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Index

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

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