\*
, 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 5.5-17AddMat
, ResidueClassRing D.2-13AddMat
, homalgTable entry B.1-13AffineDegree
5.4-21AffineDimension
5.4-20AreEqualMatrices
, ResidueClassRing D.3-1AreEqualMatrices
, homalgTable entry B.2-1AreUnitsCentral
3.3-55AssociatedGradedRing
3.4-28BasisAlgorithmRespectsPrincipalIdeals
3.3-54BasisOfColumnModule
, ResidueClassRing D.1-2BasisOfColumnModule
, for matrices 5.5-23BasisOfColumns
, for matrices 5.5-39BasisOfColumns
, for pairs of matrices 5.5-39BasisOfColumnsCoeff
, ResidueClassRing D.1-8BasisOfColumnsCoeff
, for matrices 5.5-35BasisOfRowModule
, ResidueClassRing D.1-1BasisOfRowModule
, for matrices 5.5-22BasisOfRows
, for matrices 5.5-38BasisOfRows
, for pairs of matrices 5.5-38BasisOfRowsCoeff
, ResidueClassRing D.1-7BasisOfRowsCoeff
, for matrices 5.5-34CanBeUsedToDecideZero
6.3-1CertainColumns
, ResidueClassRing D.2-7CertainColumns
, for matrices 5.5-8CertainColumns
, homalgTable entry B.1-7CertainRows
, ResidueClassRing D.2-6CertainRows
, for matrices 5.5-7CertainRows
, homalgTable entry B.1-6CoefficientsOfNumeratorOfHilbertPoincareSeries
5.4-15CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries
5.4-14CoefficientsRing
3.4-20ColumnRankOfMatrix
5.4-11Compose
, ResidueClassRing D.2-15Compose
, homalgTable entry B.1-15ConstantTermOfHilbertPolynomialn
5.4-23ConstructorForHomalgMatrices
3.4-5ContainsAField
3.3-2CoordinateRingOfGraph
, for ring maps 4.4-4DecideZero
, for matrices and relations 5.5-40DecideZeroColumns
, ResidueClassRing D.1-4DecideZeroColumns
, for pairs of matrices 5.5-25DecideZeroColumnsEffectively
, ResidueClassRing D.1-10DecideZeroColumnsEffectively
, for pairs of matrices 5.5-37DecideZeroRows
, ResidueClassRing D.1-3DecideZeroRows
, for pairs of matrices 5.5-24DecideZeroRowsEffectively
, ResidueClassRing D.1-9DecideZeroRowsEffectively
, for pairs of matrices 5.5-36DegreeOfMorphism
, for ring maps 4.4-3Determinant
, ResidueClassRing D.2-19Determinant
, homalgTable entry B.1-19DeterminantMat
5.4-3DiagMat
, ResidueClassRing D.2-10DiagMat
, for matrices 5.5-11DiagMat
, homalgTable entry B.1-10ElementaryRank
3.4-26Eliminate
5.5-21Eval
, for matrices created with AddMat C.4-15Eval
, for matrices created with CertainColumns C.4-9Eval
, for matrices created with CertainRows C.4-8Eval
, for matrices created with Compose C.4-17Eval
, for matrices created with DiagMat C.4-12Eval
, for matrices created with HomalgIdentityMatrix C.4-4Eval
, for matrices created with HomalgInitialIdentityMatrix C.4-2Eval
, for matrices created with HomalgInitialMatrix C.4-1Eval
, for matrices created with HomalgZeroMatrix C.4-3Eval
, for matrices created with Involution C.4-7Eval
, for matrices created with KroneckerMat C.4-13Eval
, for matrices created with LeftInverseLazy C.4-5Eval
, for matrices created with MulMat C.4-14Eval
, for matrices created with RightInverseLazy C.4-6Eval
, for matrices created with SubMat C.4-16Eval
, for matrices created with UnionOfColumns C.4-11Eval
, for matrices created with UnionOfRows C.4-10GeneralLinearRank
3.4-25GenerateSameColumnModule
, for pairs of matrices 5.5-50GenerateSameRowModule
, for pairs of matrices 5.5-49GetColumnIndependentUnitPositions
, for matrices 5.5-18GetColumnIndependentUnitPositions
, homalgTable entry B.2-6GetRowIndependentUnitPositions
, for matrices 5.5-19GetRowIndependentUnitPositions
, homalgTable entry B.2-7GetUnitPosition
, for matrices 5.5-20GetUnitPosition
, homalgTable entry B.2-8GlobalDimension
3.4-24HasInvariantBasisProperty
3.3-20HasLeftInvariantBasisProperty
3.3-21HasRightInvariantBasisProperty
3.3-22HilbertPoincareSeries
5.4-18HilbertPolynomial
5.4-19HomalgDiagonalMatrix
, constructor for diagonal matrices 5.2-7HomalgFieldOfRationals
, constructor for the field of rationals 3.2-2HomalgIdentityMatrix
, constructor for identity matrices 5.2-4HomalgInitialIdentityMatrix
, constructor for initial quadratic matrices with ones on the diagonal 5.2-2HomalgInitialMatrix
, constructor for initial matrices filled with zeros 5.2-1HomalgMatrix
, constructor for matrices using a list 5.2-6HomalgMatrix
, constructor for matrices using a listlist 5.2-6HomalgMatrix
, constructor for matrices using a string of a list 5.2-6HomalgMatrix
, constructor for matrices using a string of a listlist 5.2-6homalgMode
E.2-1HomalgRing
, for matrices 5.5-1HomalgRingOfIntegers
, constructor for the integers 3.2-1HomalgRingOfIntegers
, constructor for the residue class rings of the integers 3.2-1homalgTable
3.4-2HomalgVoidMatrix
, constructor for void matrices 5.2-5HomalgZeroMatrix
, constructor for zero matrices 5.2-3IdentityMatrix
, ResidueClassRing D.2-4IdentityMatrix
, homalgTable entry B.1-4IndeterminateAntiCommutingVariablesOfExteriorRing
3.4-17IndeterminateCoordinatesOfRingOfDerivations
3.4-13IndeterminateDerivationsOfRingOfDerivations
3.4-15IndeterminatesOfExteriorRing
3.4-19IndeterminatesOfPolynomialRing
3.4-11InitialIdentityMatrix
, ResidueClassRing D.2-2InitialIdentityMatrix
, homalgTable entry for initial identity matrices B.1-2InitialMatrix
, ResidueClassRing D.2-1InitialMatrix
, homalgTable entry for initial matrices B.1-1Inverse
, for homalg ring elements 3.4-1Involution
, ResidueClassRing D.2-5Involution
, for matrices 5.5-6Involution
, homalgTable entry B.1-5IsArtinian
, for rings 3.3-38IsAutomorphism
, for ring maps 4.3-6IsBasisOfColumnsMatrix
5.3-23IsBasisOfRowsMatrix
5.3-22IsBezoutRing
3.3-8IsCohenMacaulay
3.3-35IsDedekindDomain
3.3-12IsDiagonalMatrix
5.3-13IsDiagonalMatrix
, ResidueClassRing D.3-3IsDiagonalMatrix
, homalgTable entry B.2-3IsDiscreteValuationRing
3.3-13IsDivisionRingForHomalg
3.3-5IsEmptyMatrix
5.3-12IsEpimorphism
, for ring maps 4.3-4IsFieldForHomalg
3.3-4IsFiniteFreePresentationRing
3.3-48IsFreePolynomialRing
3.3-14IsGlobalDimensionFinite
3.3-17IsGorenstein
3.3-36IsHereditary
3.3-26IsHermite
3.3-29IsHomalgInternalMatrixRep
5.1-2IsHomalgInternalRingRep
3.1-4IsHomalgMatrix
5.1-1IsHomalgRing
3.1-1IsHomalgRingElement
3.1-3IsHomalgRingMap
4.1-1IsHomalgRingMapRep
4.1-3IsHomalgRingRelations
6.1-1IsHomalgRingRelationsAsGeneratorsOfLeftIdeal
6.1-2IsHomalgRingRelationsAsGeneratorsOfRightIdeal
6.1-3IsHomalgRingSelfMap
4.1-2IsIdentityMatrix
, homalgTable entry B.2-2IsIdentityMorphism
, for ring maps 4.3-2IsInitialIdentityMatrix
5.3-27IsInitialMatrix
5.3-26IsInjectivePresentation
6.3-2IsIntegersForHomalg
3.3-6IsIntegralDomain
3.3-25IsIntegrallyClosedDomain
3.3-9IsInvertibleMatrix
5.3-9IsIsomorphism
, for ring maps 4.3-5IsKaplanskyHermite
3.3-11IsKoszul
3.3-37IsLeftArtinian
3.3-39IsLeftFiniteFreePresentationRing
3.3-49IsLeftGlobalDimensionFinite
3.3-18IsLeftHereditary
3.3-27IsLeftHermite
3.3-30IsLeftInvertibleMatrix
5.3-10IsLeftNoetherian
3.3-33IsLeftOreDomain
3.3-42IsLeftPrincipalIdealRing
3.3-45IsLeftRegular
5.3-7IsLeftRegular
, for homalg ring elements 3.3-59IsLocal
3.3-23IsLocalizedWeylRing
3.3-16IsLowerStairCaseMatrix
5.3-20IsLowerTriangularMatrix
5.3-16IsMinusOne
3.3-56IsMonic
, for homalg ring elements 3.3-57IsMonicUptoUnit
, for homalg ring elements 3.3-58IsMonomorphism
, for ring maps 4.3-3IsMorphism
, for ring maps 4.3-1IsNoetherian
3.3-32IsOne
5.3-2IsOne
, ResidueClassRing D.3-2IsOreDomain
3.3-41IsPermutationMatrix
5.3-4IsPreHomalgRing
3.1-2IsPrincipalIdealRing
3.3-44IsRationalsForHomalg
3.3-3IsReducedBasisOfColumnsMatrix
5.3-25IsReducedBasisOfRowsMatrix
5.3-24IsRegular
3.3-47IsRegular
, for homalg ring elements 3.3-61IsResidueClassRingOfTheIntegers
3.3-7IsRightArtinian
3.3-40IsRightFiniteFreePresentationRing
3.3-50IsRightGlobalDimensionFinite
3.3-19IsRightHereditary
3.3-28IsRightHermite
3.3-31IsRightInvertibleMatrix
5.3-11IsRightNoetherian
3.3-34IsRightOreDomain
3.3-43IsRightPrincipalIdealRing
3.3-46IsRightRegular
5.3-8IsRightRegular
, for homalg ring elements 3.3-60IsRingRelationsRep
6.1-4IsScalarlMatrix
5.3-14IsSemiLocalRing
3.3-24IsSemiSimpleRing
3.3-52IsSimpleRing
3.3-51IsSpecialSubidentityMatrix
5.3-5IsStrictLowerTriangularMatrix
5.3-18IsStrictUpperTriangularMatrix
5.3-17IsSubidentityMatrix
5.3-6IsSuperCommutative
3.3-53IsTriangularMatrix
5.3-21IsUniqueFactorizationDomain
3.3-10IsUnitFree
5.3-3IsUpperStairCaseMatrix
5.3-19IsUpperTriangularMatrix
5.3-15IsVoidMatrix
5.3-28IsWeylRing
3.3-15IsZero
, for matrices 5.3-1IsZero
, for rings 3.3-1IsZeroMatrix
, ResidueClassRing D.2-16IsZeroMatrix
, homalgTable entry B.1-16KroneckerMat
, ResidueClassRing D.2-11KroneckerMat
, for matrices 5.5-12KroneckerMat
, homalgTable entry B.1-11KrullDimension
3.4-21LeftDivide
, for pairs of matrices 5.5-46LeftDivide
, for triples of matrices 5.5-48LeftGlobalDimension
3.4-22LeftInverse
5.4-12LeftInverse
, for matrices 5.5-2LeftInverseLazy
, for matrices 5.5-4MatrixOfSymbols
5.4-24MinusOne
3.4-8MulMat
, ResidueClassRing D.2-12MulMat
, homalgTable entry B.1-12NonZeroColumns
5.4-7NonZeroRows
5.4-6NrColumns
5.4-2NrColumns
, ResidueClassRing D.2-18NrColumns
, homalgTable entry B.1-18NrRows
5.4-1NrRows
, ResidueClassRing D.2-17NrRows
, homalgTable entry B.1-17NumeratorOfHilbertPoincareSeries
5.4-17One
, for homalg rings 3.4-7PositionOfFirstNonZeroEntryPerColumn
5.4-9PositionOfFirstNonZeroEntryPerColumn
, homalgTable entry B.2-10PositionOfFirstNonZeroEntryPerRow
5.4-8PositionOfFirstNonZeroEntryPerRow
, homalgTable entry B.2-9ProductOfIndeterminates
3.4-9ProjectiveDegree
5.4-22Range
, for ring maps 4.4-2RationalParameters
3.4-10ReducedBasisOfColumnModule
, for matrices 5.5-31ReducedBasisOfRowModule
, for matrices 5.5-30ReducedSyzygiesGeneratorsOfColumns
, for matrices 5.5-33ReducedSyzygiesGeneratorsOfRows
, for matrices 5.5-32ReducedSyzygiesOfColumns
, for matrices 5.5-44ReducedSyzygiesOfColumns
, for pairs of matrices 5.5-44ReducedSyzygiesOfRows
, for matrices 5.5-43ReducedSyzygiesOfRows
, for pairs of matrices 5.5-43RelativeIndeterminateAntiCommutingVariablesOfExteriorRing
3.4-18RelativeIndeterminateCoordinatesOfRingOfDerivations
3.4-14RelativeIndeterminateDerivationsOfRingOfDerivations
3.4-16RelativeIndeterminatesOfPolynomialRing
3.4-12RelativeSyzygiesGeneratorsOfColumns
, ResidueClassRing D.1-12RelativeSyzygiesGeneratorsOfRows
, ResidueClassRing D.1-11RightDivide
, for pairs of matrices 5.5-45RightDivide
, for triples of matrices 5.5-47RightGlobalDimension
3.4-23RightInverse
5.4-13RightInverse
, for matrices 5.5-3RightInverseLazy
, for matrices 5.5-5RingElementConstructor
3.4-3RingMap
, constructor for ring maps 4.2-1RowRankOfMatrix
5.4-10Source
, for ring maps 4.4-1StableRank
3.4-27SubMat
, ResidueClassRing D.2-14SubMat
, homalgTable entry B.1-14SyzygiesGeneratorsOfColumns
, ResidueClassRing D.1-6SyzygiesGeneratorsOfColumns
, for matrices 5.5-27SyzygiesGeneratorsOfColumns
, for pairs of matrices 5.5-29SyzygiesGeneratorsOfRows
, ResidueClassRing D.1-5SyzygiesGeneratorsOfRows
, for matrices 5.5-26SyzygiesGeneratorsOfRows
, for pairs of matrices 5.5-28SyzygiesOfColumns
, for matrices 5.5-42SyzygiesOfColumns
, for pairs of matrices 5.5-42SyzygiesOfRows
, for matrices 5.5-41SyzygiesOfRows
, for pairs of matrices 5.5-41TypeOfHomalgMatrix
3.4-4UnionOfColumns
, ResidueClassRing D.2-9UnionOfColumns
, for matrices 5.5-10UnionOfColumns
, homalgTable entry B.1-9UnionOfRows
, ResidueClassRing D.2-8UnionOfRows
, for matrices 5.5-9UnionOfRows
, homalgTable entry B.1-8UnreducedNumeratorOfHilbertPoincareSeries
5.4-16Zero
, for homalg rings 3.4-6ZeroColumns
5.4-5ZeroColumns
, ResidueClassRing D.3-5ZeroColumns
, homalgTable entry B.2-5ZeroMatrix
, ResidueClassRing D.2-3ZeroMatrix
, homalgTable entry B.1-3ZeroRows
5.4-4ZeroRows
, ResidueClassRing D.3-4ZeroRows
, homalgTable entry B.2-4
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