  
  
  [1XIndex[101X
  
  [2X\*[102X (copy a matrix over a different ring (right))  5.2-8
  [2X\*[102X (copy a matrix over a different ring)  5.2-8
  [2X\*[102X (for ring elements and matrices)  5.5-13
  [2X\*[102X (for composable matrices)  5.5-16
  [2X\+[102X (for matrices)  5.5-14
  [2X\-[102X (for matrices)  5.5-15
  [2X\/[102X (constructor for residue class rings)  3.2-3
  [2X\=[102X (for matrices)  5.5-17
  [2XAddMat[102X (homalgTable entry)  B.1-13
  [2XAddMat[102X (ResidueClassRing)  D.2-13
  [2XAffineDegree[102X  5.4-21
  [2XAffineDimension[102X  5.4-20
  [2XAreEqualMatrices[102X (homalgTable entry)  B.2-1
  [2XAreEqualMatrices[102X (ResidueClassRing)  D.3-1
  [2XAreUnitsCentral[102X  3.3-55
  [2XAssociatedGradedRing[102X  3.4-28
  [2XBasisAlgorithmRespectsPrincipalIdeals[102X  3.3-54
  [2XBasisOfColumnModule[102X (for matrices)  5.5-23
  [2XBasisOfColumnModule[102X (ResidueClassRing)  D.1-2
  [2XBasisOfColumns[102X (for matrices)  5.5-39
  [2XBasisOfColumns[102X (for pairs of matrices)  5.5-39
  [2XBasisOfColumnsCoeff[102X (for matrices)  5.5-35
  [2XBasisOfColumnsCoeff[102X (ResidueClassRing)  D.1-8
  [2XBasisOfRowModule[102X (for matrices)  5.5-22
  [2XBasisOfRowModule[102X (ResidueClassRing)  D.1-1
  [2XBasisOfRows[102X (for matrices)  5.5-38
  [2XBasisOfRows[102X (for pairs of matrices)  5.5-38
  [2XBasisOfRowsCoeff[102X (for matrices)  5.5-34
  [2XBasisOfRowsCoeff[102X (ResidueClassRing)  D.1-7
  [2XCanBeUsedToDecideZero[102X  6.3-1
  [2XCertainColumns[102X (for matrices)  5.5-8
  [2XCertainColumns[102X (homalgTable entry)  B.1-7
  [2XCertainColumns[102X (ResidueClassRing)  D.2-7
  [2XCertainRows[102X (for matrices)  5.5-7
  [2XCertainRows[102X (homalgTable entry)  B.1-6
  [2XCertainRows[102X (ResidueClassRing)  D.2-6
  [2XCoefficientsOfNumeratorOfHilbertPoincareSeries[102X  5.4-15
  [2XCoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries[102X  5.4-14
  [2XCoefficientsRing[102X  3.4-20
  [2XColumnRankOfMatrix[102X  5.4-11
  [2XCompose[102X (homalgTable entry)  B.1-15
  [2XCompose[102X (ResidueClassRing)  D.2-15
  [2XConstantTermOfHilbertPolynomialn[102X  5.4-23
  [2XConstructorForHomalgMatrices[102X  3.4-5
  [2XContainsAField[102X  3.3-2
  [2XCoordinateRingOfGraph[102X (for ring maps)  4.4-4
  [2XDecideZero[102X (for matrices and relations)  5.5-40
  [2XDecideZeroColumns[102X (for pairs of matrices)  5.5-25
  [2XDecideZeroColumns[102X (ResidueClassRing)  D.1-4
  [2XDecideZeroColumnsEffectively[102X (for pairs of matrices)  5.5-37
  [2XDecideZeroColumnsEffectively[102X (ResidueClassRing)  D.1-10
  [2XDecideZeroRows[102X (for pairs of matrices)  5.5-24
  [2XDecideZeroRows[102X (ResidueClassRing)  D.1-3
  [2XDecideZeroRowsEffectively[102X (for pairs of matrices)  5.5-36
  [2XDecideZeroRowsEffectively[102X (ResidueClassRing)  D.1-9
  [2XDegreeOfMorphism[102X (for ring maps)  4.4-3
  [2XDeterminant[102X (homalgTable entry)  B.1-19
  [2XDeterminant[102X (ResidueClassRing)  D.2-19
  [2XDeterminantMat[102X  5.4-3
  [2XDiagMat[102X (for matrices)  5.5-11
  [2XDiagMat[102X (homalgTable entry)  B.1-10
  [2XDiagMat[102X (ResidueClassRing)  D.2-10
  [2XElementaryRank[102X  3.4-26
  [2XEliminate[102X  5.5-21
  [2XEval[102X (for matrices created with HomalgInitialMatrix)  C.4-1
  [2XEval[102X (for matrices created with UnionOfRows)  C.4-10
  [2XEval[102X (for matrices created with UnionOfColumns)  C.4-11
  [2XEval[102X (for matrices created with DiagMat)  C.4-12
  [2XEval[102X (for matrices created with KroneckerMat)  C.4-13
  [2XEval[102X (for matrices created with MulMat)  C.4-14
  [2XEval[102X (for matrices created with AddMat)  C.4-15
  [2XEval[102X (for matrices created with SubMat)  C.4-16
  [2XEval[102X (for matrices created with Compose)  C.4-17
  [2XEval[102X (for matrices created with HomalgInitialIdentityMatrix)  C.4-2
  [2XEval[102X (for matrices created with HomalgZeroMatrix)  C.4-3
  [2XEval[102X (for matrices created with HomalgIdentityMatrix)  C.4-4
  [2XEval[102X (for matrices created with LeftInverseLazy)  C.4-5
  [2XEval[102X (for matrices created with RightInverseLazy)  C.4-6
  [2XEval[102X (for matrices created with Involution)  C.4-7
  [2XEval[102X (for matrices created with CertainRows)  C.4-8
  [2XEval[102X (for matrices created with CertainColumns)  C.4-9
  [2XGeneralLinearRank[102X  3.4-25
  [2XGenerateSameColumnModule[102X (for pairs of matrices)  5.5-50
  [2XGenerateSameRowModule[102X (for pairs of matrices)  5.5-49
  [2XGetColumnIndependentUnitPositions[102X (for matrices)  5.5-18
  [2XGetColumnIndependentUnitPositions[102X (homalgTable entry)  B.2-6
  [2XGetRowIndependentUnitPositions[102X (for matrices)  5.5-19
  [2XGetRowIndependentUnitPositions[102X (homalgTable entry)  B.2-7
  [2XGetUnitPosition[102X (for matrices)  5.5-20
  [2XGetUnitPosition[102X (homalgTable entry)  B.2-8
  [2XGlobalDimension[102X  3.4-24
  [2XHasInvariantBasisProperty[102X  3.3-20
  [2XHasLeftInvariantBasisProperty[102X  3.3-21
  [2XHasRightInvariantBasisProperty[102X  3.3-22
  [2XHilbertPoincareSeries[102X  5.4-18
  [2XHilbertPolynomial[102X  5.4-19
  [2XHomalgDiagonalMatrix[102X (constructor for diagonal matrices)  5.2-7
  [2XHomalgFieldOfRationals[102X (constructor for the field of rationals)  3.2-2
  [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
  [2XHomalgMatrix[102X (constructor for matrices using a listlist)  5.2-6
  [2XHomalgMatrix[102X (constructor for matrices using a string of a list)  5.2-6
  [2XHomalgMatrix[102X (constructor for matrices using a string of a listlist)  5.2-6
  [2XhomalgMode[102X  E.2-1
  [2XHomalgRing[102X (for matrices)  5.5-1
  [2XHomalgRingOfIntegers[102X (constructor for the integers)  3.2-1
  [2XHomalgRingOfIntegers[102X (constructor for the residue class rings of the integers)  3.2-1
  [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
  [2XIdentityMatrix[102X (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
  [2XInitialIdentityMatrix[102X (ResidueClassRing)  D.2-2
  [2XInitialMatrix[102X (homalgTable entry for initial matrices)  B.1-1
  [2XInitialMatrix[102X (ResidueClassRing)  D.2-1
  [2XInverse[102X (for homalg ring elements)  3.4-1
  [2XInvolution[102X (for matrices)  5.5-6
  [2XInvolution[102X (homalgTable entry)  B.1-5
  [2XInvolution[102X (ResidueClassRing)  D.2-5
  [2XIsArtinian[102X (for rings)  3.3-38
  [2XIsAutomorphism[102X (for ring maps)  4.3-6
  [2XIsBasisOfColumnsMatrix[102X  5.3-23
  [2XIsBasisOfRowsMatrix[102X  5.3-22
  [2XIsBezoutRing[102X  3.3-8
  [2XIsCohenMacaulay[102X  3.3-35
  [2XIsDedekindDomain[102X  3.3-12
  [2XIsDiagonalMatrix[102X  5.3-13
  [2XIsDiagonalMatrix[102X (homalgTable entry)  B.2-3
  [2XIsDiagonalMatrix[102X (ResidueClassRing)  D.3-3
  [2XIsDiscreteValuationRing[102X  3.3-13
  [2XIsDivisionRingForHomalg[102X  3.3-5
  [2XIsEmptyMatrix[102X  5.3-12
  [2XIsEpimorphism[102X (for ring maps)  4.3-4
  [2XIsFieldForHomalg[102X  3.3-4
  [2XIsFiniteFreePresentationRing[102X  3.3-48
  [2XIsFreePolynomialRing[102X  3.3-14
  [2XIsGlobalDimensionFinite[102X  3.3-17
  [2XIsGorenstein[102X  3.3-36
  [2XIsHereditary[102X  3.3-26
  [2XIsHermite[102X  3.3-29
  [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  3.3-6
  [2XIsIntegralDomain[102X  3.3-25
  [2XIsIntegrallyClosedDomain[102X  3.3-9
  [2XIsInvertibleMatrix[102X  5.3-9
  [2XIsIsomorphism[102X (for ring maps)  4.3-5
  [2XIsKaplanskyHermite[102X  3.3-11
  [2XIsKoszul[102X  3.3-37
  [2XIsLeftArtinian[102X  3.3-39
  [2XIsLeftFiniteFreePresentationRing[102X  3.3-49
  [2XIsLeftGlobalDimensionFinite[102X  3.3-18
  [2XIsLeftHereditary[102X  3.3-27
  [2XIsLeftHermite[102X  3.3-30
  [2XIsLeftInvertibleMatrix[102X  5.3-10
  [2XIsLeftNoetherian[102X  3.3-33
  [2XIsLeftOreDomain[102X  3.3-42
  [2XIsLeftPrincipalIdealRing[102X  3.3-45
  [2XIsLeftRegular[102X (for homalg ring elements)  3.3-59
  [2XIsLeftRegular[102X  5.3-7
  [2XIsLocal[102X  3.3-23
  [2XIsLocalizedWeylRing[102X  3.3-16
  [2XIsLowerStairCaseMatrix[102X  5.3-20
  [2XIsLowerTriangularMatrix[102X  5.3-16
  [2XIsMinusOne[102X  3.3-56
  [2XIsMonic[102X (for homalg ring elements)  3.3-57
  [2XIsMonicUptoUnit[102X (for homalg ring elements)  3.3-58
  [2XIsMonomorphism[102X (for ring maps)  4.3-3
  [2XIsMorphism[102X (for ring maps)  4.3-1
  [2XIsNoetherian[102X  3.3-32
  [2XIsOne[102X  5.3-2
  [2XIsOne[102X (ResidueClassRing)  D.3-2
  [2XIsOreDomain[102X  3.3-41
  [2XIsPermutationMatrix[102X  5.3-4
  [2XIsPreHomalgRing[102X  3.1-2
  [2XIsPrincipalIdealRing[102X  3.3-44
  [2XIsRationalsForHomalg[102X  3.3-3
  [2XIsReducedBasisOfColumnsMatrix[102X  5.3-25
  [2XIsReducedBasisOfRowsMatrix[102X  5.3-24
  [2XIsRegular[102X  3.3-47
  [2XIsRegular[102X (for homalg ring elements)  3.3-61
  [2XIsResidueClassRingOfTheIntegers[102X  3.3-7
  [2XIsRightArtinian[102X  3.3-40
  [2XIsRightFiniteFreePresentationRing[102X  3.3-50
  [2XIsRightGlobalDimensionFinite[102X  3.3-19
  [2XIsRightHereditary[102X  3.3-28
  [2XIsRightHermite[102X  3.3-31
  [2XIsRightInvertibleMatrix[102X  5.3-11
  [2XIsRightNoetherian[102X  3.3-34
  [2XIsRightOreDomain[102X  3.3-43
  [2XIsRightPrincipalIdealRing[102X  3.3-46
  [2XIsRightRegular[102X (for homalg ring elements)  3.3-60
  [2XIsRightRegular[102X  5.3-8
  [2XIsRingRelationsRep[102X  6.1-4
  [2XIsScalarlMatrix[102X  5.3-14
  [2XIsSemiLocalRing[102X  3.3-24
  [2XIsSemiSimpleRing[102X  3.3-52
  [2XIsSimpleRing[102X  3.3-51
  [2XIsSpecialSubidentityMatrix[102X  5.3-5
  [2XIsStrictLowerTriangularMatrix[102X  5.3-18
  [2XIsStrictUpperTriangularMatrix[102X  5.3-17
  [2XIsSubidentityMatrix[102X  5.3-6
  [2XIsSuperCommutative[102X  3.3-53
  [2XIsTriangularMatrix[102X  5.3-21
  [2XIsUniqueFactorizationDomain[102X  3.3-10
  [2XIsUnitFree[102X  5.3-3
  [2XIsUpperStairCaseMatrix[102X  5.3-19
  [2XIsUpperTriangularMatrix[102X  5.3-15
  [2XIsVoidMatrix[102X  5.3-28
  [2XIsWeylRing[102X  3.3-15
  [2XIsZero[102X (for rings)  3.3-1
  [2XIsZero[102X (for matrices)  5.3-1
  [2XIsZeroMatrix[102X (homalgTable entry)  B.1-16
  [2XIsZeroMatrix[102X (ResidueClassRing)  D.2-16
  [2XKroneckerMat[102X (for matrices)  5.5-12
  [2XKroneckerMat[102X (homalgTable entry)  B.1-11
  [2XKroneckerMat[102X (ResidueClassRing)  D.2-11
  [2XKrullDimension[102X  3.4-21
  [2XLeftDivide[102X (for pairs of matrices)  5.5-46
  [2XLeftDivide[102X (for triples of matrices)  5.5-48
  [2XLeftGlobalDimension[102X  3.4-22
  [2XLeftInverse[102X  5.4-12
  [2XLeftInverse[102X (for matrices)  5.5-2
  [2XLeftInverseLazy[102X (for matrices)  5.5-4
  [5XMatricesForHomalg[105X  .-2
  [2XMatrixOfSymbols[102X  5.4-24
  [2XMinusOne[102X  3.4-8
  [2XMulMat[102X (homalgTable entry)  B.1-12
  [2XMulMat[102X (ResidueClassRing)  D.2-12
  [2XNonZeroColumns[102X  5.4-7
  [2XNonZeroRows[102X  5.4-6
  [2XNrColumns[102X  5.4-2
  [2XNrColumns[102X (homalgTable entry)  B.1-18
  [2XNrColumns[102X (ResidueClassRing)  D.2-18
  [2XNrRows[102X  5.4-1
  [2XNrRows[102X (homalgTable entry)  B.1-17
  [2XNrRows[102X (ResidueClassRing)  D.2-17
  [2XNumeratorOfHilbertPoincareSeries[102X  5.4-17
  [2XOne[102X (for homalg rings)  3.4-7
  [2XPositionOfFirstNonZeroEntryPerColumn[102X  5.4-9
  [2XPositionOfFirstNonZeroEntryPerColumn[102X (homalgTable entry)  B.2-10
  [2XPositionOfFirstNonZeroEntryPerRow[102X  5.4-8
  [2XPositionOfFirstNonZeroEntryPerRow[102X (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)  5.5-31
  [2XReducedBasisOfRowModule[102X (for matrices)  5.5-30
  [2XReducedSyzygiesGeneratorsOfColumns[102X (for matrices)  5.5-33
  [2XReducedSyzygiesGeneratorsOfRows[102X (for matrices)  5.5-32
  [2XReducedSyzygiesOfColumns[102X (for matrices)  5.5-44
  [2XReducedSyzygiesOfColumns[102X (for pairs of matrices)  5.5-44
  [2XReducedSyzygiesOfRows[102X (for matrices)  5.5-43
  [2XReducedSyzygiesOfRows[102X (for pairs of matrices)  5.5-43
  [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)  5.5-45
  [2XRightDivide[102X (for triples of matrices)  5.5-47
  [2XRightGlobalDimension[102X  3.4-23
  [2XRightInverse[102X  5.4-13
  [2XRightInverse[102X (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
  [2XSource[102X (for ring maps)  4.4-1
  [2XStableRank[102X  3.4-27
  [2XSubMat[102X (homalgTable entry)  B.1-14
  [2XSubMat[102X (ResidueClassRing)  D.2-14
  [2XSyzygiesGeneratorsOfColumns[102X (for matrices)  5.5-27
  [2XSyzygiesGeneratorsOfColumns[102X (for pairs of matrices)  5.5-29
  [2XSyzygiesGeneratorsOfColumns[102X (ResidueClassRing)  D.1-6
  [2XSyzygiesGeneratorsOfRows[102X (for matrices)  5.5-26
  [2XSyzygiesGeneratorsOfRows[102X (for pairs of matrices)  5.5-28
  [2XSyzygiesGeneratorsOfRows[102X (ResidueClassRing)  D.1-5
  [2XSyzygiesOfColumns[102X (for matrices)  5.5-42
  [2XSyzygiesOfColumns[102X (for pairs of matrices)  5.5-42
  [2XSyzygiesOfRows[102X (for matrices)  5.5-41
  [2XSyzygiesOfRows[102X (for pairs of matrices)  5.5-41
  [2XTypeOfHomalgMatrix[102X  3.4-4
  [2XUnionOfColumns[102X (for matrices)  5.5-10
  [2XUnionOfColumns[102X (homalgTable entry)  B.1-9
  [2XUnionOfColumns[102X (ResidueClassRing)  D.2-9
  [2XUnionOfRows[102X (for matrices)  5.5-9
  [2XUnionOfRows[102X (homalgTable entry)  B.1-8
  [2XUnionOfRows[102X (ResidueClassRing)  D.2-8
  [2XUnreducedNumeratorOfHilbertPoincareSeries[102X  5.4-16
  [2XZero[102X (for homalg rings)  3.4-6
  [2XZeroColumns[102X  5.4-5
  [2XZeroColumns[102X (homalgTable entry)  B.2-5
  [2XZeroColumns[102X (ResidueClassRing)  D.3-5
  [2XZeroMatrix[102X (homalgTable entry)  B.1-3
  [2XZeroMatrix[102X (ResidueClassRing)  D.2-3
  [2XZeroRows[102X  5.4-4
  [2XZeroRows[102X (homalgTable entry)  B.2-4
  [2XZeroRows[102X (ResidueClassRing)  D.3-4
  
  
  -------------------------------------------------------
