\*, copy a matrix over a different ring 5.2-8\*, copy a matrix over a different ring (right) 5.2-8\*, for composable matrices 5.5-16\*, for ring elements and matrices 5.5-13\+, for matrices 5.5-14\-, for matrices 5.5-15\/, constructor for residue class rings 3.2-3\=, for matrices 5.5-17AddMat, ResidueClassRing D.2-13AddMat, homalgTable entry B.1-13AffineDegree 5.4-21AffineDimension 5.4-20AreEqualMatrices, ResidueClassRing D.3-1AreEqualMatrices, homalgTable entry B.2-1AreUnitsCentral 3.3-55AssociatedGradedRing 3.4-28BasisAlgorithmRespectsPrincipalIdeals 3.3-54BasisOfColumnModule, ResidueClassRing D.1-2BasisOfColumnModule, for matrices 5.5-23BasisOfColumns, for matrices 5.5-39BasisOfColumns, for pairs of matrices 5.5-39BasisOfColumnsCoeff, ResidueClassRing D.1-8BasisOfColumnsCoeff, for matrices 5.5-35BasisOfRowModule, ResidueClassRing D.1-1BasisOfRowModule, for matrices 5.5-22BasisOfRows, for matrices 5.5-38BasisOfRows, for pairs of matrices 5.5-38BasisOfRowsCoeff, ResidueClassRing D.1-7BasisOfRowsCoeff, for matrices 5.5-34CanBeUsedToDecideZero 6.3-1CertainColumns, ResidueClassRing D.2-7CertainColumns, for matrices 5.5-8CertainColumns, homalgTable entry B.1-7CertainRows, ResidueClassRing D.2-6CertainRows, for matrices 5.5-7CertainRows, homalgTable entry B.1-6CoefficientsOfNumeratorOfHilbertPoincareSeries 5.4-15CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries 5.4-14CoefficientsRing 3.4-20ColumnRankOfMatrix 5.4-11Compose, ResidueClassRing D.2-15Compose, homalgTable entry B.1-15ConstantTermOfHilbertPolynomialn 5.4-23ConstructorForHomalgMatrices 3.4-5ContainsAField 3.3-2CoordinateRingOfGraph, for ring maps 4.4-4DecideZero, for matrices and relations 5.5-40DecideZeroColumns, ResidueClassRing D.1-4DecideZeroColumns, for pairs of matrices 5.5-25DecideZeroColumnsEffectively, ResidueClassRing D.1-10DecideZeroColumnsEffectively, for pairs of matrices 5.5-37DecideZeroRows, ResidueClassRing D.1-3DecideZeroRows, for pairs of matrices 5.5-24DecideZeroRowsEffectively, ResidueClassRing D.1-9DecideZeroRowsEffectively, for pairs of matrices 5.5-36DegreeOfMorphism, for ring maps 4.4-3Determinant, ResidueClassRing D.2-19Determinant, homalgTable entry B.1-19DeterminantMat 5.4-3DiagMat, ResidueClassRing D.2-10DiagMat, for matrices 5.5-11DiagMat, homalgTable entry B.1-10ElementaryRank 3.4-26Eliminate 5.5-21Eval, for matrices created with AddMat C.4-15Eval, for matrices created with CertainColumns C.4-9Eval, for matrices created with CertainRows C.4-8Eval, for matrices created with Compose C.4-17Eval, for matrices created with DiagMat C.4-12Eval, for matrices created with HomalgIdentityMatrix C.4-4Eval, for matrices created with HomalgInitialIdentityMatrix C.4-2Eval, for matrices created with HomalgInitialMatrix C.4-1Eval, for matrices created with HomalgZeroMatrix C.4-3Eval, for matrices created with Involution C.4-7Eval, for matrices created with KroneckerMat C.4-13Eval, for matrices created with LeftInverseLazy C.4-5Eval, for matrices created with MulMat C.4-14Eval, for matrices created with RightInverseLazy C.4-6Eval, for matrices created with SubMat C.4-16Eval, for matrices created with UnionOfColumns C.4-11Eval, for matrices created with UnionOfRows C.4-10GeneralLinearRank 3.4-25GenerateSameColumnModule, for pairs of matrices 5.5-50GenerateSameRowModule, for pairs of matrices 5.5-49GetColumnIndependentUnitPositions, for matrices 5.5-18GetColumnIndependentUnitPositions, homalgTable entry B.2-6GetRowIndependentUnitPositions, for matrices 5.5-19GetRowIndependentUnitPositions, homalgTable entry B.2-7GetUnitPosition, for matrices 5.5-20GetUnitPosition, homalgTable entry B.2-8GlobalDimension 3.4-24HasInvariantBasisProperty 3.3-20HasLeftInvariantBasisProperty 3.3-21HasRightInvariantBasisProperty 3.3-22HilbertPoincareSeries 5.4-18HilbertPolynomial 5.4-19HomalgDiagonalMatrix, constructor for diagonal matrices 5.2-7HomalgFieldOfRationals, constructor for the field of rationals 3.2-2HomalgIdentityMatrix, constructor for identity matrices 5.2-4HomalgInitialIdentityMatrix, constructor for initial quadratic matrices with ones on the diagonal 5.2-2HomalgInitialMatrix, constructor for initial matrices filled with zeros 5.2-1HomalgMatrix, constructor for matrices using a list 5.2-6HomalgMatrix, constructor for matrices using a listlist 5.2-6HomalgMatrix, constructor for matrices using a string of a list 5.2-6HomalgMatrix, constructor for matrices using a string of a listlist 5.2-6homalgMode E.2-1HomalgRing, for matrices 5.5-1HomalgRingOfIntegers, constructor for the integers 3.2-1HomalgRingOfIntegers, constructor for the residue class rings of the integers 3.2-1homalgTable 3.4-2HomalgVoidMatrix, constructor for void matrices 5.2-5HomalgZeroMatrix, constructor for zero matrices 5.2-3IdentityMatrix, ResidueClassRing D.2-4IdentityMatrix, homalgTable entry B.1-4IndeterminateAntiCommutingVariablesOfExteriorRing 3.4-17IndeterminateCoordinatesOfRingOfDerivations 3.4-13IndeterminateDerivationsOfRingOfDerivations 3.4-15IndeterminatesOfExteriorRing 3.4-19IndeterminatesOfPolynomialRing 3.4-11InitialIdentityMatrix, ResidueClassRing D.2-2InitialIdentityMatrix, homalgTable entry for initial identity matrices B.1-2InitialMatrix, ResidueClassRing D.2-1InitialMatrix, homalgTable entry for initial matrices B.1-1Inverse, for homalg ring elements 3.4-1Involution, ResidueClassRing D.2-5Involution, for matrices 5.5-6Involution, homalgTable entry B.1-5IsArtinian, for rings 3.3-38IsAutomorphism, for ring maps 4.3-6IsBasisOfColumnsMatrix 5.3-23IsBasisOfRowsMatrix 5.3-22IsBezoutRing 3.3-8IsCohenMacaulay 3.3-35IsDedekindDomain 3.3-12IsDiagonalMatrix 5.3-13IsDiagonalMatrix, ResidueClassRing D.3-3IsDiagonalMatrix, homalgTable entry B.2-3IsDiscreteValuationRing 3.3-13IsDivisionRingForHomalg 3.3-5IsEmptyMatrix 5.3-12IsEpimorphism, for ring maps 4.3-4IsFieldForHomalg 3.3-4IsFiniteFreePresentationRing 3.3-48IsFreePolynomialRing 3.3-14IsGlobalDimensionFinite 3.3-17IsGorenstein 3.3-36IsHereditary 3.3-26IsHermite 3.3-29IsHomalgInternalMatrixRep 5.1-2IsHomalgInternalRingRep 3.1-4IsHomalgMatrix 5.1-1IsHomalgRing 3.1-1IsHomalgRingElement 3.1-3IsHomalgRingMap 4.1-1IsHomalgRingMapRep 4.1-3IsHomalgRingRelations 6.1-1IsHomalgRingRelationsAsGeneratorsOfLeftIdeal 6.1-2IsHomalgRingRelationsAsGeneratorsOfRightIdeal 6.1-3IsHomalgRingSelfMap 4.1-2IsIdentityMatrix, homalgTable entry B.2-2IsIdentityMorphism, for ring maps 4.3-2IsInitialIdentityMatrix 5.3-27IsInitialMatrix 5.3-26IsInjectivePresentation 6.3-2IsIntegersForHomalg 3.3-6IsIntegralDomain 3.3-25IsIntegrallyClosedDomain 3.3-9IsInvertibleMatrix 5.3-9IsIsomorphism, for ring maps 4.3-5IsKaplanskyHermite 3.3-11IsKoszul 3.3-37IsLeftArtinian 3.3-39IsLeftFiniteFreePresentationRing 3.3-49IsLeftGlobalDimensionFinite 3.3-18IsLeftHereditary 3.3-27IsLeftHermite 3.3-30IsLeftInvertibleMatrix 5.3-10IsLeftNoetherian 3.3-33IsLeftOreDomain 3.3-42IsLeftPrincipalIdealRing 3.3-45IsLeftRegular 5.3-7IsLeftRegular, for homalg ring elements 3.3-59IsLocal 3.3-23IsLocalizedWeylRing 3.3-16IsLowerStairCaseMatrix 5.3-20IsLowerTriangularMatrix 5.3-16IsMinusOne 3.3-56IsMonic, for homalg ring elements 3.3-57IsMonicUptoUnit, for homalg ring elements 3.3-58IsMonomorphism, for ring maps 4.3-3IsMorphism, for ring maps 4.3-1IsNoetherian 3.3-32IsOne 5.3-2IsOne, ResidueClassRing D.3-2IsOreDomain 3.3-41IsPermutationMatrix 5.3-4IsPreHomalgRing 3.1-2IsPrincipalIdealRing 3.3-44IsRationalsForHomalg 3.3-3IsReducedBasisOfColumnsMatrix 5.3-25IsReducedBasisOfRowsMatrix 5.3-24IsRegular 3.3-47IsRegular, for homalg ring elements 3.3-61IsResidueClassRingOfTheIntegers 3.3-7IsRightArtinian 3.3-40IsRightFiniteFreePresentationRing 3.3-50IsRightGlobalDimensionFinite 3.3-19IsRightHereditary 3.3-28IsRightHermite 3.3-31IsRightInvertibleMatrix 5.3-11IsRightNoetherian 3.3-34IsRightOreDomain 3.3-43IsRightPrincipalIdealRing 3.3-46IsRightRegular 5.3-8IsRightRegular, for homalg ring elements 3.3-60IsRingRelationsRep 6.1-4IsScalarlMatrix 5.3-14IsSemiLocalRing 3.3-24IsSemiSimpleRing 3.3-52IsSimpleRing 3.3-51IsSpecialSubidentityMatrix 5.3-5IsStrictLowerTriangularMatrix 5.3-18IsStrictUpperTriangularMatrix 5.3-17IsSubidentityMatrix 5.3-6IsSuperCommutative 3.3-53IsTriangularMatrix 5.3-21IsUniqueFactorizationDomain 3.3-10IsUnitFree 5.3-3IsUpperStairCaseMatrix 5.3-19IsUpperTriangularMatrix 5.3-15IsVoidMatrix 5.3-28IsWeylRing 3.3-15IsZero, for matrices 5.3-1IsZero, for rings 3.3-1IsZeroMatrix, ResidueClassRing D.2-16IsZeroMatrix, homalgTable entry B.1-16KroneckerMat, ResidueClassRing D.2-11KroneckerMat, for matrices 5.5-12KroneckerMat, homalgTable entry B.1-11KrullDimension 3.4-21LeftDivide, for pairs of matrices 5.5-46LeftDivide, for triples of matrices 5.5-48LeftGlobalDimension 3.4-22LeftInverse 5.4-12LeftInverse, for matrices 5.5-2LeftInverseLazy, for matrices 5.5-4MatrixOfSymbols 5.4-24MinusOne 3.4-8MulMat, ResidueClassRing D.2-12MulMat, homalgTable entry B.1-12NonZeroColumns 5.4-7NonZeroRows 5.4-6NrColumns 5.4-2NrColumns, ResidueClassRing D.2-18NrColumns, homalgTable entry B.1-18NrRows 5.4-1NrRows, ResidueClassRing D.2-17NrRows, homalgTable entry B.1-17NumeratorOfHilbertPoincareSeries 5.4-17One, for homalg rings 3.4-7PositionOfFirstNonZeroEntryPerColumn 5.4-9PositionOfFirstNonZeroEntryPerColumn, homalgTable entry B.2-10PositionOfFirstNonZeroEntryPerRow 5.4-8PositionOfFirstNonZeroEntryPerRow, homalgTable entry B.2-9ProductOfIndeterminates 3.4-9ProjectiveDegree 5.4-22Range, for ring maps 4.4-2RationalParameters 3.4-10ReducedBasisOfColumnModule, for matrices 5.5-31ReducedBasisOfRowModule, for matrices 5.5-30ReducedSyzygiesGeneratorsOfColumns, for matrices 5.5-33ReducedSyzygiesGeneratorsOfRows, for matrices 5.5-32ReducedSyzygiesOfColumns, for matrices 5.5-44ReducedSyzygiesOfColumns, for pairs of matrices 5.5-44ReducedSyzygiesOfRows, for matrices 5.5-43ReducedSyzygiesOfRows, for pairs of matrices 5.5-43RelativeIndeterminateAntiCommutingVariablesOfExteriorRing 3.4-18RelativeIndeterminateCoordinatesOfRingOfDerivations 3.4-14RelativeIndeterminateDerivationsOfRingOfDerivations 3.4-16RelativeIndeterminatesOfPolynomialRing 3.4-12RelativeSyzygiesGeneratorsOfColumns, ResidueClassRing D.1-12RelativeSyzygiesGeneratorsOfRows, ResidueClassRing D.1-11RightDivide, for pairs of matrices 5.5-45RightDivide, for triples of matrices 5.5-47RightGlobalDimension 3.4-23RightInverse 5.4-13RightInverse, for matrices 5.5-3RightInverseLazy, for matrices 5.5-5RingElementConstructor 3.4-3RingMap, constructor for ring maps 4.2-1RowRankOfMatrix 5.4-10Source, for ring maps 4.4-1StableRank 3.4-27SubMat, ResidueClassRing D.2-14SubMat, homalgTable entry B.1-14SyzygiesGeneratorsOfColumns, ResidueClassRing D.1-6SyzygiesGeneratorsOfColumns, for matrices 5.5-27SyzygiesGeneratorsOfColumns, for pairs of matrices 5.5-29SyzygiesGeneratorsOfRows, ResidueClassRing D.1-5SyzygiesGeneratorsOfRows, for matrices 5.5-26SyzygiesGeneratorsOfRows, for pairs of matrices 5.5-28SyzygiesOfColumns, for matrices 5.5-42SyzygiesOfColumns, for pairs of matrices 5.5-42SyzygiesOfRows, for matrices 5.5-41SyzygiesOfRows, for pairs of matrices 5.5-41TypeOfHomalgMatrix 3.4-4UnionOfColumns, ResidueClassRing D.2-9UnionOfColumns, for matrices 5.5-10UnionOfColumns, homalgTable entry B.1-9UnionOfRows, ResidueClassRing D.2-8UnionOfRows, for matrices 5.5-9UnionOfRows, homalgTable entry B.1-8UnreducedNumeratorOfHilbertPoincareSeries 5.4-16Zero, for homalg rings 3.4-6ZeroColumns 5.4-5ZeroColumns, ResidueClassRing D.3-5ZeroColumns, homalgTable entry B.2-5ZeroMatrix, ResidueClassRing D.2-3ZeroMatrix, homalgTable entry B.1-3ZeroRows 5.4-4ZeroRows, ResidueClassRing D.3-4ZeroRows, homalgTable entry B.2-4
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