulMat}!ResidueClassRing|hyperpage}{97}
\indexentry{AddMat@\texttt  {AddMat}!ResidueClassRing|hyperpage}{97}
\indexentry{SubMat@\texttt  {SubMat}!ResidueClassRing|hyperpage}{98}
\indexentry{Compose@\texttt  {Compose}!ResidueClassRing|hyperpage}{98}
\indexentry{IsZeroMatrix@\texttt  {IsZeroMatrix}!ResidueClassRing|hyperpage}{98}
\indexentry{NrRows@\texttt  {NrRows}!ResidueClassRing|hyperpage}{98}
\indexentry{NrColumns@\texttt  {NrColumns}!ResidueClassRing|hyperpage}{98}
\indexentry{Determinant@\texttt  {Determinant}!ResidueClassRing|hyperpage}{99}
\indexentry{AreEqualMatrices@\texttt  {AreEqualMatrices}!ResidueClassRing|hyperpage}{99}
\indexentry{IsOne@\texttt  {IsOne}!ResidueClassRing|hyperpage}{99}
\indexentry{IsDiagonalMatrix@\texttt  {IsDiagonalMatrix}!ResidueClassRing|hyperpage}{99}
\indexentry{ZeroRows@\texttt  {ZeroRows}!ResidueClassRing|hyperpage}{100}
\indexentry{ZeroColumns@\texttt  {ZeroColumns}!ResidueClassRing|hyperpage}{100}
\indexentry{homalgMode@\texttt  {homalgMode}|hyperpage}{103}
