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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 5.5-12
\*, for ring elements and matrices 5.5-9
\+, for matrices 5.5-10
\-, for matrices 5.5-11
\/, constructor for residue class rings 3.2-3
\=, for matrices 5.5-13
AddMat, ResidueClassRing D.2-13
AddMat, homalgTable entry B.1-13
AreEqualMatrices, ResidueClassRing D.3-1
AreEqualMatrices, homalgTable entry B.2-1
BasisAlgorithmRespectsPrincipalIdeals 3.3-48
BasisOfColumnModule, ResidueClassRing D.1-2
BasisOfColumnModule, for matrices 5.5-18
BasisOfColumns, for matrices 5.5-34
BasisOfColumns, for pairs of matrices 5.5-34
BasisOfColumnsCoeff, ResidueClassRing D.1-8
BasisOfColumnsCoeff, for matrices 5.5-30
BasisOfRowModule, ResidueClassRing D.1-1
BasisOfRowModule, for matrices 5.5-17
BasisOfRows, for matrices 5.5-33
BasisOfRows, for pairs of matrices 5.5-33
BasisOfRowsCoeff, ResidueClassRing D.1-7
BasisOfRowsCoeff, for matrices 5.5-29
CanBeUsedToDecideZero 6.3-1
CertainColumns, ResidueClassRing D.2-7
CertainColumns, for matrices 5.5-4
CertainColumns, homalgTable entry B.1-7
CertainRows, ResidueClassRing D.2-6
CertainRows, for matrices 5.5-3
CertainRows, homalgTable entry B.1-6
CoefficientsRing 3.4-18
ColumnRankOfMatrix 5.4-12
Compose, ResidueClassRing D.2-15
Compose, homalgTable entry B.1-15
ConstructorForHomalgMatrices 3.4-6
ContainsAField 3.3-1
CoordinateRingOfGraph, for ring maps 4.4-4
DecideZero, for matrices and relations 5.5-35
DecideZeroColumns, ResidueClassRing D.1-4
DecideZeroColumns, for pairs of matrices 5.5-20
DecideZeroColumnsEffectively, ResidueClassRing D.1-10
DecideZeroColumnsEffectively, for pairs of matrices 5.5-32
DecideZeroRows, ResidueClassRing D.1-3
DecideZeroRows, for pairs of matrices 5.5-19
DecideZeroRowsEffectively, ResidueClassRing D.1-9
DecideZeroRowsEffectively, for pairs of matrices 5.5-31
DegreeOfMorphism, for ring maps 4.4-3
DegreesOfEntries 5.4-10
DegreesOfEntries, homalgTable entry B.2-9
Determinant, ResidueClassRing D.2-19
Determinant, homalgTable entry B.1-19
DeterminantMat 5.4-3
DiagMat, ResidueClassRing D.2-10
DiagMat, for matrices 5.5-7
DiagMat, homalgTable entry B.1-10
ElementaryRank 3.4-24
Eval, for matrices created with AddMat C.4-13
Eval, for matrices created with CertainColumns C.4-7
Eval, for matrices created with CertainRows C.4-6
Eval, for matrices created with Compose C.4-15
Eval, for matrices created with DiagMat C.4-10
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.4-5
Eval, for matrices created with KroneckerMat C.4-11
Eval, for matrices created with LeftInverse C.4-16
Eval, for matrices created with MulMat C.4-12
Eval, for matrices created with RightInverse C.4-17
Eval, for matrices created with SubMat C.4-14
Eval, for matrices created with UnionOfColumns C.4-9
Eval, for matrices created with UnionOfRows C.4-8
GeneralLinearRank 3.4-23
GenerateSameColumnModule, for pairs of matrices 5.5-45
GenerateSameRowModule, for pairs of matrices 5.5-44
GetColumnIndependentUnitPositions, for matrices 5.5-14
GetColumnIndependentUnitPositions, homalgTable entry B.2-6
GetRowIndependentUnitPositions, for matrices 5.5-15
GetRowIndependentUnitPositions, homalgTable entry B.2-7
GetUnitPosition, for matrices 5.5-16
GetUnitPosition, homalgTable entry B.2-8
GlobalDimension 3.4-22
HasInvariantBasisProperty 3.3-18
HasLeftInvariantBasisProperty 3.3-19
HasRightInvariantBasisProperty 3.3-20
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 3.4-3
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 3.4-14
IndeterminateCoordinatesOfRingOfDerivations 3.4-12
IndeterminateDerivationsOfRingOfDerivations 3.4-13
IndeterminatesOfExteriorRing 3.4-15
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
Involution, ResidueClassRing D.2-5
Involution, for matrices 5.5-2
Involution, homalgTable entry B.1-5
IsArtinian, for rings 3.3-33
IsAutomorphism, for ring maps 4.3-6
IsBasisOfColumnsMatrix 5.3-22
IsBasisOfRowsMatrix 5.3-21
IsBezoutRing 3.3-7
IsDedekindDomain 3.3-11
IsDiagonalMatrix 5.3-12
IsDiagonalMatrix, ResidueClassRing D.3-3
IsDiagonalMatrix, homalgTable entry B.2-3
IsDiscreteValuationRing 3.3-12
IsDivisionRingForHomalg 3.3-4
IsEmptyMatrix 5.3-11
IsEpimorphism, for ring maps 4.3-4
IsFieldForHomalg 3.3-3
IsFiniteFreePresentationRing 3.3-43
IsFreePolynomialRing 3.3-13
IsGlobalDimensionFinite 3.3-15
IsHereditary 3.3-24
IsHermite 3.3-27
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 3.3-5
IsIntegralDomain 3.3-23
IsIntegrallyClosedDomain 3.3-8
IsInvertibleMatrix 5.3-8
IsIsomorphism, for ring maps 4.3-5
IsKaplanskyHermite 3.3-10
IsLeftArtinian 3.3-34
IsLeftFiniteFreePresentationRing 3.3-44
IsLeftGlobalDimensionFinite 3.3-16
IsLeftHereditary 3.3-25
IsLeftHermite 3.3-28
IsLeftInvertibleMatrix 5.3-9
IsLeftNoetherian 3.3-31
IsLeftOreDomain 3.3-37
IsLeftPrincipalIdealRing 3.3-40
IsLeftRegularMatrix 5.3-6
IsLocalRing 3.3-21
IsLowerStairCaseMatrix 5.3-19
IsLowerTriangularMatrix 5.3-15
IsMinusOne 3.3-49
IsMonomorphism, for ring maps 4.3-3
IsMorphism, for ring maps 4.3-1
IsMutableMatrix 5.3-25
IsNoetherian 3.3-30
IsOne 5.3-2
IsOne, ResidueClassRing D.3-2
IsOreDomain 3.3-36
IsPermutationMatrix 5.3-3
IsPreHomalgRing 3.1-2
IsPrincipalIdealRing 3.3-39
IsRationalsForHomalg 3.3-2
IsReducedBasisOfColumnsMatrix 5.3-24
IsReducedBasisOfRowsMatrix 5.3-23
IsRegular 3.3-42
IsResidueClassRingOfTheIntegers 3.3-6
IsRightArtinian 3.3-35
IsRightFiniteFreePresentationRing 3.3-45
IsRightGlobalDimensionFinite 3.3-17
IsRightHereditary 3.3-26
IsRightHermite 3.3-29
IsRightInvertibleMatrix 5.3-10
IsRightNoetherian 3.3-32
IsRightOreDomain 3.3-38
IsRightPrincipalIdealRing 3.3-41
IsRightRegularMatrix 5.3-7
IsRingRelationsRep 6.1-4
IsScalarlMatrix 5.3-13
IsSemiLocalRing 3.3-22
IsSemiSimpleRing 3.3-47
IsSimpleRing 3.3-46
IsSpecialSubidentityMatrix 5.3-4
IsStrictLowerTriangularMatrix 5.3-17
IsStrictUpperTriangularMatrix 5.3-16
IsSubidentityMatrix 5.3-5
IsTriangularMatrix 5.3-20
IsUniqueFactorizationDomain 3.3-9
IsUpperStairCaseMatrix 5.3-18
IsUpperTriangularMatrix 5.3-14
IsVoidMatrix 5.3-28
IsWeylRing 3.3-14
IsZero, for matrices 5.3-1
IsZeroMatrix, ResidueClassRing D.2-16
IsZeroMatrix, homalgTable entry B.1-16
KroneckerMat, ResidueClassRing D.2-11
KroneckerMat, for matrices 5.5-8
KroneckerMat, homalgTable entry B.1-11
KrullDimension 3.4-19
LeftDivide, for pairs of matrices 5.5-41
LeftDivide, for triples of matrices 5.5-43
LeftGlobalDimension 3.4-20
LeftInverse, for matrices 5.4-13
MatrixOfWeightsOfIndeterminates 3.4-17
MinusOne 3.4-9
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
One, for homalg ring elements 3.4-2
One, for homalg rings 3.4-8
PositionOfFirstNonZeroEntryPerColumn 5.4-9
PositionOfFirstNonZeroEntryPerRow 5.4-8
Range, for ring maps 4.4-2
RationalParameters 3.4-10
ReducedBasisOfColumnModule, for matrices 5.5-26
ReducedBasisOfRowModule, for matrices 5.5-25
ReducedSyzygiesGeneratorsOfColumns, for matrices 5.5-28
ReducedSyzygiesGeneratorsOfRows, for matrices 5.5-27
ReducedSyzygiesOfColumns, for matrices 5.5-39
ReducedSyzygiesOfColumns, for pairs of matrices 5.5-39
ReducedSyzygiesOfRows, for matrices 5.5-38
ReducedSyzygiesOfRows, for pairs of matrices 5.5-38
RelativeSyzygiesGeneratorsOfColumns, ResidueClassRing D.1-12
RelativeSyzygiesGeneratorsOfRows, ResidueClassRing D.1-11
RightDivide, for pairs of matrices 5.5-40
RightDivide, for triples of matrices 5.5-42
RightGlobalDimension 3.4-21
RightInverse, for matrices 5.4-14
RingElementConstructor 3.4-4
RingMap, constructor for ring maps 4.2-1
RowRankOfMatrix 5.4-11
Source, for ring maps 4.4-1
StableRank 3.4-25
SubMat, ResidueClassRing D.2-14
SubMat, homalgTable entry B.1-14
SyzygiesGeneratorsOfColumns, ResidueClassRing D.1-6
SyzygiesGeneratorsOfColumns, for matrices 5.5-22
SyzygiesGeneratorsOfColumns, for pairs of matrices 5.5-24
SyzygiesGeneratorsOfRows, ResidueClassRing D.1-5
SyzygiesGeneratorsOfRows, for matrices 5.5-21
SyzygiesGeneratorsOfRows, for pairs of matrices 5.5-23
SyzygiesOfColumns, for matrices 5.5-37
SyzygiesOfColumns, for pairs of matrices 5.5-37
SyzygiesOfRows, for matrices 5.5-36
SyzygiesOfRows, for pairs of matrices 5.5-36
TypeOfHomalgMatrix 3.4-5
UnionOfColumns, ResidueClassRing D.2-9
UnionOfColumns, for matrices 5.5-6
UnionOfColumns, homalgTable entry B.1-9
UnionOfRows, ResidueClassRing D.2-8
UnionOfRows, for matrices 5.5-5
UnionOfRows, homalgTable entry B.1-8
WeightsOfIndeterminates 3.4-16
Zero, for homalg ring elements 3.4-1
Zero, for homalg rings 3.4-7
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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