\*, copy a matrix over a different ring 5.2-8 \+, for matrices 5.5-14 \-, for matrices 5.5-15 \/, constructor for residue class rings 3.2-3 \=, for matrices 5.5-17 AddMat, homalgTable entry B.1-13 AffineDegree 5.4-21 AffineDimension 5.4-20 AreEqualMatrices, homalgTable entry B.2-1 AreUnitsCentral 3.3-55 AssociatedGradedRing 3.4-28 BasisAlgorithmRespectsPrincipalIdeals 3.3-54 BasisOfColumnModule, for matrices 5.5-23 BasisOfColumns, for matrices 5.5-39 BasisOfColumnsCoeff, for matrices 5.5-35 BasisOfRowModule, for matrices 5.5-22 BasisOfRows, for matrices 5.5-38 BasisOfRowsCoeff, for matrices 5.5-34 CanBeUsedToDecideZero 6.3-1 CertainColumns, for matrices 5.5-8 CertainRows, for matrices 5.5-7 CoefficientsOfNumeratorOfHilbertPoincareSeries 5.4-15 CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries 5.4-14 CoefficientsRing 3.4-20 ColumnRankOfMatrix 5.4-11 Compose, homalgTable entry B.1-15 ConstantTermOfHilbertPolynomialn 5.4-23 ConstructorForHomalgMatrices 3.4-5 ContainsAField 3.3-2 CoordinateRingOfGraph, for ring maps 4.4-4 DecideZero, for matrices and relations 5.5-40 DecideZeroColumns, for pairs of matrices 5.5-25 DecideZeroColumnsEffectively, for pairs of matrices 5.5-37 DecideZeroRows, for pairs of matrices 5.5-24 DecideZeroRowsEffectively, for pairs of matrices 5.5-36 DegreeOfMorphism, for ring maps 4.4-3 Determinant, homalgTable entry B.1-19 DeterminantMat 5.4-3 DiagMat, for matrices 5.5-11 ElementaryRank 3.4-26 Eliminate 5.5-21 Eval, for matrices created with AddMat C.4-15 GeneralLinearRank 3.4-25 GenerateSameColumnModule, for pairs of matrices 5.5-50 GenerateSameRowModule, for pairs of matrices 5.5-49 GetColumnIndependentUnitPositions, for matrices 5.5-18 GetRowIndependentUnitPositions, for matrices 5.5-19 GetUnitPosition, for matrices 5.5-20 GlobalDimension 3.4-24 HasInvariantBasisProperty 3.3-20 HasLeftInvariantBasisProperty 3.3-21 HasRightInvariantBasisProperty 3.3-22 HilbertPoincareSeries 5.4-18 HilbertPolynomial 5.4-19 HomalgDiagonalMatrix, constructor for diagonal matrices 5.2-7 HomalgFieldOfRationals, constructor for the field of rationals 3.2-2 HomalgIdentityMatrix, constructor for identity matrices 5.2-4 HomalgInitialIdentityMatrix, constructor for initial quadratic matrices with ones on the diagonal 5.2-2 HomalgInitialMatrix, constructor for initial matrices filled with zeros 5.2-1 HomalgMatrix, constructor for matrices using a list 5.2-6 homalgMode E.2-1 HomalgRing, for matrices 5.5-1 HomalgRingOfIntegers, constructor for the integers 3.2-1 homalgTable 3.4-2 HomalgVoidMatrix, constructor for void matrices 5.2-5 HomalgZeroMatrix, constructor for zero matrices 5.2-3 IdentityMatrix, homalgTable entry B.1-4 IndeterminateAntiCommutingVariablesOfExteriorRing 3.4-17 IndeterminateCoordinatesOfRingOfDerivations 3.4-13 IndeterminateDerivationsOfRingOfDerivations 3.4-15 IndeterminatesOfExteriorRing 3.4-19 IndeterminatesOfPolynomialRing 3.4-11 InitialIdentityMatrix, homalgTable entry for initial identity matrices B.1-2 InitialMatrix, homalgTable entry for initial matrices B.1-1 Inverse, for homalg ring elements 3.4-1 Involution, for matrices 5.5-6 IsArtinian, for rings 3.3-38 IsAutomorphism, for ring maps 4.3-6 IsBasisOfColumnsMatrix 5.3-23 IsBasisOfRowsMatrix 5.3-22 IsBezoutRing 3.3-8 IsCohenMacaulay 3.3-35 IsDedekindDomain 3.3-12 IsDiagonalMatrix 5.3-13 IsDiscreteValuationRing 3.3-13 IsDivisionRingForHomalg 3.3-5 IsEmptyMatrix 5.3-12 IsEpimorphism, for ring maps 4.3-4 IsFieldForHomalg 3.3-4 IsFiniteFreePresentationRing 3.3-48 IsFreePolynomialRing 3.3-14 IsGlobalDimensionFinite 3.3-17 IsGorenstein 3.3-36 IsHereditary 3.3-26 IsHermite 3.3-29 IsHomalgInternalMatrixRep 5.1-2 IsHomalgInternalRingRep 3.1-4 IsHomalgMatrix 5.1-1 IsHomalgRing 3.1-1 IsHomalgRingElement 3.1-3 IsHomalgRingMap 4.1-1 IsHomalgRingMapRep 4.1-3 IsHomalgRingRelations 6.1-1 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal 6.1-2 IsHomalgRingRelationsAsGeneratorsOfRightIdeal 6.1-3 IsHomalgRingSelfMap 4.1-2 IsIdentityMatrix, homalgTable entry B.2-2 IsIdentityMorphism, for ring maps 4.3-2 IsInitialIdentityMatrix 5.3-27 IsInitialMatrix 5.3-26 IsInjectivePresentation 6.3-2 IsIntegersForHomalg 3.3-6 IsIntegralDomain 3.3-25 IsIntegrallyClosedDomain 3.3-9 IsInvertibleMatrix 5.3-9 IsIsomorphism, for ring maps 4.3-5 IsKaplanskyHermite 3.3-11 IsKoszul 3.3-37 IsLeftArtinian 3.3-39 IsLeftFiniteFreePresentationRing 3.3-49 IsLeftGlobalDimensionFinite 3.3-18 IsLeftHereditary 3.3-27 IsLeftHermite 3.3-30 IsLeftInvertibleMatrix 5.3-10 IsLeftNoetherian 3.3-33 IsLeftOreDomain 3.3-42 IsLeftPrincipalIdealRing 3.3-45 IsLeftRegular 5.3-7 IsLocal 3.3-23 IsLocalizedWeylRing 3.3-16 IsLowerStairCaseMatrix 5.3-20 IsLowerTriangularMatrix 5.3-16 IsMinusOne 3.3-56 IsMonic, for homalg ring elements 3.3-57 IsMonicUptoUnit, for homalg ring elements 3.3-58 IsMonomorphism, for ring maps 4.3-3 IsMorphism, for ring maps 4.3-1 IsNoetherian 3.3-32 IsOne 5.3-2 IsOreDomain 3.3-41 IsPermutationMatrix 5.3-4 IsPreHomalgRing 3.1-2 IsPrincipalIdealRing 3.3-44 IsRationalsForHomalg 3.3-3 IsReducedBasisOfColumnsMatrix 5.3-25 IsReducedBasisOfRowsMatrix 5.3-24 IsRegular 3.3-47 IsResidueClassRingOfTheIntegers 3.3-7 IsRightArtinian 3.3-40 IsRightFiniteFreePresentationRing 3.3-50 IsRightGlobalDimensionFinite 3.3-19 IsRightHereditary 3.3-28 IsRightHermite 3.3-31 IsRightInvertibleMatrix 5.3-11 IsRightNoetherian 3.3-34 IsRightOreDomain 3.3-43 IsRightPrincipalIdealRing 3.3-46 IsRightRegular 5.3-8 IsRingRelationsRep 6.1-4 IsScalarlMatrix 5.3-14 IsSemiLocalRing 3.3-24 IsSemiSimpleRing 3.3-52 IsSimpleRing 3.3-51 IsSpecialSubidentityMatrix 5.3-5 IsStrictLowerTriangularMatrix 5.3-18 IsStrictUpperTriangularMatrix 5.3-17 IsSubidentityMatrix 5.3-6 IsSuperCommutative 3.3-53 IsTriangularMatrix 5.3-21 IsUniqueFactorizationDomain 3.3-10 IsUnitFree 5.3-3 IsUpperStairCaseMatrix 5.3-19 IsUpperTriangularMatrix 5.3-15 IsVoidMatrix 5.3-28 IsWeylRing 3.3-15 IsZero, for matrices 5.3-1 IsZeroMatrix, homalgTable entry B.1-16 KroneckerMat, for matrices 5.5-12 KrullDimension 3.4-21 LeftDivide, for pairs of matrices 5.5-46 LeftGlobalDimension 3.4-22 LeftInverse 5.4-12 LeftInverseLazy, for matrices 5.5-4 MatrixOfSymbols 5.4-24 MinusOne 3.4-8 MulMat, homalgTable entry B.1-12 NonZeroColumns 5.4-7 NonZeroRows 5.4-6 NrColumns 5.4-2 NrRows 5.4-1 NumeratorOfHilbertPoincareSeries 5.4-17 One, for homalg rings 3.4-7 PositionOfFirstNonZeroEntryPerColumn 5.4-9 PositionOfFirstNonZeroEntryPerRow 5.4-8 ProductOfIndeterminates 3.4-9 ProjectiveDegree 5.4-22 Range, for ring maps 4.4-2 RationalParameters 3.4-10 ReducedBasisOfColumnModule, for matrices 5.5-31 ReducedBasisOfRowModule, for matrices 5.5-30 ReducedSyzygiesGeneratorsOfColumns, for matrices 5.5-33 ReducedSyzygiesGeneratorsOfRows, for matrices 5.5-32 ReducedSyzygiesOfColumns, for matrices 5.5-44 ReducedSyzygiesOfRows, for matrices 5.5-43 RelativeIndeterminateAntiCommutingVariablesOfExteriorRing 3.4-18 RelativeIndeterminateCoordinatesOfRingOfDerivations 3.4-14 RelativeIndeterminateDerivationsOfRingOfDerivations 3.4-16 RelativeIndeterminatesOfPolynomialRing 3.4-12 RelativeSyzygiesGeneratorsOfColumns, ResidueClassRing D.1-12 RelativeSyzygiesGeneratorsOfRows, ResidueClassRing D.1-11 RightDivide, for pairs of matrices 5.5-45 RightGlobalDimension 3.4-23 RightInverse 5.4-13 RightInverseLazy, for matrices 5.5-5 RingElementConstructor 3.4-3 RingMap, constructor for ring maps 4.2-1 RowRankOfMatrix 5.4-10 Source, for ring maps 4.4-1 StableRank 3.4-27 SubMat, homalgTable entry B.1-14 SyzygiesGeneratorsOfColumns, for matrices 5.5-27 SyzygiesGeneratorsOfRows, for matrices 5.5-26 SyzygiesOfColumns, for matrices 5.5-42 SyzygiesOfRows, for matrices 5.5-41 TypeOfHomalgMatrix 3.4-4 UnionOfColumns, for matrices 5.5-10 UnionOfRows, for matrices 5.5-9 UnreducedNumeratorOfHilbertPoincareSeries 5.4-16 Zero, for homalg rings 3.4-6 ZeroColumns 5.4-5 ZeroMatrix, homalgTable entry B.1-3 ZeroRows 5.4-4
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