  
  
  [1XIndex[101X
  
  [2X\*[102X, copy a matrix over a different ring 5.2-11 
      copy a matrix over a different ring (right) 5.2-11 
      for composable matrices 5.5-22 
      for ring elements and matrices 5.5-19 
  [2X\+[102X, for matrices 5.5-20 
  [2X\-[102X, for matrices 5.5-21 
  [2X\/[102X, constructor for residue class rings 3.2-2 
  [2X\=[102X, for matrices 5.5-23 
  [2XAddMat[102X, homalgTable entry B.1-17 
      ResidueClassRing D.2-15 
  [2XAffineDegree[102X 5.4-21 
  [2XAffineDimension[102X 5.4-20 
  [2XAreEqualMatrices[102X, homalgTable entry B.2-1 
      ResidueClassRing D.3-1 
  [2XAreUnitsCentral[102X 3.3-54 
  [2XAssociatedGradedRing[102X 3.4-28 
  [2XBasisAlgorithmRespectsPrincipalIdeals[102X 3.3-53 
  [2XBasisOfColumnModule[102X, for matrices 5.5-29 
      ResidueClassRing D.1-2 
  [2XBasisOfColumns[102X, for matrices 5.5-45 
      for pairs of matrices 5.5-45 
  [2XBasisOfColumnsCoeff[102X, for matrices 5.5-41 
      ResidueClassRing D.1-8 
  [2XBasisOfRowModule[102X, for matrices 5.5-28 
      ResidueClassRing D.1-1 
  [2XBasisOfRows[102X, for matrices 5.5-44 
      for pairs of matrices 5.5-44 
  [2XBasisOfRowsCoeff[102X, for matrices 5.5-40 
      ResidueClassRing D.1-7 
  [2XCanBeUsedToDecideZero[102X 6.3-1 
  [2XCertainColumns[102X, for matrices 5.5-9 
      homalgTable entry B.1-8 
      ResidueClassRing D.2-8 
  [2XCertainRows[102X, for matrices 5.5-8 
      homalgTable entry B.1-7 
      ResidueClassRing D.2-7 
  [2XCoefficientsOfNumeratorOfHilbertPoincareSeries[102X 5.4-15 
  [2XCoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries[102X 5.4-14 
  [2XCoefficientsRing[102X 3.4-20 
  [2XCoefficientsWithGivenMonomials[102X, for two homalg matrices 5.5-60 
      homalgTable entry B.1-24 
  [2XCoercedMatrix[102X, copy a matrix over a different ring 5.2-12 
      copy a matrix over a different ring (convenience) 5.2-12 
  [2XColumnRankOfMatrix[102X 5.4-11 
  [2XCompose[102X, homalgTable entry B.1-19 
      ResidueClassRing D.2-17 
  [2XConstantTermOfHilbertPolynomialn[102X 5.4-23 
  [2XConstructorForHomalgMatrices[102X 3.4-5 
  [2XContainsAField[102X 3.3-3 
  [2XConvertColumnToMatrix[102X, for matrices 5.5-13 
  [2XConvertMatrixToColumn[102X, for matrices 5.5-15 
  [2XConvertMatrixToRow[102X, for matrices 5.5-14 
  [2XConvertRowToMatrix[102X, for matrices 5.5-12 
  [2XCoordinateRingOfGraph[102X, for ring maps 4.4-4 
  [2XDecideZero[102X, for matrices and relations 5.5-46 
  [2XDecideZeroColumns[102X, for pairs of matrices 5.5-31 
      ResidueClassRing D.1-4 
  [2XDecideZeroColumnsEffectively[102X, for pairs of matrices 5.5-43 
      ResidueClassRing D.1-10 
  [2XDecideZeroRows[102X, for pairs of matrices 5.5-30 
      ResidueClassRing D.1-3 
  [2XDecideZeroRowsEffectively[102X, for pairs of matrices 5.5-42 
      ResidueClassRing D.1-9 
  [2XDegreeOfMorphism[102X, for ring maps 4.4-3 
  [2XDeterminant[102X, homalgTable entry B.1-23 
      ResidueClassRing D.2-21 
  [2XDeterminantMat[102X 5.4-3 
  [2XDiagMat[102X, for a homalg ring and a list of homalg matrices 5.5-16 
      homalgTable entry B.1-13 
      ResidueClassRing D.2-11 
  [2XDualKroneckerMat[102X, for matrices 5.5-18 
      homalgTable entry B.1-15 
      ResidueClassRing D.2-13 
  [2XElementaryRank[102X 3.4-26 
  [2XEliminate[102X 5.5-27 
  [2XEval[102X, for matrices created with AddMat C.4-18 
      for matrices created with CertainColumns C.4-11 
      for matrices created with CertainRows C.4-10 
      for matrices created with CoefficientsWithGivenMonomials C.4-21 
      for matrices created with CoercedMatrix C.4-9 
      for matrices created with Compose C.4-20 
      for matrices created with DiagMat C.4-14 
      for matrices created with DualKroneckerMat C.4-16 
      for matrices created with HomalgIdentityMatrix C.4-4 
      for matrices created with HomalgInitialIdentityMatrix C.4-2 
      for matrices created with HomalgInitialMatrix C.4-1 
      for matrices created with HomalgZeroMatrix C.4-3 
      for matrices created with Involution C.4-7 
      for matrices created with KroneckerMat C.4-15 
      for matrices created with LeftInverseLazy C.4-5 
      for matrices created with MulMat C.4-17 
      for matrices created with RightInverseLazy C.4-6 
      for matrices created with SubMat C.4-19 
      for matrices created with TransposedMatrix C.4-8 
      for matrices created with UnionOfColumns C.4-13 
      for matrices created with UnionOfRows C.4-12 
  [2XGeneralLinearRank[102X 3.4-25 
  [2XGenerateSameColumnModule[102X, for pairs of matrices 5.5-56 
  [2XGenerateSameRowModule[102X, for pairs of matrices 5.5-55 
  [2XGetColumnIndependentUnitPositions[102X, for matrices 5.5-24 
      homalgTable entry B.2-6 
  [2XGetRowIndependentUnitPositions[102X, for matrices 5.5-25 
      homalgTable entry B.2-7 
  [2XGetUnitPosition[102X, for matrices 5.5-26 
      homalgTable entry B.2-8 
  [2XGlobalDimension[102X 3.4-24 
  [2XHasInvariantBasisProperty[102X 3.3-21 
  [2XHilbertPoincareSeries[102X 5.4-18 
  [2XHilbertPolynomial[102X 5.4-19 
  [2XHomalgColumnVector[102X, constructor for matrices with a single column 5.2-9 
  [2XHomalgDiagonalMatrix[102X, constructor for diagonal matrices 5.2-10 
  [2XHomalgIdentityMatrix[102X, constructor for identity matrices 5.2-4 
  [2XHomalgInitialIdentityMatrix[102X, constructor for initial quadratic matrices with ones on the diagonal 5.2-2 
  [2XHomalgInitialMatrix[102X, constructor for initial matrices filled with zeros 5.2-1 
  [2XHomalgMatrix[102X, constructor for matrices using a list 5.2-6 
      constructor for matrices using a listlist 5.2-6 
      constructor for matrices using a listlist with given dimensions 5.2-6 
      constructor for matrices using a string of a list 5.2-6 
      constructor for matrices using a string of a listlist 5.2-6 
  [2XHomalgMatrixListList[102X, constructor for matrices using a listlist with given dimensions 5.2-7 
  [2XhomalgMode[102X E.2-1 
  [2XHomalgRing[102X, for matrices 5.5-1 
  [2XHomalgRingOfIntegers[102X, constructor for the integers 3.2-1 
      constructor for the residue class rings of the integers 3.2-1 
  [2XHomalgRowVector[102X, constructor for matrices with a single row 5.2-8 
  [2XhomalgTable[102X 3.4-2 
  [2XHomalgVoidMatrix[102X, constructor for void matrices 5.2-5 
  [2XHomalgZeroMatrix[102X, constructor for zero matrices 5.2-3 
  [2XIdentityMatrix[102X, homalgTable entry B.1-4 
      ResidueClassRing D.2-4 
  [2XIndeterminateAntiCommutingVariablesOfExteriorRing[102X 3.4-17 
  [2XIndeterminateCoordinatesOfRingOfDerivations[102X 3.4-13 
  [2XIndeterminateDerivationsOfRingOfDerivations[102X 3.4-15 
  [2XIndeterminatesOfExteriorRing[102X 3.4-19 
  [2XIndeterminatesOfPolynomialRing[102X 3.4-11 
  [2XInitialIdentityMatrix[102X, homalgTable entry for initial identity matrices B.1-2 
      ResidueClassRing D.2-2 
  [2XInitialMatrix[102X, homalgTable entry for initial matrices B.1-1 
      ResidueClassRing D.2-1 
  [2XInverse[102X, for homalg ring elements 3.4-1 
  [2XInvolution[102X, for matrices 5.5-6 
      homalgTable entry B.1-5 
      ResidueClassRing D.2-5 
  [2XIsArtinian[102X, for rings 3.3-37 
  [2XIsAutomorphism[102X, for ring maps 4.3-6 
  [2XIsBasisOfColumnsMatrix[102X 5.3-23 
  [2XIsBasisOfRowsMatrix[102X 5.3-22 
  [2XIsBezoutRing[102X 3.3-9 
  [2XIsCohenMacaulay[102X 3.3-34 
  [2XIsDedekindDomain[102X 3.3-13 
  [2XIsDiagonalMatrix[102X 5.3-13 
      homalgTable entry B.2-3 
      ResidueClassRing D.3-3 
  [2XIsDiscreteValuationRing[102X 3.3-14 
  [2XIsDivisionRingForHomalg[102X 3.3-6 
  [2XIsEmptyMatrix[102X 5.3-12 
  [2XIsEpimorphism[102X, for ring maps 4.3-4 
  [2XIsFieldForHomalg[102X 3.3-5 
  [2XIsFiniteFreePresentationRing[102X 3.3-47 
  [2XIsFreePolynomialRing[102X 3.3-15 
  [2XIsGlobalDimensionFinite[102X 3.3-18 
  [2XIsGorenstein[102X 3.3-35 
  [2XIsHereditary[102X 3.3-25 
  [2XIsHermite[102X 3.3-28 
  [2XIsHomalgInternalMatrixRep[102X 5.1-2 
  [2XIsHomalgInternalRingRep[102X 3.1-4 
  [2XIsHomalgMatrix[102X 5.1-1 
  [2XIsHomalgRing[102X 3.1-1 
  [2XIsHomalgRingElement[102X 3.1-3 
  [2XIsHomalgRingMap[102X 4.1-1 
  [2XIsHomalgRingMapRep[102X 4.1-3 
  [2XIsHomalgRingRelations[102X 6.1-1 
  [2XIsHomalgRingRelationsAsGeneratorsOfLeftIdeal[102X 6.1-2 
  [2XIsHomalgRingRelationsAsGeneratorsOfRightIdeal[102X 6.1-3 
  [2XIsHomalgRingSelfMap[102X 4.1-2 
  [2XIsIdentityMatrix[102X, homalgTable entry B.2-2 
  [2XIsIdentityMorphism[102X, for ring maps 4.3-2 
  [2XIsInitialIdentityMatrix[102X 5.3-27 
  [2XIsInitialMatrix[102X 5.3-26 
  [2XIsInjectivePresentation[102X 6.3-2 
  [2XIsIntegersForHomalg[102X 3.3-7 
  [2XIsIntegralDomain[102X 3.3-24 
  [2XIsIntegrallyClosedDomain[102X 3.3-10 
  [2XIsInvertibleMatrix[102X 5.3-9 
  [2XIsIsomorphism[102X, for ring maps 4.3-5 
  [2XIsKaplanskyHermite[102X 3.3-12 
  [2XIsKoszul[102X 3.3-36 
  [2XIsLeftArtinian[102X 3.3-38 
  [2XIsLeftFiniteFreePresentationRing[102X 3.3-48 
  [2XIsLeftGlobalDimensionFinite[102X 3.3-19 
  [2XIsLeftHereditary[102X 3.3-26 
  [2XIsLeftHermite[102X 3.3-29 
  [2XIsLeftInvertibleMatrix[102X 5.3-10 
  [2XIsLeftNoetherian[102X 3.3-32 
  [2XIsLeftOreDomain[102X 3.3-41 
  [2XIsLeftPrincipalIdealRing[102X 3.3-44 
  [2XIsLeftRegular[102X 5.3-7 
      for homalg ring elements 3.3-58 
  [2XIsLocal[102X 3.3-22 
  [2XIsLocalizedWeylRing[102X 3.3-17 
  [2XIsLowerStairCaseMatrix[102X 5.3-20 
  [2XIsLowerTriangularMatrix[102X 5.3-16 
  [2XIsMinusOne[102X 3.3-55 
  [2XIsMonic[102X, for homalg ring elements 3.3-56 
  [2XIsMonicUptoUnit[102X, for homalg ring elements 3.3-57 
  [2XIsMonomorphism[102X, for ring maps 4.3-3 
  [2XIsMorphism[102X, for ring maps 4.3-1 
  [2XIsNoetherian[102X 3.3-31 
  [2XIsNonZeroRing[102X, for rings 3.3-2 
  [2XIsOne[102X 5.3-2 
      ResidueClassRing D.3-2 
  [2XIsOreDomain[102X 3.3-40 
  [2XIsPermutationMatrix[102X 5.3-4 
  [2XIsPreHomalgRing[102X 3.1-2 
  [2XIsPrincipalIdealRing[102X 3.3-43 
  [2XIsRationalsForHomalg[102X 3.3-4 
  [2XIsReducedBasisOfColumnsMatrix[102X 5.3-25 
  [2XIsReducedBasisOfRowsMatrix[102X 5.3-24 
  [2XIsRegular[102X 3.3-46 
      for homalg ring elements 3.3-60 
  [2XIsResidueClassRingOfTheIntegers[102X 3.3-8 
  [2XIsRightArtinian[102X 3.3-39 
  [2XIsRightFiniteFreePresentationRing[102X 3.3-49 
  [2XIsRightGlobalDimensionFinite[102X 3.3-20 
  [2XIsRightHereditary[102X 3.3-27 
  [2XIsRightHermite[102X 3.3-30 
  [2XIsRightInvertibleMatrix[102X 5.3-11 
  [2XIsRightNoetherian[102X 3.3-33 
  [2XIsRightOreDomain[102X 3.3-42 
  [2XIsRightPrincipalIdealRing[102X 3.3-45 
  [2XIsRightRegular[102X 5.3-8 
      for homalg ring elements 3.3-59 
  [2XIsRingRelationsRep[102X 6.1-4 
  [2XIsScalarlMatrix[102X 5.3-14 
  [2XIsSemiLocalRing[102X 3.3-23 
  [2XIsSemiSimpleRing[102X 3.3-51 
  [2XIsSimpleRing[102X 3.3-50 
  [2XIsSpecialSubidentityMatrix[102X 5.3-5 
  [2XIsStrictLowerTriangularMatrix[102X 5.3-18 
  [2XIsStrictUpperTriangularMatrix[102X 5.3-17 
  [2XIsSubidentityMatrix[102X 5.3-6 
  [2XIsSuperCommutative[102X 3.3-52 
  [2XIsTriangularMatrix[102X 5.3-21 
  [2XIsUniqueFactorizationDomain[102X 3.3-11 
  [2XIsUnitFree[102X 5.3-3 
  [2XIsUpperStairCaseMatrix[102X 5.3-19 
  [2XIsUpperTriangularMatrix[102X 5.3-15 
  [2XIsVoidMatrix[102X 5.3-28 
  [2XIsWeylRing[102X 3.3-16 
  [2XIsZero[102X, for matrices 5.3-1 
      for rings 3.3-1 
  [2XIsZeroMatrix[102X, homalgTable entry B.1-20 
      ResidueClassRing D.2-18 
  [2XKroneckerMat[102X, for matrices 5.5-17 
      homalgTable entry B.1-14 
      ResidueClassRing D.2-12 
  [2XKrullDimension[102X 3.4-21 
  [2XLeftDivide[102X, for pairs of matrices 5.5-52 
      for triples of matrices 5.5-54 
  [2XLeftGlobalDimension[102X 3.4-22 
  [2XLeftInverse[102X 5.4-12 
      for matrices 5.5-2 
  [2XLeftInverseLazy[102X, for matrices 5.5-4 
  [5XMatricesForHomalg[105X .-1 
  [2XMatrixOfSymbols[102X 5.4-24 
  [2XMinusOne[102X 3.4-8 
  [2XMulMat[102X, homalgTable entry B.1-16 
      ResidueClassRing D.2-14 
  [2XNonZeroColumns[102X 5.4-7 
  [2XNonZeroRows[102X 5.4-6 
  [2XNrColumns[102X 5.4-2 
      homalgTable entry B.1-22 
      ResidueClassRing D.2-20 
  [2XNrRows[102X 5.4-1 
      homalgTable entry B.1-21 
      ResidueClassRing D.2-19 
  [2XNumeratorOfHilbertPoincareSeries[102X 5.4-17 
  [2XOne[102X, for homalg rings 3.4-7 
  [2XPositionOfFirstNonZeroEntryPerColumn[102X 5.4-9 
      homalgTable entry B.2-10 
  [2XPositionOfFirstNonZeroEntryPerRow[102X 5.4-8 
      homalgTable entry B.2-9 
  [2XProductOfIndeterminates[102X 3.4-9 
  [2XProjectiveDegree[102X 5.4-22 
  [2XRange[102X, for ring maps 4.4-2 
  [2XRationalParameters[102X 3.4-10 
  [2XReducedBasisOfColumnModule[102X, for matrices 5.5-37 
  [2XReducedBasisOfRowModule[102X, for matrices 5.5-36 
  [2XReducedSyzygiesGeneratorsOfColumns[102X, for matrices 5.5-39 
  [2XReducedSyzygiesGeneratorsOfRows[102X, for matrices 5.5-38 
  [2XReducedSyzygiesOfColumns[102X, for matrices 5.5-50 
      for pairs of matrices 5.5-50 
  [2XReducedSyzygiesOfRows[102X, for matrices 5.5-49 
      for pairs of matrices 5.5-49 
  [2XRelativeIndeterminateAntiCommutingVariablesOfExteriorRing[102X 3.4-18 
  [2XRelativeIndeterminateCoordinatesOfRingOfDerivations[102X 3.4-14 
  [2XRelativeIndeterminateDerivationsOfRingOfDerivations[102X 3.4-16 
  [2XRelativeIndeterminatesOfPolynomialRing[102X 3.4-12 
  [2XRelativeSyzygiesGeneratorsOfColumns[102X, ResidueClassRing D.1-12 
  [2XRelativeSyzygiesGeneratorsOfRows[102X, ResidueClassRing D.1-11 
  [2XRightDivide[102X, for pairs of matrices 5.5-51 
      for triples of matrices 5.5-53 
  [2XRightGlobalDimension[102X 3.4-23 
  [2XRightInverse[102X 5.4-13 
      for matrices 5.5-3 
  [2XRightInverseLazy[102X, for matrices 5.5-5 
  [2XRingElementConstructor[102X 3.4-3 
  [2XRingMap[102X, constructor for ring maps 4.2-1 
  [2XRowRankOfMatrix[102X 5.4-10 
  [2XSimplifyHomalgMatrixByLeftAndRightMultiplicationWithInvertibleMatrices[102X, for matrices 5.5-57 
  [2XSimplifyHomalgMatrixByLeftMultiplicationWithInvertibleMatrix[102X, for matrices 5.5-58 
  [2XSimplifyHomalgMatrixByRightMultiplicationWithInvertibleMatrix[102X, for matrices 5.5-59 
  [2XSource[102X, for ring maps 4.4-1 
  [2XStableRank[102X 3.4-27 
  [2XSubMat[102X, homalgTable entry B.1-18 
      ResidueClassRing D.2-16 
  [2XSyzygiesGeneratorsOfColumns[102X, for matrices 5.5-33 
      for pairs of matrices 5.5-35 
      ResidueClassRing D.1-6 
  [2XSyzygiesGeneratorsOfRows[102X, for matrices 5.5-32 
      for pairs of matrices 5.5-34 
      ResidueClassRing D.1-5 
  [2XSyzygiesOfColumns[102X, for matrices 5.5-48 
      for pairs of matrices 5.5-48 
  [2XSyzygiesOfRows[102X, for matrices 5.5-47 
      for pairs of matrices 5.5-47 
  [2XTransposedMatrix[102X, for matrices 5.5-7 
      homalgTable entry B.1-6 
      ResidueClassRing D.2-6 
  [2XTypeOfHomalgMatrix[102X 3.4-4 
  [2XUnionOfColumns[102X, for a homalg ring, an integer and a list of homalg matrices 5.5-11 
      homalgTable entry B.1-11 
      ResidueClassRing D.2-10 
  [2XUnionOfColumnsPair[102X, homalgTable entry B.1-12 
  [2XUnionOfRows[102X, for a homalg ring, an integer and a list of homalg matrices 5.5-10 
      homalgTable entry B.1-9 
      ResidueClassRing D.2-9 
  [2XUnionOfRowsPair[102X, homalgTable entry B.1-10 
  [2XUnreducedNumeratorOfHilbertPoincareSeries[102X 5.4-16 
  [2XZero[102X, for homalg rings 3.4-6 
  [2XZeroColumns[102X 5.4-5 
      homalgTable entry B.2-5 
      ResidueClassRing D.3-5 
  [2XZeroMatrix[102X, homalgTable entry B.1-3 
      ResidueClassRing D.2-3 
  [2XZeroRows[102X 5.4-4 
      homalgTable entry B.2-4 
      ResidueClassRing D.3-4 
  
  
  -------------------------------------------------------
