\*
, 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 5.5-13AddMat
, ResidueClassRing D.2-13AddMat
, homalgTable entry B.1-13AreEqualMatrices
, ResidueClassRing D.3-1AreEqualMatrices
, homalgTable entry B.2-1BasisAlgorithmRespectsPrincipalIdeals
3.3-48BasisOfColumnModule
, ResidueClassRing D.1-2BasisOfColumnModule
, for matrices 5.5-18BasisOfColumns
, for matrices 5.5-34BasisOfColumns
, for pairs of matrices 5.5-34BasisOfColumnsCoeff
, ResidueClassRing D.1-8BasisOfColumnsCoeff
, for matrices 5.5-30BasisOfRowModule
, ResidueClassRing D.1-1BasisOfRowModule
, for matrices 5.5-17BasisOfRows
, for matrices 5.5-33BasisOfRows
, for pairs of matrices 5.5-33BasisOfRowsCoeff
, ResidueClassRing D.1-7BasisOfRowsCoeff
, for matrices 5.5-29CanBeUsedToDecideZero
6.3-1CertainColumns
, ResidueClassRing D.2-7CertainColumns
, for matrices 5.5-4CertainColumns
, homalgTable entry B.1-7CertainRows
, ResidueClassRing D.2-6CertainRows
, for matrices 5.5-3CertainRows
, homalgTable entry B.1-6CoefficientsRing
3.4-18ColumnRankOfMatrix
5.4-12Compose
, ResidueClassRing D.2-15Compose
, homalgTable entry B.1-15ConstructorForHomalgMatrices
3.4-6ContainsAField
3.3-1CoordinateRingOfGraph
, for ring maps 4.4-4DecideZero
, for matrices and relations 5.5-35DecideZeroColumns
, ResidueClassRing D.1-4DecideZeroColumns
, for pairs of matrices 5.5-20DecideZeroColumnsEffectively
, ResidueClassRing D.1-10DecideZeroColumnsEffectively
, for pairs of matrices 5.5-32DecideZeroRows
, ResidueClassRing D.1-3DecideZeroRows
, for pairs of matrices 5.5-19DecideZeroRowsEffectively
, ResidueClassRing D.1-9DecideZeroRowsEffectively
, for pairs of matrices 5.5-31DegreeOfMorphism
, for ring maps 4.4-3DegreesOfEntries
5.4-10DegreesOfEntries
, homalgTable entry B.2-9Determinant
, ResidueClassRing D.2-19Determinant
, homalgTable entry B.1-19DeterminantMat
5.4-3DiagMat
, ResidueClassRing D.2-10DiagMat
, for matrices 5.5-7DiagMat
, homalgTable entry B.1-10ElementaryRank
3.4-24Eval
, for matrices created with AddMat C.4-13Eval
, for matrices created with CertainColumns C.4-7Eval
, for matrices created with CertainRows C.4-6Eval
, for matrices created with Compose C.4-15Eval
, for matrices created with DiagMat C.4-10Eval
, 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.4-5Eval
, for matrices created with KroneckerMat C.4-11Eval
, for matrices created with LeftInverse C.4-16Eval
, for matrices created with MulMat C.4-12Eval
, for matrices created with RightInverse C.4-17Eval
, for matrices created with SubMat C.4-14Eval
, for matrices created with UnionOfColumns C.4-9Eval
, for matrices created with UnionOfRows C.4-8GeneralLinearRank
3.4-23GenerateSameColumnModule
, for pairs of matrices 5.5-45GenerateSameRowModule
, for pairs of matrices 5.5-44GetColumnIndependentUnitPositions
, for matrices 5.5-14GetColumnIndependentUnitPositions
, homalgTable entry B.2-6GetRowIndependentUnitPositions
, for matrices 5.5-15GetRowIndependentUnitPositions
, homalgTable entry B.2-7GetUnitPosition
, for matrices 5.5-16GetUnitPosition
, homalgTable entry B.2-8GlobalDimension
3.4-22HasInvariantBasisProperty
3.3-18HasLeftInvariantBasisProperty
3.3-19HasRightInvariantBasisProperty
3.3-20HomalgDiagonalMatrix
, 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
3.4-3HomalgVoidMatrix
, constructor for void matrices 5.2-5HomalgZeroMatrix
, constructor for zero matrices 5.2-3IdentityMatrix
, ResidueClassRing D.2-4IdentityMatrix
, homalgTable entry B.1-4IndeterminateAntiCommutingVariablesOfExteriorRing
3.4-14IndeterminateCoordinatesOfRingOfDerivations
3.4-12IndeterminateDerivationsOfRingOfDerivations
3.4-13IndeterminatesOfExteriorRing
3.4-15IndeterminatesOfPolynomialRing
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.1-1Involution
, ResidueClassRing D.2-5Involution
, for matrices 5.5-2Involution
, homalgTable entry B.1-5IsArtinian
, for rings 3.3-33IsAutomorphism
, for ring maps 4.3-6IsBasisOfColumnsMatrix
5.3-22IsBasisOfRowsMatrix
5.3-21IsBezoutRing
3.3-7IsDedekindDomain
3.3-11IsDiagonalMatrix
5.3-12IsDiagonalMatrix
, ResidueClassRing D.3-3IsDiagonalMatrix
, homalgTable entry B.2-3IsDiscreteValuationRing
3.3-12IsDivisionRingForHomalg
3.3-4IsEmptyMatrix
5.3-11IsEpimorphism
, for ring maps 4.3-4IsFieldForHomalg
3.3-3IsFiniteFreePresentationRing
3.3-43IsFreePolynomialRing
3.3-13IsGlobalDimensionFinite
3.3-15IsHereditary
3.3-24IsHermite
3.3-27IsHomalgInternalMatrixRep
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
3.3-5IsIntegralDomain
3.3-23IsIntegrallyClosedDomain
3.3-8IsInvertibleMatrix
5.3-8IsIsomorphism
, for ring maps 4.3-5IsKaplanskyHermite
3.3-10IsLeftArtinian
3.3-34IsLeftFiniteFreePresentationRing
3.3-44IsLeftGlobalDimensionFinite
3.3-16IsLeftHereditary
3.3-25IsLeftHermite
3.3-28IsLeftInvertibleMatrix
5.3-9IsLeftNoetherian
3.3-31IsLeftOreDomain
3.3-37IsLeftPrincipalIdealRing
3.3-40IsLeftRegularMatrix
5.3-6IsLocalRing
3.3-21IsLowerStairCaseMatrix
5.3-19IsLowerTriangularMatrix
5.3-15IsMinusOne
3.3-49IsMonomorphism
, for ring maps 4.3-3IsMorphism
, for ring maps 4.3-1IsMutableMatrix
5.3-25IsNoetherian
3.3-30IsOne
5.3-2IsOne
, ResidueClassRing D.3-2IsOreDomain
3.3-36IsPermutationMatrix
5.3-3IsPreHomalgRing
3.1-2IsPrincipalIdealRing
3.3-39IsRationalsForHomalg
3.3-2IsReducedBasisOfColumnsMatrix
5.3-24IsReducedBasisOfRowsMatrix
5.3-23IsRegular
3.3-42IsResidueClassRingOfTheIntegers
3.3-6IsRightArtinian
3.3-35IsRightFiniteFreePresentationRing
3.3-45IsRightGlobalDimensionFinite
3.3-17IsRightHereditary
3.3-26IsRightHermite
3.3-29IsRightInvertibleMatrix
5.3-10IsRightNoetherian
3.3-32IsRightOreDomain
3.3-38IsRightPrincipalIdealRing
3.3-41IsRightRegularMatrix
5.3-7IsRingRelationsRep
6.1-4IsScalarlMatrix
5.3-13IsSemiLocalRing
3.3-22IsSemiSimpleRing
3.3-47IsSimpleRing
3.3-46IsSpecialSubidentityMatrix
5.3-4IsStrictLowerTriangularMatrix
5.3-17IsStrictUpperTriangularMatrix
5.3-16IsSubidentityMatrix
5.3-5IsTriangularMatrix
5.3-20IsUniqueFactorizationDomain
3.3-9IsUpperStairCaseMatrix
5.3-18IsUpperTriangularMatrix
5.3-14IsVoidMatrix
5.3-28IsWeylRing
3.3-14IsZero
, for matrices 5.3-1IsZeroMatrix
, ResidueClassRing D.2-16IsZeroMatrix
, homalgTable entry B.1-16KroneckerMat
, ResidueClassRing D.2-11KroneckerMat
, for matrices 5.5-8KroneckerMat
, homalgTable entry B.1-11KrullDimension
3.4-19LeftDivide
, for pairs of matrices 5.5-41LeftDivide
, for triples of matrices 5.5-43LeftGlobalDimension
3.4-20LeftInverse
, for matrices 5.4-13MatrixOfWeightsOfIndeterminates
3.4-17MinusOne
3.4-9MulMat
, 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.1-17One
, for homalg ring elements 3.4-2One
, for homalg rings 3.4-8PositionOfFirstNonZeroEntryPerColumn
5.4-9PositionOfFirstNonZeroEntryPerRow
5.4-8Range
, for ring maps 4.4-2RationalParameters
3.4-10ReducedBasisOfColumnModule
, for matrices 5.5-26ReducedBasisOfRowModule
, for matrices 5.5-25ReducedSyzygiesGeneratorsOfColumns
, for matrices 5.5-28ReducedSyzygiesGeneratorsOfRows
, for matrices 5.5-27ReducedSyzygiesOfColumns
, for matrices 5.5-39ReducedSyzygiesOfColumns
, for pairs of matrices 5.5-39ReducedSyzygiesOfRows
, for matrices 5.5-38ReducedSyzygiesOfRows
, for pairs of matrices 5.5-38RelativeSyzygiesGeneratorsOfColumns
, ResidueClassRing D.1-12RelativeSyzygiesGeneratorsOfRows
, ResidueClassRing D.1-11RightDivide
, for pairs of matrices 5.5-40RightDivide
, for triples of matrices 5.5-42RightGlobalDimension
3.4-21RightInverse
, for matrices 5.4-14RingElementConstructor
3.4-4RingMap
, constructor for ring maps 4.2-1RowRankOfMatrix
5.4-11Source
, for ring maps 4.4-1StableRank
3.4-25SubMat
, ResidueClassRing D.2-14SubMat
, homalgTable entry B.1-14SyzygiesGeneratorsOfColumns
, ResidueClassRing D.1-6SyzygiesGeneratorsOfColumns
, for matrices 5.5-22SyzygiesGeneratorsOfColumns
, for pairs of matrices 5.5-24SyzygiesGeneratorsOfRows
, ResidueClassRing D.1-5SyzygiesGeneratorsOfRows
, for matrices 5.5-21SyzygiesGeneratorsOfRows
, for pairs of matrices 5.5-23SyzygiesOfColumns
, for matrices 5.5-37SyzygiesOfColumns
, for pairs of matrices 5.5-37SyzygiesOfRows
, for matrices 5.5-36SyzygiesOfRows
, for pairs of matrices 5.5-36TypeOfHomalgMatrix
3.4-5UnionOfColumns
, ResidueClassRing D.2-9UnionOfColumns
, for matrices 5.5-6UnionOfColumns
, homalgTable entry B.1-9UnionOfRows
, ResidueClassRing D.2-8UnionOfRows
, for matrices 5.5-5UnionOfRows
, homalgTable entry B.1-8WeightsOfIndeterminates
3.4-16Zero
, for homalg ring elements 3.4-1Zero
, for homalg rings 3.4-7ZeroColumns
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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