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