GAP (MatricesForHomalg) - Index

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### Index

MatricesForHomalg .-1
`\*`, 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
`\+`, 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
ResidueClassRing D.2-15
`AffineDegree` 5.4-21
`AffineDimension` 5.4-20
`AreEqualMatrices`, homalgTable entry B.2-1
ResidueClassRing D.3-1
`AreUnitsCentral` 3.3-54
`AssociatedGradedRing` 3.4-28
`BasisAlgorithmRespectsPrincipalIdeals` 3.3-53
`BasisOfColumnModule`, for matrices 5.5-29
ResidueClassRing D.1-2
`BasisOfColumns`, for matrices 5.5-45
for pairs of matrices 5.5-45
`BasisOfColumnsCoeff`, for matrices 5.5-41
ResidueClassRing D.1-8
`BasisOfRowModule`, for matrices 5.5-28
ResidueClassRing D.1-1
`BasisOfRows`, for matrices 5.5-44
for pairs of matrices 5.5-44
`BasisOfRowsCoeff`, for matrices 5.5-40
ResidueClassRing D.1-7
`CanBeUsedToDecideZero` 6.3-1
`CertainColumns`, for matrices 5.5-9
homalgTable entry B.1-8
ResidueClassRing D.2-8
`CertainRows`, for matrices 5.5-8
homalgTable entry B.1-7
ResidueClassRing D.2-7
`CoefficientsOfNumeratorOfHilbertPoincareSeries` 5.4-15
`CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries` 5.4-14
`CoefficientsRing` 3.4-20
`CoefficientsWithGivenMonomials`, for two homalg matrices 5.5-64
homalgTable entry B.1-24
`CoercedMatrix`, copy a matrix over a different ring 5.2-12
copy a matrix over a different ring (convenience) 5.2-12
`ColumnRankOfMatrix` 5.4-11
`Compose`, homalgTable entry B.1-19
ResidueClassRing D.2-17
`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
ResidueClassRing D.1-4
`DecideZeroColumnsEffectively`, for pairs of matrices 5.5-43
ResidueClassRing D.1-10
`DecideZeroRows`, for pairs of matrices 5.5-30
ResidueClassRing D.1-3
`DecideZeroRowsEffectively`, for pairs of matrices 5.5-42
ResidueClassRing D.1-9
`DegreeOfMorphism`, for ring maps 4.4-3
`Determinant`, homalgTable entry B.1-23
ResidueClassRing D.2-21
`DeterminantMat` 5.4-3
`DiagMat`, for a homalg ring and a list of homalg matrices 5.5-16
homalgTable entry B.1-13
ResidueClassRing D.2-11
`DualKroneckerMat`, for matrices 5.5-18
homalgTable entry B.1-15
ResidueClassRing D.2-13
`ElementaryRank` 3.4-26
`Eliminate` 5.5-27
`Eval`, 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
`GeneralLinearRank` 3.4-25
`GenerateSameColumnModule`, for pairs of matrices 5.5-60
`GenerateSameRowModule`, for pairs of matrices 5.5-59
`GetColumnIndependentUnitPositions`, for matrices 5.5-24
homalgTable entry B.2-6
`GetRowIndependentUnitPositions`, for matrices 5.5-25
homalgTable entry B.2-7
`GetUnitPosition`, for matrices 5.5-26
homalgTable entry B.2-8
`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
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
`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
constructor for the residue class rings of 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
ResidueClassRing D.2-4
`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
ResidueClassRing D.2-2
`InitialMatrix`, homalgTable entry for initial matrices B.1-1
ResidueClassRing D.2-1
`Inverse`, for homalg ring elements 3.4-1
`Involution`, for matrices 5.5-6
homalgTable entry B.1-5
ResidueClassRing D.2-5
`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
homalgTable entry B.2-3
ResidueClassRing D.3-3
`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
for homalg ring elements 3.3-58
`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
ResidueClassRing D.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
for homalg ring elements 3.3-60
`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
for homalg ring elements 3.3-59
`IsRingRelationsRep` 6.1-4
`IsScalarMatrix` 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
for rings 3.3-1
`IsZeroMatrix`, homalgTable entry B.1-20
ResidueClassRing D.2-18
`KroneckerMat`, for matrices 5.5-17
homalgTable entry B.1-14
ResidueClassRing D.2-12
`KrullDimension` 3.4-21
`LeftDivide`, for pairs of matrices 5.5-52
for triples of matrices 5.5-54
`LeftGlobalDimension` 3.4-22
`LeftInverse` 5.4-12
for matrices 5.5-2
`LeftInverseLazy`, for matrices 5.5-4
`MatrixOfSymbols` 5.4-24
`MinusOne` 3.4-8
`MulMat`, homalgTable entry B.1-16
ResidueClassRing D.2-14
`NonZeroColumns` 5.4-7
`NonZeroRows` 5.4-6
`NumberColumns` 5.4-2
homalgTable entry B.1-22
ResidueClassRing D.2-20
`NumberRows` 5.4-1
homalgTable entry B.1-21
ResidueClassRing D.2-19
`NumeratorOfHilbertPoincareSeries` 5.4-17
`One`, for homalg rings 3.4-7
`PositionOfFirstNonZeroEntryPerColumn` 5.4-9
homalgTable entry B.2-10
`PositionOfFirstNonZeroEntryPerRow` 5.4-8
homalgTable entry B.2-9
`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
for pairs of matrices 5.5-50
`ReducedSyzygiesOfRows`, for matrices 5.5-49
for pairs of 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
for triples of matrices 5.5-53
`RightGlobalDimension` 3.4-23
`RightInverse` 5.4-13
for matrices 5.5-3
`RightInverseLazy`, for matrices 5.5-5
`RingElementConstructor` 3.4-3
`RingMap`, constructor for ring maps 4.2-1
`RowRankOfMatrix` 5.4-10
`SafeLeftDivide`, for pairs of matrices 5.5-56
`SafeRightDivide`, for pairs of matrices 5.5-55
`SimplifyHomalgMatrixByLeftAndRightMultiplicationWithInvertibleMatrices`, for matrices 5.5-61
`SimplifyHomalgMatrixByLeftMultiplicationWithInvertibleMatrix`, for matrices 5.5-62
`SimplifyHomalgMatrixByRightMultiplicationWithInvertibleMatrix`, for matrices 5.5-63
`Source`, for ring maps 4.4-1
`StableRank` 3.4-27
`SubMat`, homalgTable entry B.1-18
ResidueClassRing D.2-16
`SyzygiesGeneratorsOfColumns`, for matrices 5.5-33
for pairs of matrices 5.5-35
ResidueClassRing D.1-6
`SyzygiesGeneratorsOfRows`, for matrices 5.5-32
for pairs of matrices 5.5-34
ResidueClassRing D.1-5
`SyzygiesOfColumns`, for matrices 5.5-48
for pairs of matrices 5.5-48
`SyzygiesOfRows`, for matrices 5.5-47
for pairs of matrices 5.5-47
`TransposedMatrix`, for matrices 5.5-7
homalgTable entry B.1-6
ResidueClassRing D.2-6
`TypeOfHomalgMatrix` 3.4-4
`UnionOfColumns`, for a homalg ring, an integer and a list of homalg matrices 5.5-11
homalgTable entry B.1-11
ResidueClassRing D.2-10
`UnionOfColumnsPair`, homalgTable entry B.1-12
`UnionOfRows`, for a homalg ring, an integer and a list of homalg matrices 5.5-10
homalgTable entry B.1-9
ResidueClassRing D.2-9
`UnionOfRowsPair`, homalgTable entry B.1-10
`UniqueLeftDivide`, for pairs of matrices 5.5-58
`UniqueRightDivide`, for pairs of matrices 5.5-57
`UnreducedNumeratorOfHilbertPoincareSeries` 5.4-16
`Zero`, for homalg rings 3.4-6
`ZeroColumns` 5.4-5
homalgTable entry B.2-5
ResidueClassRing D.3-5
`ZeroMatrix`, homalgTable entry B.1-3
ResidueClassRing D.2-3
`ZeroRows` 5.4-4
homalgTable entry B.2-4
ResidueClassRing D.3-4

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