  
  
  [1XIndex[0X
  
  [2X\*[0X (copy a matrix over a different ring (right))  5.2-8
  [2X\*[0X (copy a matrix over a different ring)  5.2-8
  [2X\*[0X (for composable matrices)  5.5-12
  [2X\*[0X (for ring elements and matrices)  5.5-9
  [2X\+[0X (for matrices)  5.5-10
  [2X\-[0X (for matrices)  5.5-11
  [2X\/[0X (constructor for residue class rings)  3.2-3
  [2X\=[0X (for matrices)  5.5-13
  [2XAddMat[0X (homalgTable entry)  B.1-13
  [2XAddMat[0X (ResidueClassRing)  D.2-13
  [2XAreEqualMatrices[0X (homalgTable entry)  B.2-1
  [2XAreEqualMatrices[0X (ResidueClassRing)  D.3-1
  [2XBasisAlgorithmRespectsPrincipalIdeals[0X  3.3-48
  [2XBasisOfColumnModule[0X (for matrices)  5.5-18
  [2XBasisOfColumnModule[0X (ResidueClassRing)  D.1-2
  [2XBasisOfColumns[0X (for matrices)  5.5-34
  [2XBasisOfColumns[0X (for pairs of matrices)  5.5-34
  [2XBasisOfColumnsCoeff[0X (for matrices)  5.5-30
  [2XBasisOfColumnsCoeff[0X (ResidueClassRing)  D.1-8
  [2XBasisOfRowModule[0X (for matrices)  5.5-17
  [2XBasisOfRowModule[0X (ResidueClassRing)  D.1-1
  [2XBasisOfRows[0X (for matrices)  5.5-33
  [2XBasisOfRows[0X (for pairs of matrices)  5.5-33
  [2XBasisOfRowsCoeff[0X (for matrices)  5.5-29
  [2XBasisOfRowsCoeff[0X (ResidueClassRing)  D.1-7
  [2XCanBeUsedToDecideZero[0X  6.3-1
  [2XCertainColumns[0X (for matrices)  5.5-4
  [2XCertainColumns[0X (homalgTable entry)  B.1-7
  [2XCertainColumns[0X (ResidueClassRing)  D.2-7
  [2XCertainRows[0X (for matrices)  5.5-3
  [2XCertainRows[0X (homalgTable entry)  B.1-6
  [2XCertainRows[0X (ResidueClassRing)  D.2-6
  [2XCoefficientsRing[0X  3.4-18
  [2XColumnRankOfMatrix[0X  5.4-12
  [2XCompose[0X (homalgTable entry)  B.1-15
  [2XCompose[0X (ResidueClassRing)  D.2-15
  [2XConstructorForHomalgMatrices[0X  3.4-6
  [2XContainsAField[0X  3.3-1
  [2XCoordinateRingOfGraph[0X (for ring maps)  4.4-4
  [2XDecideZero[0X (for matrices and relations)  5.5-35
  [2XDecideZeroColumns[0X (for pairs of matrices)  5.5-20
  [2XDecideZeroColumns[0X (ResidueClassRing)  D.1-4
  [2XDecideZeroColumnsEffectively[0X (for pairs of matrices)  5.5-32
  [2XDecideZeroColumnsEffectively[0X (ResidueClassRing)  D.1-10
  [2XDecideZeroRows[0X (for pairs of matrices)  5.5-19
  [2XDecideZeroRows[0X (ResidueClassRing)  D.1-3
  [2XDecideZeroRowsEffectively[0X (for pairs of matrices)  5.5-31
  [2XDecideZeroRowsEffectively[0X (ResidueClassRing)  D.1-9
  [2XDegreeOfMorphism[0X (for ring maps)  4.4-3
  [2XDegreesOfEntries[0X  5.4-10
  [2XDegreesOfEntries[0X (homalgTable entry)  B.2-9
  [2XDeterminant[0X (homalgTable entry)  B.1-19
  [2XDeterminant[0X (ResidueClassRing)  D.2-19
  [2XDeterminantMat[0X  5.4-3
  [2XDiagMat[0X (for matrices)  5.5-7
  [2XDiagMat[0X (homalgTable entry)  B.1-10
  [2XDiagMat[0X (ResidueClassRing)  D.2-10
  [2XElementaryRank[0X  3.4-24
  [2XEval[0X (for matrices created with HomalgInitialMatrix)  C.4-1
  [2XEval[0X (for matrices created with DiagMat)  C.4-10
  [2XEval[0X (for matrices created with KroneckerMat)  C.4-11
  [2XEval[0X (for matrices created with MulMat)  C.4-12
  [2XEval[0X (for matrices created with AddMat)  C.4-13
  [2XEval[0X (for matrices created with SubMat)  C.4-14
  [2XEval[0X (for matrices created with Compose)  C.4-15
  [2XEval[0X (for matrices created with LeftInverse)  C.4-16
  [2XEval[0X (for matrices created with RightInverse)  C.4-17
  [2XEval[0X (for matrices created with HomalgInitialIdentityMatrix)  C.4-2
  [2XEval[0X (for matrices created with HomalgZeroMatrix)  C.4-3
  [2XEval[0X (for matrices created with HomalgIdentityMatrix)  C.4-4
  [2XEval[0X (for matrices created with Involution)  C.4-5
  [2XEval[0X (for matrices created with CertainRows)  C.4-6
  [2XEval[0X (for matrices created with CertainColumns)  C.4-7
  [2XEval[0X (for matrices created with UnionOfRows)  C.4-8
  [2XEval[0X (for matrices created with UnionOfColumns)  C.4-9
  [2XGeneralLinearRank[0X  3.4-23
  [2XGenerateSameColumnModule[0X (for pairs of matrices)  5.5-45
  [2XGenerateSameRowModule[0X (for pairs of matrices)  5.5-44
  [2XGetColumnIndependentUnitPositions[0X (for matrices)  5.5-14
  [2XGetColumnIndependentUnitPositions[0X (homalgTable entry)  B.2-6
  [2XGetRowIndependentUnitPositions[0X (for matrices)  5.5-15
  [2XGetRowIndependentUnitPositions[0X (homalgTable entry)  B.2-7
  [2XGetUnitPosition[0X (for matrices)  5.5-16
  [2XGetUnitPosition[0X (homalgTable entry)  B.2-8
  [2XGlobalDimension[0X  3.4-22
  [2XHasInvariantBasisProperty[0X  3.3-18
  [2XHasLeftInvariantBasisProperty[0X  3.3-19
  [2XHasRightInvariantBasisProperty[0X  3.3-20
  [2XHomalgDiagonalMatrix[0X (constructor for diagonal matrices)  5.2-7
  [2XHomalgFieldOfRationals[0X (constructor for the field of rationals)  3.2-2
  [2XHomalgIdentityMatrix[0X (constructor for identity matrices)  5.2-4
  [2XHomalgInitialIdentityMatrix[0X (constructor for initial quadratic matrices with ones on the diagonal)  5.2-2
  [2XHomalgInitialMatrix[0X (constructor for initial matrices filled with zeros)  5.2-1
  [2XHomalgMatrix[0X (constructor for matrices using a list)  5.2-6
  [2XHomalgMatrix[0X (constructor for matrices using a listlist)  5.2-6
  [2XHomalgMatrix[0X (constructor for matrices using a string of a list)  5.2-6
  [2XHomalgMatrix[0X (constructor for matrices using a string of a listlist)  5.2-6
  [2XhomalgMode[0X  E.2-1
  [2XHomalgRing[0X (for matrices)  5.5-1
  [2XHomalgRingOfIntegers[0X (constructor for the integers)  3.2-1
  [2XHomalgRingOfIntegers[0X (constructor for the residue class rings of the integers)  3.2-1
  [2XhomalgTable[0X  3.4-3
  [2XHomalgVoidMatrix[0X (constructor for void matrices)  5.2-5
  [2XHomalgZeroMatrix[0X (constructor for zero matrices)  5.2-3
  [2XIdentityMatrix[0X (homalgTable entry)  B.1-4
  [2XIdentityMatrix[0X (ResidueClassRing)  D.2-4
  [2XIndeterminateAntiCommutingVariablesOfExteriorRing[0X  3.4-14
  [2XIndeterminateCoordinatesOfRingOfDerivations[0X  3.4-12
  [2XIndeterminateDerivationsOfRingOfDerivations[0X  3.4-13
  [2XIndeterminatesOfExteriorRing[0X  3.4-15
  [2XIndeterminatesOfPolynomialRing[0X  3.4-11
  [2XInitialIdentityMatrix[0X (homalgTable entry for initial identity matrices)  B.1-2
  [2XInitialIdentityMatrix[0X (ResidueClassRing)  D.2-2
  [2XInitialMatrix[0X (homalgTable entry for initial matrices)  B.1-1
  [2XInitialMatrix[0X (ResidueClassRing)  D.2-1
  [2XInvolution[0X (for matrices)  5.5-2
  [2XInvolution[0X (homalgTable entry)  B.1-5
  [2XInvolution[0X (ResidueClassRing)  D.2-5
  [2XIsArtinian[0X (for rings)  3.3-33
  [2XIsAutomorphism[0X (for ring maps)  4.3-6
  [2XIsBasisOfColumnsMatrix[0X  5.3-22
  [2XIsBasisOfRowsMatrix[0X  5.3-21
  [2XIsBezoutRing[0X  3.3-7
  [2XIsDedekindDomain[0X  3.3-11
  [2XIsDiagonalMatrix[0X  5.3-12
  [2XIsDiagonalMatrix[0X (homalgTable entry)  B.2-3
  [2XIsDiagonalMatrix[0X (ResidueClassRing)  D.3-3
  [2XIsDiscreteValuationRing[0X  3.3-12
  [2XIsDivisionRingForHomalg[0X  3.3-4
  [2XIsEmptyMatrix[0X  5.3-11
  [2XIsEpimorphism[0X (for ring maps)  4.3-4
  [2XIsFieldForHomalg[0X  3.3-3
  [2XIsFiniteFreePresentationRing[0X  3.3-43
  [2XIsFreePolynomialRing[0X  3.3-13
  [2XIsGlobalDimensionFinite[0X  3.3-15
  [2XIsHereditary[0X  3.3-24
  [2XIsHermite[0X  3.3-27
  [2XIsHomalgInternalMatrixRep[0X  5.1-2
  [2XIsHomalgInternalRingRep[0X  3.1-4
  [2XIsHomalgMatrix[0X  5.1-1
  [2XIsHomalgRing[0X  3.1-1
  [2XIsHomalgRingElement[0X  3.1-3
  [2XIsHomalgRingMap[0X  4.1-1
  [2XIsHomalgRingMapRep[0X  4.1-3
  [2XIsHomalgRingRelations[0X  6.1-1
  [2XIsHomalgRingRelationsAsGeneratorsOfLeftIdeal[0X  6.1-2
  [2XIsHomalgRingRelationsAsGeneratorsOfRightIdeal[0X  6.1-3
  [2XIsHomalgRingSelfMap[0X  4.1-2
  [2XIsIdentityMatrix[0X (homalgTable entry)  B.2-2
  [2XIsIdentityMorphism[0X (for ring maps)  4.3-2
  [2XIsInitialIdentityMatrix[0X  5.3-27
  [2XIsInitialMatrix[0X  5.3-26
  [2XIsInjectivePresentation[0X  6.3-2
  [2XIsIntegersForHomalg[0X  3.3-5
  [2XIsIntegralDomain[0X  3.3-23
  [2XIsIntegrallyClosedDomain[0X  3.3-8
  [2XIsInvertibleMatrix[0X  5.3-8
  [2XIsIsomorphism[0X (for ring maps)  4.3-5
  [2XIsKaplanskyHermite[0X  3.3-10
  [2XIsLeftArtinian[0X  3.3-34
  [2XIsLeftFiniteFreePresentationRing[0X  3.3-44
  [2XIsLeftGlobalDimensionFinite[0X  3.3-16
  [2XIsLeftHereditary[0X  3.3-25
  [2XIsLeftHermite[0X  3.3-28
  [2XIsLeftInvertibleMatrix[0X  5.3-9
  [2XIsLeftNoetherian[0X  3.3-31
  [2XIsLeftOreDomain[0X  3.3-37
  [2XIsLeftPrincipalIdealRing[0X  3.3-40
  [2XIsLeftRegularMatrix[0X  5.3-6
  [2XIsLocalRing[0X  3.3-21
  [2XIsLowerStairCaseMatrix[0X  5.3-19
  [2XIsLowerTriangularMatrix[0X  5.3-15
  [2XIsMinusOne[0X  3.3-49
  [2XIsMonomorphism[0X (for ring maps)  4.3-3
  [2XIsMorphism[0X (for ring maps)  4.3-1
  [2XIsMutableMatrix[0X  5.3-25
  [2XIsNoetherian[0X  3.3-30
  [2XIsOne[0X  5.3-2
  [2XIsOne[0X (ResidueClassRing)  D.3-2
  [2XIsOreDomain[0X  3.3-36
  [2XIsPermutationMatrix[0X  5.3-3
  [2XIsPreHomalgRing[0X  3.1-2
  [2XIsPrincipalIdealRing[0X  3.3-39
  [2XIsRationalsForHomalg[0X  3.3-2
  [2XIsReducedBasisOfColumnsMatrix[0X  5.3-24
  [2XIsReducedBasisOfRowsMatrix[0X  5.3-23
  [2XIsRegular[0X  3.3-42
  [2XIsResidueClassRingOfTheIntegers[0X  3.3-6
  [2XIsRightArtinian[0X  3.3-35
  [2XIsRightFiniteFreePresentationRing[0X  3.3-45
  [2XIsRightGlobalDimensionFinite[0X  3.3-17
  [2XIsRightHereditary[0X  3.3-26
  [2XIsRightHermite[0X  3.3-29
  [2XIsRightInvertibleMatrix[0X  5.3-10
  [2XIsRightNoetherian[0X  3.3-32
  [2XIsRightOreDomain[0X  3.3-38
  [2XIsRightPrincipalIdealRing[0X  3.3-41
  [2XIsRightRegularMatrix[0X  5.3-7
  [2XIsRingRelationsRep[0X  6.1-4
  [2XIsScalarlMatrix[0X  5.3-13
  [2XIsSemiLocalRing[0X  3.3-22
  [2XIsSemiSimpleRing[0X  3.3-47
  [2XIsSimpleRing[0X  3.3-46
  [2XIsSpecialSubidentityMatrix[0X  5.3-4
  [2XIsStrictLowerTriangularMatrix[0X  5.3-17
  [2XIsStrictUpperTriangularMatrix[0X  5.3-16
  [2XIsSubidentityMatrix[0X  5.3-5
  [2XIsTriangularMatrix[0X  5.3-20
  [2XIsUniqueFactorizationDomain[0X  3.3-9
  [2XIsUpperStairCaseMatrix[0X  5.3-18
  [2XIsUpperTriangularMatrix[0X  5.3-14
  [2XIsVoidMatrix[0X  5.3-28
  [2XIsWeylRing[0X  3.3-14
  [2XIsZero[0X (for matrices)  5.3-1
  [2XIsZeroMatrix[0X (homalgTable entry)  B.1-16
  [2XIsZeroMatrix[0X (ResidueClassRing)  D.2-16
  [2XKroneckerMat[0X (for matrices)  5.5-8
  [2XKroneckerMat[0X (homalgTable entry)  B.1-11
  [2XKroneckerMat[0X (ResidueClassRing)  D.2-11
  [2XKrullDimension[0X  3.4-19
  [2XLeftDivide[0X (for pairs of matrices)  5.5-41
  [2XLeftDivide[0X (for triples of matrices)  5.5-43
  [2XLeftGlobalDimension[0X  3.4-20
  [2XLeftInverse[0X (for matrices)  5.4-13
  [5XMatricesForHomalg[0m  .-2
  [2XMatrixOfWeightsOfIndeterminates[0X  3.4-17
  [2XMinusOne[0X  3.4-9
  [2XMulMat[0X (homalgTable entry)  B.1-12
  [2XMulMat[0X (ResidueClassRing)  D.2-12
  [2XNonZeroColumns[0X  5.4-7
  [2XNonZeroRows[0X  5.4-6
  [2XNrColumns[0X  5.4-2
  [2XNrColumns[0X (homalgTable entry)  B.1-18
  [2XNrColumns[0X (ResidueClassRing)  D.2-18
  [2XNrRows[0X  5.4-1
  [2XNrRows[0X (homalgTable entry)  B.1-17
  [2XNrRows[0X (ResidueClassRing)  D.2-17
  [2XOne[0X (for homalg ring elements)  3.4-2
  [2XOne[0X (for homalg rings)  3.4-8
  [2XPositionOfFirstNonZeroEntryPerColumn[0X  5.4-9
  [2XPositionOfFirstNonZeroEntryPerRow[0X  5.4-8
  [2XRange[0X (for ring maps)  4.4-2
  [2XRationalParameters[0X  3.4-10
  [2XReducedBasisOfColumnModule[0X (for matrices)  5.5-26
  [2XReducedBasisOfRowModule[0X (for matrices)  5.5-25
  [2XReducedSyzygiesGeneratorsOfColumns[0X (for matrices)  5.5-28
  [2XReducedSyzygiesGeneratorsOfRows[0X (for matrices)  5.5-27
  [2XReducedSyzygiesOfColumns[0X (for matrices)  5.5-39
  [2XReducedSyzygiesOfColumns[0X (for pairs of matrices)  5.5-39
  [2XReducedSyzygiesOfRows[0X (for matrices)  5.5-38
  [2XReducedSyzygiesOfRows[0X (for pairs of matrices)  5.5-38
  [2XRelativeSyzygiesGeneratorsOfColumns[0X (ResidueClassRing)  D.1-12
  [2XRelativeSyzygiesGeneratorsOfRows[0X (ResidueClassRing)  D.1-11
  [2XRightDivide[0X (for pairs of matrices)  5.5-40
  [2XRightDivide[0X (for triples of matrices)  5.5-42
  [2XRightGlobalDimension[0X  3.4-21
  [2XRightInverse[0X (for matrices)  5.4-14
  [2XRingElementConstructor[0X  3.4-4
  [2XRingMap[0X (constructor for ring maps)  4.2-1
  [2XRowRankOfMatrix[0X  5.4-11
  [2XSource[0X (for ring maps)  4.4-1
  [2XStableRank[0X  3.4-25
  [2XSubMat[0X (homalgTable entry)  B.1-14
  [2XSubMat[0X (ResidueClassRing)  D.2-14
  [2XSyzygiesGeneratorsOfColumns[0X (for matrices)  5.5-22
  [2XSyzygiesGeneratorsOfColumns[0X (for pairs of matrices)  5.5-24
  [2XSyzygiesGeneratorsOfColumns[0X (ResidueClassRing)  D.1-6
  [2XSyzygiesGeneratorsOfRows[0X (for matrices)  5.5-21
  [2XSyzygiesGeneratorsOfRows[0X (for pairs of matrices)  5.5-23
  [2XSyzygiesGeneratorsOfRows[0X (ResidueClassRing)  D.1-5
  [2XSyzygiesOfColumns[0X (for matrices)  5.5-37
  [2XSyzygiesOfColumns[0X (for pairs of matrices)  5.5-37
  [2XSyzygiesOfRows[0X (for matrices)  5.5-36
  [2XSyzygiesOfRows[0X (for pairs of matrices)  5.5-36
  [2XTypeOfHomalgMatrix[0X  3.4-5
  [2XUnionOfColumns[0X (for matrices)  5.5-6
  [2XUnionOfColumns[0X (homalgTable entry)  B.1-9
  [2XUnionOfColumns[0X (ResidueClassRing)  D.2-9
  [2XUnionOfRows[0X (for matrices)  5.5-5
  [2XUnionOfRows[0X (homalgTable entry)  B.1-8
  [2XUnionOfRows[0X (ResidueClassRing)  D.2-8
  [2XWeightsOfIndeterminates[0X  3.4-16
  [2XZero[0X (for homalg ring elements)  3.4-1
  [2XZero[0X (for homalg rings)  3.4-7
  [2XZeroColumns[0X  5.4-5
  [2XZeroColumns[0X (homalgTable entry)  B.2-5
  [2XZeroColumns[0X (ResidueClassRing)  D.3-5
  [2XZeroMatrix[0X (homalgTable entry)  B.1-3
  [2XZeroMatrix[0X (ResidueClassRing)  D.2-3
  [2XZeroRows[0X  5.4-4
  [2XZeroRows[0X (homalgTable entry)  B.2-4
  [2XZeroRows[0X (ResidueClassRing)  D.3-4
  
  
  -------------------------------------------------------
