\*, copy a matrix over a different ring 5.2-11 \+, for matrices 5.5-20 \-, for matrices 5.5-21 \/, constructor for residue class rings 3.2-2 \=, for matrices 5.5-23 AddMat, homalgTable entry B.1-17 AffineDegree 5.4-21 AffineDimension 5.4-20 AreEqualMatrices, homalgTable entry B.2-1 AreUnitsCentral 3.3-54 AssociatedGradedRing 3.4-28 BasisAlgorithmRespectsPrincipalIdeals 3.3-53 BasisOfColumnModule, for matrices 5.5-29 BasisOfColumns, for matrices 5.5-45 BasisOfColumnsCoeff, for matrices 5.5-41 BasisOfRowModule, for matrices 5.5-28 BasisOfRows, for matrices 5.5-44 BasisOfRowsCoeff, for matrices 5.5-40 CanBeUsedToDecideZero 6.3-1 CertainColumns, for matrices 5.5-9 CertainRows, for matrices 5.5-8 CoefficientsOfNumeratorOfHilbertPoincareSeries 5.4-15 CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries 5.4-14 CoefficientsRing 3.4-20 CoefficientsWithGivenMonomials, for two homalg matrices 5.5-60 CoercedMatrix, copy a matrix over a different ring 5.2-12 ColumnRankOfMatrix 5.4-11 Compose, homalgTable entry B.1-19 ConstantTermOfHilbertPolynomialn 5.4-23 ConstructorForHomalgMatrices 3.4-5 ContainsAField 3.3-3 ConvertColumnToMatrix, for matrices 5.5-13 ConvertMatrixToColumn, for matrices 5.5-15 ConvertMatrixToRow, for matrices 5.5-14 ConvertRowToMatrix, for matrices 5.5-12 CoordinateRingOfGraph, for ring maps 4.4-4 DecideZero, for matrices and relations 5.5-46 DecideZeroColumns, for pairs of matrices 5.5-31 DecideZeroColumnsEffectively, for pairs of matrices 5.5-43 DecideZeroRows, for pairs of matrices 5.5-30 DecideZeroRowsEffectively, for pairs of matrices 5.5-42 DegreeOfMorphism, for ring maps 4.4-3 Determinant, homalgTable entry B.1-23 DeterminantMat 5.4-3 DiagMat, for a homalg ring and a list of homalg matrices 5.5-16 DualKroneckerMat, for matrices 5.5-18 ElementaryRank 3.4-26 Eliminate 5.5-27 Eval, for matrices created with AddMat C.4-18 GeneralLinearRank 3.4-25 GenerateSameColumnModule, for pairs of matrices 5.5-56 GenerateSameRowModule, for pairs of matrices 5.5-55 GetColumnIndependentUnitPositions, for matrices 5.5-24 GetRowIndependentUnitPositions, for matrices 5.5-25 GetUnitPosition, for matrices 5.5-26 GlobalDimension 3.4-24 HasInvariantBasisProperty 3.3-21 HilbertPoincareSeries 5.4-18 HilbertPolynomial 5.4-19 HomalgColumnVector, constructor for matrices with a single column 5.2-9 HomalgDiagonalMatrix, constructor for diagonal matrices 5.2-10 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 HomalgMatrixListList, constructor for matrices using a listlist with given dimensions 5.2-7 homalgMode E.2-1 HomalgRing, for matrices 5.5-1 HomalgRingOfIntegers, constructor for the integers 3.2-1 HomalgRowVector, constructor for matrices with a single row 5.2-8 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 3.3-37 IsAutomorphism, for ring maps 4.3-6 IsBasisOfColumnsMatrix 5.3-23 IsBasisOfRowsMatrix 5.3-22 IsBezoutRing 3.3-9 IsCohenMacaulay 3.3-34 IsDedekindDomain 3.3-13 IsDiagonalMatrix 5.3-13 IsDiscreteValuationRing 3.3-14 IsDivisionRingForHomalg 3.3-6 IsEmptyMatrix 5.3-12 IsEpimorphism, for ring maps 4.3-4 IsFieldForHomalg 3.3-5 IsFiniteFreePresentationRing 3.3-47 IsFreePolynomialRing 3.3-15 IsGlobalDimensionFinite 3.3-18 IsGorenstein 3.3-35 IsHereditary 3.3-25 IsHermite 3.3-28 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 3.3-7 IsIntegralDomain 3.3-24 IsIntegrallyClosedDomain 3.3-10 IsInvertibleMatrix 5.3-9 IsIsomorphism, for ring maps 4.3-5 IsKaplanskyHermite 3.3-12 IsKoszul 3.3-36 IsLeftArtinian 3.3-38 IsLeftFiniteFreePresentationRing 3.3-48 IsLeftGlobalDimensionFinite 3.3-19 IsLeftHereditary 3.3-26 IsLeftHermite 3.3-29 IsLeftInvertibleMatrix 5.3-10 IsLeftNoetherian 3.3-32 IsLeftOreDomain 3.3-41 IsLeftPrincipalIdealRing 3.3-44 IsLeftRegular 5.3-7 IsLocal 3.3-22 IsLocalizedWeylRing 3.3-17 IsLowerStairCaseMatrix 5.3-20 IsLowerTriangularMatrix 5.3-16 IsMinusOne 3.3-55 IsMonic, for homalg ring elements 3.3-56 IsMonicUptoUnit, for homalg ring elements 3.3-57 IsMonomorphism, for ring maps 4.3-3 IsMorphism, for ring maps 4.3-1 IsNoetherian 3.3-31 IsNonZeroRing, for rings 3.3-2 IsOne 5.3-2 IsOreDomain 3.3-40 IsPermutationMatrix 5.3-4 IsPreHomalgRing 3.1-2 IsPrincipalIdealRing 3.3-43 IsRationalsForHomalg 3.3-4 IsReducedBasisOfColumnsMatrix 5.3-25 IsReducedBasisOfRowsMatrix 5.3-24 IsRegular 3.3-46 IsResidueClassRingOfTheIntegers 3.3-8 IsRightArtinian 3.3-39 IsRightFiniteFreePresentationRing 3.3-49 IsRightGlobalDimensionFinite 3.3-20 IsRightHereditary 3.3-27 IsRightHermite 3.3-30 IsRightInvertibleMatrix 5.3-11 IsRightNoetherian 3.3-33 IsRightOreDomain 3.3-42 IsRightPrincipalIdealRing 3.3-45 IsRightRegular 5.3-8 IsRingRelationsRep 6.1-4 IsScalarlMatrix 5.3-14 IsSemiLocalRing 3.3-23 IsSemiSimpleRing 3.3-51 IsSimpleRing 3.3-50 IsSpecialSubidentityMatrix 5.3-5 IsStrictLowerTriangularMatrix 5.3-18 IsStrictUpperTriangularMatrix 5.3-17 IsSubidentityMatrix 5.3-6 IsSuperCommutative 3.3-52 IsTriangularMatrix 5.3-21 IsUniqueFactorizationDomain 3.3-11 IsUnitFree 5.3-3 IsUpperStairCaseMatrix 5.3-19 IsUpperTriangularMatrix 5.3-15 IsVoidMatrix 5.3-28 IsWeylRing 3.3-16 IsZero, for matrices 5.3-1 IsZeroMatrix, homalgTable entry B.1-20 KroneckerMat, for matrices 5.5-17 KrullDimension 3.4-21 LeftDivide, for pairs of matrices 5.5-52 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.1-16 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 5.5-37 ReducedBasisOfRowModule, for matrices 5.5-36 ReducedSyzygiesGeneratorsOfColumns, for matrices 5.5-39 ReducedSyzygiesGeneratorsOfRows, for matrices 5.5-38 ReducedSyzygiesOfColumns, for matrices 5.5-50 ReducedSyzygiesOfRows, for matrices 5.5-49 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 5.5-51 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 SimplifyHomalgMatrixByLeftAndRightMultiplicationWithInvertibleMatrices, for matrices 5.5-57 SimplifyHomalgMatrixByLeftMultiplicationWithInvertibleMatrix, for matrices 5.5-58 SimplifyHomalgMatrixByRightMultiplicationWithInvertibleMatrix, for matrices 5.5-59 Source, for ring maps 4.4-1 StableRank 3.4-27 SubMat, homalgTable entry B.1-18 SyzygiesGeneratorsOfColumns, for matrices 5.5-33 SyzygiesGeneratorsOfRows, for matrices 5.5-32 SyzygiesOfColumns, for matrices 5.5-48 SyzygiesOfRows, for matrices 5.5-47 TransposedMatrix, for matrices 5.5-7 TypeOfHomalgMatrix 3.4-4 UnionOfColumns, for a homalg ring, an integer and a list of homalg matrices 5.5-11 UnionOfColumnsPair, homalgTable entry B.1-12 UnionOfRows, for a homalg ring, an integer and a list of homalg matrices 5.5-10 UnionOfRowsPair, homalgTable entry B.1-10 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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