\makelabel{homalg:Title page}{}
\makelabel{homalg:Copyright}{}
\makelabel{homalg:Acknowledgements}{}
\makelabel{homalg:Table of Contents}{}
\makelabel{homalg:Introduction}{1}
\makelabel{homalg:What is the role of the homalg package in the homalg project?}{1.1}
\makelabel{homalg:Philosophy}{1.1.1}
\makelabel{homalg:homalg provides ...}{1.1.2}
\makelabel{homalg:homalg delegates ...}{1.1.3}
\makelabel{homalg:Rings supported in a sufficient way}{1.1.4}
\makelabel{homalg:Principal limitation}{1.1.5}
\makelabel{homalg:The black box concept}{1.1.6}
\makelabel{homalg:homalg's dictionaries (technical)}{1.1.7}
\makelabel{homalg:The advantages of the outsourcing concept}{1.1.8}
\makelabel{homalg:Does this mean that homalg has only algorithms for the generic case?}{1.1.9}
\makelabel{homalg:The principle of least communication (technical)}{1.1.10}
\makelabel{homalg:Building upon the homalg package}{1.1.11}
\makelabel{homalg:Frequently asked questions}{1.1.12}
\makelabel{homalg:This manual}{1.2}
\makelabel{homalg:Installation of the homalg Package}{2}
\makelabel{homalg:Quick Start}{3}
\makelabel{homalg:Why are all examples in this manual over ℤ or ℤ/mℤ?}{3.1}
\makelabel{homalg:gap> ExamplesForHomalg();}{3.2}
\makelabel{homalg:A typical example}{3.3}
\makelabel{homalg:HomHom}{3.3.1}
\makelabel{homalg:Rings}{4}
\makelabel{homalg:Rings: Category and Representations}{4.1}
\makelabel{homalg:Rings: Constructors}{4.2}
\makelabel{homalg:Rings: Properties}{4.3}
\makelabel{homalg:Rings: Attributes}{4.4}
\makelabel{homalg:Rings: Operations and Functions}{4.5}
\makelabel{homalg:Ring Maps}{5}
\makelabel{homalg:Ring Maps: Category and Representations}{5.1}
\makelabel{homalg:Ring Maps: Constructors}{5.2}
\makelabel{homalg:Ring Maps: Properties}{5.3}
\makelabel{homalg:Ring Maps: Attributes}{5.4}
\makelabel{homalg:Ring Maps: Operations and Functions}{5.5}
\makelabel{homalg:Matrices}{6}
\makelabel{homalg:Matrices: Category and Representations}{6.1}
\makelabel{homalg:Matrices: Constructors}{6.2}
\makelabel{homalg:Matrices: Properties}{6.3}
\makelabel{homalg:Matrices: Attributes}{6.4}
\makelabel{homalg:Matrices: Operations and Functions}{6.5}
\makelabel{homalg:Relations}{7}
\makelabel{homalg:Relations: Categories and Representations}{7.1}
\makelabel{homalg:Relations: Constructors}{7.2}
\makelabel{homalg:Relations: Properties}{7.3}
\makelabel{homalg:Relations: Attributes}{7.4}
\makelabel{homalg:Relations: Operations and Functions}{7.5}
\makelabel{homalg:Generators}{8}
\makelabel{homalg:Generators: Categories and Representations}{8.1}
\makelabel{homalg:Generators: Constructors}{8.2}
\makelabel{homalg:Generators: Properties}{8.3}
\makelabel{homalg:Generators: Attributes}{8.4}
\makelabel{homalg:Generators: Operations and Functions}{8.5}
\makelabel{homalg:Modules}{9}
\makelabel{homalg:Modules: Category and Representations}{9.1}
\makelabel{homalg:Modules: Constructors}{9.2}
\makelabel{homalg:Modules: Properties}{9.3}
\makelabel{homalg:Modules: Attributes}{9.4}
\makelabel{homalg:Modules: Operations and Functions}{9.5}
\makelabel{homalg:Maps}{10}
\makelabel{homalg:Maps: Categories and Representations}{10.1}
\makelabel{homalg:Maps: Constructors}{10.2}
\makelabel{homalg:Maps: Properties}{10.3}
\makelabel{homalg:Maps: Attributes}{10.4}
\makelabel{homalg:Maps: Operations and Functions}{10.5}
\makelabel{homalg:Complexes}{11}
\makelabel{homalg:Complexes: Category and Representations}{11.1}
\makelabel{homalg:Complexes: Constructors}{11.2}
\makelabel{homalg:Complexes: Properties}{11.3}
\makelabel{homalg:Complexes: Attributes}{11.4}
\makelabel{homalg:Complexes: Operations and Functions}{11.5}
\makelabel{homalg:Chain Maps}{12}
\makelabel{homalg:ChainMaps: Categories and Representations}{12.1}
\makelabel{homalg:Chain Maps: Constructors}{12.2}
\makelabel{homalg:Chain Maps: Properties}{12.3}
\makelabel{homalg:Chain Maps: Attributes}{12.4}
\makelabel{homalg:Chain Maps: Operations and Functions}{12.5}
\makelabel{homalg:Bicomplexes}{13}
\makelabel{homalg:Bicomplexes: Category and Representations}{13.1}
\makelabel{homalg:Bicomplexes: Constructors}{13.2}
\makelabel{homalg:Bicomplexes: Properties}{13.3}
\makelabel{homalg:Bicomplexes: Attributes}{13.4}
\makelabel{homalg:Bicomplexes: Operations and Functions}{13.5}
\makelabel{homalg:Bigraded Objects}{14}
\makelabel{homalg:BigradedObjects: Categories and Representations}{14.1}
\makelabel{homalg:Bigraded Objects: Constructors}{14.2}
\makelabel{homalg:Bigraded Objects: Properties}{14.3}
\makelabel{homalg:Bigraded Objects: Operations and Functions}{14.4}
\makelabel{homalg:Spectral Sequences}{15}
\makelabel{homalg:SpectralSequences: Categorie and Representations}{15.1}
\makelabel{homalg:Spectral Sequences: Constructors}{15.2}
\makelabel{homalg:Spectral Sequences: Attributes}{15.3}
\makelabel{homalg:Spectral Sequences: Operations and Functions}{15.4}
\makelabel{homalg:Functors}{16}
\makelabel{homalg:Functors: Category and Representations}{16.1}
\makelabel{homalg:Functors: Constructors}{16.2}
\makelabel{homalg:Functors: Attributes}{16.3}
\makelabel{homalg:Basic Functors}{16.4}
\makelabel{homalg:Tool Functors}{16.5}
\makelabel{homalg:Other Functors}{16.6}
\makelabel{homalg:Functors: Operations and Functions}{16.7}
\makelabel{homalg:Examples}{17}
\makelabel{homalg:ExtExt}{17.1}
\makelabel{homalg:Purity}{17.2}
\makelabel{homalg:TorExt-Grothendieck}{17.3}
\makelabel{homalg:TorExt}{17.4}
\makelabel{homalg:Development}{A}
\makelabel{homalg:Why was homalg discontinued in Maple?}{A.1}
\makelabel{homalg:Why GAP4?}{A.2}
\makelabel{homalg:GAP is free and open software}{A.2.1}
\makelabel{homalg:GAP has an area of expertise}{A.2.2}
\makelabel{homalg:GAP4 can communicate}{A.2.3}
\makelabel{homalg:GAP4 is a mathematical object-oriented programming language}{A.2.4}
\makelabel{homalg:GAP4 packages are easily extendible}{A.2.5}
\makelabel{homalg:Why not Sage?}{A.3}
\makelabel{homalg:How does homalg compare to Sage?}{A.4}
\makelabel{homalg:They differ in objectives and scale}{A.4.1}
\makelabel{homalg:They differ in the programming language}{A.4.2}
\makelabel{homalg:They differ in the way they communicate with the outer world}{A.4.3}
\makelabel{homalg:The Mathematical Idea behind homalg}{B}
\makelabel{homalg:The Basic Matrix Operations}{C}
\makelabel{homalg:Main}{C.1}
\makelabel{homalg:Effective}{C.2}
\makelabel{homalg:Relative}{C.3}
\makelabel{homalg:Reduced}{C.4}
\makelabel{homalg:The Matrix Tool Operations}{D}
\makelabel{homalg:The Tool Operations without a Fallback Method}{D.1}
\makelabel{homalg:The Tool Operations with a Fallback Method}{D.2}
\makelabel{homalg:Logic Subpackages}{E}
\makelabel{homalg:LIRNG: Logical Implications for Rings}{E.1}
\makelabel{homalg:LIMAP: Logical Implications for Ring Maps}{E.2}
\makelabel{homalg:LIMAT: Logical Implications for Matrices}{E.3}
\makelabel{homalg:COLEM: Clever Operations for Lazy Evaluated Matrices}{E.4}
\makelabel{homalg:LIMOD: Logical Implications for Modules}{E.5}
\makelabel{homalg:LIMOR: Logical Implications for Morphisms}{E.6}
\makelabel{homalg:LICPX: Logical Implications for Complexes}{E.7}
\makelabel{homalg:The subpackage ResidueClassRingForHomalg as a sample ring package}{F}
\makelabel{homalg:The Mandatory Basic Operations}{F.1}
\makelabel{homalg:The Mandatory Tool Operations}{F.2}
\makelabel{homalg:Some of the Recommended Tool Operations}{F.3}
\makelabel{homalg:Debugging homalg}{G}
\makelabel{homalg:Increase the assertion level}{G.1}
\makelabel{homalg:Use homalgMode}{G.2}
\makelabel{homalg:The Core Packages and the Idea behind their Splitting}{H}
\makelabel{homalg:The 5=1+4 split}{H.1}
\makelabel{homalg:Logically independent}{H.1.1}
\makelabel{homalg:Black boxes}{H.1.2}
\makelabel{homalg:Summing up}{H.1.3}
\makelabel{homalg:The 4=1+1+1+1 split}{H.2}
\makelabel{homalg:HomalgToCAS}{H.2.1}
\makelabel{homalg:IOForHomalg and Alternatives}{H.2.2}
\makelabel{homalg:RingsForHomalg}{H.2.3}
\makelabel{homalg:Your own RingsForHomalg}{H.2.4}
\makelabel{homalg:ExamplesForHomalg}{H.2.5}
\makelabel{homalg:Documentation}{H.2.6}
\makelabel{homalg:Crediting}{H.2.7}
\makelabel{homalg:Stability}{H.2.8}
\makelabel{homalg:Overview of the homalg Package Source Code}{I}
\makelabel{homalg:Rings, Ring Maps, Matrices, Relations, and Generators}{I.1}
\makelabel{homalg:The Basic Objects}{I.2}
\makelabel{homalg:The Low Level Algorithms}{I.3}
\makelabel{homalg:The High Level Algorithms}{I.4}
\makelabel{homalg:Logical Implications for homalg Objects}{I.5}
\makelabel{homalg:The subpackage ResidueClassRingForHomalg}{I.6}
\makelabel{homalg:The homalgTable for GAP4 built-in rings}{I.7}
\makelabel{homalg:Bibliography}{Bib}
\makelabel{homalg:References}{Bib}
\makelabel{homalg:Index}{Ind}
\makelabel{homalg:homalg}{}
\makelabel{homalg:IsHomalgRing}{4.1.1}
\makelabel{homalg:IsPreHomalgRing}{4.1.2}
\makelabel{homalg:IsHomalgRingElement}{4.1.3}
\makelabel{homalg:IsHomalgInternalRingRep}{4.1.4}
\makelabel{homalg:HomalgRingOfIntegers (constructor for the integers)}{4.2.1}
\makelabel{homalg:HomalgRingOfIntegers (constructor for the residue class rings of the integers)}{4.2.1}
\makelabel{homalg:HomalgFieldOfRationals (constructor for the field of rationals)}{4.2.2}
\makelabel{homalg:\/ (constructor for residue class rings)}{4.2.3}
\makelabel{homalg:ContainsAField}{4.3.1}
\makelabel{homalg:IsRationalsForHomalg}{4.3.2}
\makelabel{homalg:IsFieldForHomalg}{4.3.3}
\makelabel{homalg:IsDivisionRingForHomalg}{4.3.4}
\makelabel{homalg:IsIntegersForHomalg}{4.3.5}
\makelabel{homalg:IsResidueClassRingOfTheIntegers}{4.3.6}
\makelabel{homalg:IsBezoutRing}{4.3.7}
\makelabel{homalg:IsIntegrallyClosedDomain}{4.3.8}
\makelabel{homalg:IsUniqueFactorizationDomain}{4.3.9}
\makelabel{homalg:IsKaplanskyHermite}{4.3.10}
\makelabel{homalg:IsDedekindDomain}{4.3.11}
\makelabel{homalg:IsDiscreteValuationRing}{4.3.12}
\makelabel{homalg:IsFreePolynomialRing}{4.3.13}
\makelabel{homalg:IsWeylRing}{4.3.14}
\makelabel{homalg:IsGlobalDimensionFinite}{4.3.15}
\makelabel{homalg:IsLeftGlobalDimensionFinite}{4.3.16}
\makelabel{homalg:IsRightGlobalDimensionFinite}{4.3.17}
\makelabel{homalg:HasInvariantBasisProperty}{4.3.18}
\makelabel{homalg:HasLeftInvariantBasisProperty}{4.3.19}
\makelabel{homalg:HasRightInvariantBasisProperty}{4.3.20}
\makelabel{homalg:IsLocalRing}{4.3.21}
\makelabel{homalg:IsSemiLocalRing}{4.3.22}
\makelabel{homalg:IsIntegralDomain}{4.3.23}
\makelabel{homalg:IsHereditary}{4.3.24}
\makelabel{homalg:IsLeftHereditary}{4.3.25}
\makelabel{homalg:IsRightHereditary}{4.3.26}
\makelabel{homalg:IsHermite}{4.3.27}
\makelabel{homalg:IsLeftHermite}{4.3.28}
\makelabel{homalg:IsRightHermite}{4.3.29}
\makelabel{homalg:IsNoetherian}{4.3.30}
\makelabel{homalg:IsLeftNoetherian}{4.3.31}
\makelabel{homalg:IsRightNoetherian}{4.3.32}
\makelabel{homalg:IsArtinian (for rings)}{4.3.33}
\makelabel{homalg:IsLeftArtinian}{4.3.34}
\makelabel{homalg:IsRightArtinian}{4.3.35}
\makelabel{homalg:IsOreDomain}{4.3.36}
\makelabel{homalg:IsLeftOreDomain}{4.3.37}
\makelabel{homalg:IsRightOreDomain}{4.3.38}
\makelabel{homalg:IsPrincipalIdealRing}{4.3.39}
\makelabel{homalg:IsLeftPrincipalIdealRing}{4.3.40}
\makelabel{homalg:IsRightPrincipalIdealRing}{4.3.41}
\makelabel{homalg:IsRegular}{4.3.42}
\makelabel{homalg:IsFiniteFreePresentationRing}{4.3.43}
\makelabel{homalg:IsLeftFiniteFreePresentationRing}{4.3.44}
\makelabel{homalg:IsRightFiniteFreePresentationRing}{4.3.45}
\makelabel{homalg:IsSimpleRing}{4.3.46}
\makelabel{homalg:IsSemiSimpleRing}{4.3.47}
\makelabel{homalg:BasisAlgorithmRespectsPrincipalIdeals}{4.3.48}
\makelabel{homalg:IsMinusOne}{4.3.49}
\makelabel{homalg:Zero (for homalg ring elements)}{4.4.1}
\makelabel{homalg:One (for homalg ring elements)}{4.4.2}
\makelabel{homalg:homalgTable}{4.4.3}
\makelabel{homalg:RingElementConstructor}{4.4.4}
\makelabel{homalg:TypeOfHomalgMatrix}{4.4.5}
\makelabel{homalg:ConstructorForHomalgMatrices}{4.4.6}
\makelabel{homalg:Zero (for homalg rings)}{4.4.7}
\makelabel{homalg:One (for homalg rings)}{4.4.8}
\makelabel{homalg:MinusOne}{4.4.9}
\makelabel{homalg:IndeterminatesOfPolynomialRing}{4.4.10}
\makelabel{homalg:IndeterminateCoordinatesOfRingOfDerivations}{4.4.11}
\makelabel{homalg:IndeterminateDerivationsOfRingOfDerivations}{4.4.12}
\makelabel{homalg:IndeterminateAntiCommutingVariablesOfExteriorRing}{4.4.13}
\makelabel{homalg:IndeterminatesOfExteriorRing}{4.4.14}
\makelabel{homalg:WeightsOfIndeterminates}{4.4.15}
\makelabel{homalg:MatrixOfWeightsOfIndeterminates}{4.4.16}
\makelabel{homalg:CoefficientsRing}{4.4.17}
\makelabel{homalg:KrullDimension}{4.4.18}
\makelabel{homalg:LeftGlobalDimension}{4.4.19}
\makelabel{homalg:RightGlobalDimension}{4.4.20}
\makelabel{homalg:GlobalDimension}{4.4.21}
\makelabel{homalg:GeneralLinearRank}{4.4.22}
\makelabel{homalg:ElementaryRank}{4.4.23}
\makelabel{homalg:StableRank}{4.4.24}
\makelabel{homalg:IsHomalgRingMap}{5.1.1}
\makelabel{homalg:IsHomalgRingSelfMap}{5.1.2}
\makelabel{homalg:IsHomalgRingMapRep}{5.1.3}
\makelabel{homalg:RingMap (constructor for ring maps)}{5.2.1}
\makelabel{homalg:IsMorphism (for ring maps)}{5.3.1}
\makelabel{homalg:IsIdentityMorphism (for ring maps)}{5.3.2}
\makelabel{homalg:IsMonomorphism (for ring maps)}{5.3.3}
\makelabel{homalg:IsEpimorphism (for ring maps)}{5.3.4}
\makelabel{homalg:IsIsomorphism (for ring maps)}{5.3.5}
\makelabel{homalg:IsAutomorphism (for ring maps)}{5.3.6}
\makelabel{homalg:Source (for ring maps)}{5.4.1}
\makelabel{homalg:Range (for ring maps)}{5.4.2}
\makelabel{homalg:DegreeOfMorphism (for ring maps)}{5.4.3}
\makelabel{homalg:CoordinateRingOfGraph (for ring maps)}{5.4.4}
\makelabel{homalg:KernelSubmodule (for ring maps)}{5.4.5}
\makelabel{homalg:KernelEmb (for ring maps)}{5.4.6}
\makelabel{homalg:Kernel (for ring maps)}{5.5.1}
\makelabel{homalg:IsHomalgMatrix}{6.1.1}
\makelabel{homalg:IsHomalgInternalMatrixRep}{6.1.2}
\makelabel{homalg:HomalgInitialMatrix (constructor for initial matrices filled with zeros)}{6.2.1}
\makelabel{homalg:HomalgInitialIdentityMatrix (constructor for initial quadratic matrices with ones on the diagonal)}{6.2.2}
\makelabel{homalg:HomalgZeroMatrix (constructor for zero matrices)}{6.2.3}
\makelabel{homalg:HomalgIdentityMatrix (constructor for identity matrices)}{6.2.4}
\makelabel{homalg:HomalgVoidMatrix (constructor for void matrices)}{6.2.5}
\makelabel{homalg:HomalgMatrix (constructor for matrices using a listlist)}{6.2.6}
\makelabel{homalg:HomalgMatrix (constructor for matrices using a list)}{6.2.6}
\makelabel{homalg:HomalgMatrix (constructor for matrices using a string of a listlist)}{6.2.6}
\makelabel{homalg:HomalgMatrix (constructor for matrices using a string of a list)}{6.2.6}
\makelabel{homalg:HomalgDiagonalMatrix (constructor for diagonal matrices)}{6.2.7}
\makelabel{homalg:\* (copy a matrix over a different ring)}{6.2.8}
\makelabel{homalg:\* (copy a matrix over a different ring (right))}{6.2.8}
\makelabel{homalg:IsZero (for matrices)}{6.3.1}
\makelabel{homalg:IsIdentityMatrix}{6.3.2}
\makelabel{homalg:IsPermutationMatrix}{6.3.3}
\makelabel{homalg:IsSpecialSubidentityMatrix}{6.3.4}
\makelabel{homalg:IsSubidentityMatrix}{6.3.5}
\makelabel{homalg:IsLeftRegularMatrix}{6.3.6}
\makelabel{homalg:IsRightRegularMatrix}{6.3.7}
\makelabel{homalg:IsInvertibleMatrix}{6.3.8}
\makelabel{homalg:IsLeftInvertibleMatrix}{6.3.9}
\makelabel{homalg:IsRightInvertibleMatrix}{6.3.10}
\makelabel{homalg:IsEmptyMatrix}{6.3.11}
\makelabel{homalg:IsDiagonalMatrix}{6.3.12}
\makelabel{homalg:IsScalarlMatrix}{6.3.13}
\makelabel{homalg:IsUpperTriangularMatrix}{6.3.14}
\makelabel{homalg:IsLowerTriangularMatrix}{6.3.15}
\makelabel{homalg:IsStrictUpperTriangularMatrix}{6.3.16}
\makelabel{homalg:IsStrictLowerTriangularMatrix}{6.3.17}
\makelabel{homalg:IsUpperStairCaseMatrix}{6.3.18}
\makelabel{homalg:IsLowerStairCaseMatrix}{6.3.19}
\makelabel{homalg:IsTriangularMatrix}{6.3.20}
\makelabel{homalg:IsBasisOfRowsMatrix}{6.3.21}
\makelabel{homalg:IsBasisOfColumnsMatrix}{6.3.22}
\makelabel{homalg:IsReducedBasisOfRowsMatrix}{6.3.23}
\makelabel{homalg:IsReducedBasisOfColumnsMatrix}{6.3.24}
\makelabel{homalg:IsMutableMatrix}{6.3.25}
\makelabel{homalg:IsInitialMatrix}{6.3.26}
\makelabel{homalg:IsInitialIdentityMatrix}{6.3.27}
\makelabel{homalg:IsVoidMatrix}{6.3.28}
\makelabel{homalg:NrRows}{6.4.1}
\makelabel{homalg:NrColumns}{6.4.2}
\makelabel{homalg:DeterminantMat}{6.4.3}
\makelabel{homalg:ZeroRows}{6.4.4}
\makelabel{homalg:ZeroColumns}{6.4.5}
\makelabel{homalg:NonZeroRows}{6.4.6}
\makelabel{homalg:NonZeroColumns}{6.4.7}
\makelabel{homalg:PositionOfFirstNonZeroEntryPerRow}{6.4.8}
\makelabel{homalg:PositionOfFirstNonZeroEntryPerColumn}{6.4.9}
\makelabel{homalg:DegreesOfEntries}{6.4.10}
\makelabel{homalg:RowRankOfMatrix}{6.4.11}
\makelabel{homalg:ColumnRankOfMatrix}{6.4.12}
\makelabel{homalg:LeftInverse (for matrices)}{6.4.13}
\makelabel{homalg:RightInverse (for matrices)}{6.4.14}
\makelabel{homalg:HomalgRing (for matrices)}{6.5.1}
\makelabel{homalg:Involution (for matrices)}{6.5.2}
\makelabel{homalg:CertainRows (for matrices)}{6.5.3}
\makelabel{homalg:CertainColumns (for matrices)}{6.5.4}
\makelabel{homalg:UnionOfRows (for matrices)}{6.5.5}
\makelabel{homalg:UnionOfColumns (for matrices)}{6.5.6}
\makelabel{homalg:DiagMat (for matrices)}{6.5.7}
\makelabel{homalg:KroneckerMat (for matrices)}{6.5.8}
\makelabel{homalg:\* (for ring elements and matrices)}{6.5.9}
\makelabel{homalg:\+ (for matrices)}{6.5.10}
\makelabel{homalg:\- (for matrices)}{6.5.11}
\makelabel{homalg:\* (for composable matrices)}{6.5.12}
\makelabel{homalg:\= (for matrices)}{6.5.13}
\makelabel{homalg:GetColumnIndependentUnitPositions (for matrices)}{6.5.14}
\makelabel{homalg:GetRowIndependentUnitPositions (for matrices)}{6.5.15}
\makelabel{homalg:GetUnitPosition (for matrices)}{6.5.16}
\makelabel{homalg:BasisOfRowModule (for matrices)}{6.5.17}
\makelabel{homalg:BasisOfColumnModule (for matrices)}{6.5.18}
\makelabel{homalg:DecideZeroRows (for pairs of matrices)}{6.5.19}
\makelabel{homalg:DecideZeroColumns (for pairs of matrices)}{6.5.20}
\makelabel{homalg:SyzygiesGeneratorsOfRows (for matrices)}{6.5.21}
\makelabel{homalg:SyzygiesGeneratorsOfColumns (for matrices)}{6.5.22}
\makelabel{homalg:SyzygiesGeneratorsOfRows (for pairs of matrices)}{6.5.23}
\makelabel{homalg:SyzygiesGeneratorsOfColumns (for pairs of matrices)}{6.5.24}
\makelabel{homalg:ReducedBasisOfRowModule (for matrices)}{6.5.25}
\makelabel{homalg:ReducedBasisOfColumnModule (for matrices)}{6.5.26}
\makelabel{homalg:ReducedSyzygiesGeneratorsOfRows (for matrices)}{6.5.27}
\makelabel{homalg:ReducedSyzygiesGeneratorsOfColumns (for matrices)}{6.5.28}
\makelabel{homalg:BasisOfRowsCoeff (for matrices)}{6.5.29}
\makelabel{homalg:BasisOfColumnsCoeff (for matrices)}{6.5.30}
\makelabel{homalg:DecideZeroRowsEffectively (for pairs of matrices)}{6.5.31}
\makelabel{homalg:DecideZeroColumnsEffectively (for pairs of matrices)}{6.5.32}
\makelabel{homalg:BasisOfRows (for matrices)}{6.5.33}
\makelabel{homalg:BasisOfRows (for pairs of matrices)}{6.5.33}
\makelabel{homalg:BasisOfColumns (for matrices)}{6.5.34}
\makelabel{homalg:BasisOfColumns (for pairs of matrices)}{6.5.34}
\makelabel{homalg:DecideZero (for matrices and relations)}{6.5.35}
\makelabel{homalg:SyzygiesOfRows (for matrices)}{6.5.36}
\makelabel{homalg:SyzygiesOfRows (for pairs of matrices)}{6.5.36}
\makelabel{homalg:SyzygiesOfColumns (for matrices)}{6.5.37}
\makelabel{homalg:SyzygiesOfColumns (for pairs of matrices)}{6.5.37}
\makelabel{homalg:ReducedSyzygiesOfRows (for matrices)}{6.5.38}
\makelabel{homalg:ReducedSyzygiesOfRows (for pairs of matrices)}{6.5.38}
\makelabel{homalg:ReducedSyzygiesOfColumns (for matrices)}{6.5.39}
\makelabel{homalg:ReducedSyzygiesOfColumns (for pairs of matrices)}{6.5.39}
\makelabel{homalg:RightDivide (for pairs of matrices)}{6.5.40}
\makelabel{homalg:LeftDivide (for pairs of matrices)}{6.5.41}
\makelabel{homalg:RightDivide (for triples of matrices)}{6.5.42}
\makelabel{homalg:RightDivide (for pairs matrices and a set of relations)}{6.5.42}
\makelabel{homalg:LeftDivide (for triples of matrices)}{6.5.43}
\makelabel{homalg:LeftDivide (for pairs matrices and a set of relations)}{6.5.43}
\makelabel{homalg:GenerateSameRowModule (for pairs of matrices)}{6.5.44}
\makelabel{homalg:GenerateSameColumnModule (for pairs of matrices)}{6.5.45}
\makelabel{homalg:IsHomalgRelations}{7.1.1}
\makelabel{homalg:IsHomalgRelationsOfLeftModule}{7.1.2}
\makelabel{homalg:IsHomalgRelationsOfRightModule}{7.1.3}
\makelabel{homalg:IsRelationsOfFinitelyPresentedModuleRep}{7.1.4}
\makelabel{homalg:CanBeUsedToDecideZeroEffectively}{7.3.1}
\makelabel{homalg:IsInjectivePresentation}{7.3.2}
\makelabel{homalg:FreeResolution}{7.4.1}
\makelabel{homalg:IsHomalgGenerators}{8.1.1}
\makelabel{homalg:IsHomalgGeneratorsOfLeftModule}{8.1.2}
\makelabel{homalg:IsHomalgGeneratorsOfRightModule}{8.1.3}
\makelabel{homalg:IsGeneratorsOfFinitelyGeneratedModuleRep}{8.1.4}
\makelabel{homalg:IsReduced}{8.3.1}
\makelabel{homalg:ProcedureToReadjustGenerators}{8.4.1}
\makelabel{homalg:IsHomalgModule}{9.1.1}
\makelabel{homalg:IsFinitelyPresentedModuleOrSubmoduleRep}{9.1.2}
\makelabel{homalg:IsFinitelyPresentedModuleRep}{9.1.3}
\makelabel{homalg:IsFinitelyPresentedSubmoduleRep}{9.1.4}
\makelabel{homalg:LeftPresentation (constructor for left modules)}{9.2.1}
\makelabel{homalg:RightPresentation (constructor for right modules)}{9.2.2}
\makelabel{homalg:HomalgFreeLeftModule (constructor for free left modules)}{9.2.3}
\makelabel{homalg:HomalgFreeRightModule (constructor for free right modules)}{9.2.4}
\makelabel{homalg:HomalgZeroLeftModule (constructor for zero left modules)}{9.2.5}
\makelabel{homalg:HomalgZeroRightModule (constructor for zero right modules)}{9.2.6}
\makelabel{homalg:\* (transfer a module over a different ring)}{9.2.7}
\makelabel{homalg:\* (transfer a module over a different ring (right))}{9.2.7}
\makelabel{homalg:Subobject (constructor for submodules using maps)}{9.2.8}
\makelabel{homalg:Subobject (constructor for submodules using matrices)}{9.2.9}
\makelabel{homalg:Subobject (constructor for submodules using a list of ring elements)}{9.2.10}
\makelabel{homalg:LeftSubmodule (constructor for left submodules)}{9.2.11}
\makelabel{homalg:RightSubmodule (constructor for right submodules)}{9.2.12}
\makelabel{homalg:IsFree}{9.3.1}
\makelabel{homalg:IsStablyFree}{9.3.2}
\makelabel{homalg:IsProjective}{9.3.3}
\makelabel{homalg:FiniteFreeResolutionExists}{9.3.4}
\makelabel{homalg:IsReflexive}{9.3.5}
\makelabel{homalg:IsTorsionFree}{9.3.6}
\makelabel{homalg:IsArtinian (for modules)}{9.3.7}
\makelabel{homalg:IsCyclic}{9.3.8}
\makelabel{homalg:IsTorsion}{9.3.9}
\makelabel{homalg:IsHolonomic}{9.3.10}
\makelabel{homalg:IsPure}{9.3.11}
\makelabel{homalg:HasConstantRank}{9.3.12}
\makelabel{homalg:ConstructedAsAnIdeal}{9.3.13}
\makelabel{homalg:IsPrimeIdeal}{9.3.14}
\makelabel{homalg:TheZeroMorphism}{9.4.1}
\makelabel{homalg:TheIdentityMorphism}{9.4.2}
\makelabel{homalg:FullSubmodule}{9.4.3}
\makelabel{homalg:EmbeddingInSuperObject}{9.4.4}
\makelabel{homalg:FactorObject}{9.4.5}
\makelabel{homalg:ResidueClassRing}{9.4.6}
\makelabel{homalg:UnderlyingSubobject}{9.4.7}
\makelabel{homalg:NatTrIdToHomHomR (for maps)}{9.4.8}
\makelabel{homalg:PrimaryDecomposition}{9.4.9}
\makelabel{homalg:ElementaryDivisors}{9.4.10}
\makelabel{homalg:RankOfModule}{9.4.11}
\makelabel{homalg:ProjectiveDimension}{9.4.12}
\makelabel{homalg:DegreeOfTorsionFreeness}{9.4.13}
\makelabel{homalg:Codim}{9.4.14}
\makelabel{homalg:PurityFiltration}{9.4.15}
\makelabel{homalg:CodegreeOfPurity}{9.4.16}
\makelabel{homalg:BettiDiagram (for modules)}{9.4.17}
\makelabel{homalg:CastelnuovoMumfordRegularity}{9.4.18}
\makelabel{homalg:HomalgRing (for modules)}{9.5.1}
\makelabel{homalg:ByASmallerPresentation (for modules)}{9.5.2}
\makelabel{homalg:UnderlyingObject (for submodules)}{9.5.3}
\makelabel{homalg:SuperObject (for submodules)}{9.5.4}
\makelabel{homalg:\* (constructor for ideal multiples)}{9.5.5}
\makelabel{homalg:SubmoduleQuotient (for submodules)}{9.5.6}
\makelabel{homalg:Saturate (for ideals)}{9.5.7}
\makelabel{homalg:IsHomalgMap}{10.1.1}
\makelabel{homalg:IsHomalgSelfMap}{10.1.2}
\makelabel{homalg:IsMapOfFinitelyGeneratedModulesRep}{10.1.3}
\makelabel{homalg:HomalgMap (constructor for maps)}{10.2.1}
\makelabel{homalg:HomalgMap (constructor for maps between free modules)}{10.2.1}
\makelabel{homalg:HomalgZeroMap (constructor for zero maps)}{10.2.2}
\makelabel{homalg:HomalgIdentityMap (constructor for identity maps)}{10.2.3}
\makelabel{homalg:IsMorphism (for maps)}{10.3.1}
\makelabel{homalg:IsGeneralizedMorphism (for maps)}{10.3.2}
\makelabel{homalg:IsGeneralizedEpimorphism (for maps)}{10.3.3}
\makelabel{homalg:IsGeneralizedMonomorphism (for maps)}{10.3.4}
\makelabel{homalg:IsGeneralizedIsomorphism (for maps)}{10.3.5}
\makelabel{homalg:IsIdentityMorphism (for maps)}{10.3.6}
\makelabel{homalg:IsMonomorphism (for maps)}{10.3.7}
\makelabel{homalg:IsEpimorphism (for maps)}{10.3.8}
\makelabel{homalg:IsSplitMonomorphism (for maps)}{10.3.9}
\makelabel{homalg:IsSplitEpimorphism (for maps)}{10.3.10}
\makelabel{homalg:IsIsomorphism (for maps)}{10.3.11}
\makelabel{homalg:IsAutomorphism (for maps)}{10.3.12}
\makelabel{homalg:Source (for maps)}{10.4.1}
\makelabel{homalg:Range (for maps)}{10.4.2}
\makelabel{homalg:DegreeOfMorphism (for maps)}{10.4.3}
\makelabel{homalg:CokernelEpi (for maps)}{10.4.4}
\makelabel{homalg:CokernelNaturalGeneralizedIsomorphism (for maps)}{10.4.5}
\makelabel{homalg:KernelSubmodule (for maps)}{10.4.6}
\makelabel{homalg:KernelEmb (for maps)}{10.4.7}
\makelabel{homalg:ImageSubmodule (for maps)}{10.4.8}
\makelabel{homalg:ImageModuleEmb (for maps)}{10.4.9}
\makelabel{homalg:ImageModuleEpi (for maps)}{10.4.10}
\makelabel{homalg:MorphismAidMap (for maps)}{10.4.11}
\makelabel{homalg:HomalgRing (for maps)}{10.5.1}
\makelabel{homalg:ByASmallerPresentation (for maps)}{10.5.2}
\makelabel{homalg:PreInverse (for maps)}{10.5.3}
\makelabel{homalg:IsHomalgComplex}{11.1.1}
\makelabel{homalg:IsComplexOfFinitelyPresentedObjectsRep}{11.1.2}
\makelabel{homalg:IsCocomplexOfFinitelyPresentedObjectsRep}{11.1.3}
\makelabel{homalg:HomalgComplex (constructor for complexes given a module)}{11.2.1}
\makelabel{homalg:HomalgComplex (constructor for complexes given a map)}{11.2.1}
\makelabel{homalg:HomalgComplex (constructor for complexes given a complex)}{11.2.1}
\makelabel{homalg:HomalgComplex (constructor for complexes given a chain map)}{11.2.1}
\makelabel{homalg:HomalgCocomplex (constructor for cocomplexes given a module)}{11.2.2}
\makelabel{homalg:HomalgCocomplex (constructor for cocomplexes given a map)}{11.2.2}
\makelabel{homalg:HomalgCocomplex (constructor for cocomplexes given a complex)}{11.2.2}
\makelabel{homalg:HomalgCocomplex (constructor for cocomplexes given a chain map)}{11.2.2}
\makelabel{homalg:IsSequence}{11.3.1}
\makelabel{homalg:IsComplex}{11.3.2}
\makelabel{homalg:IsAcyclic}{11.3.3}
\makelabel{homalg:IsRightAcyclic}{11.3.4}
\makelabel{homalg:IsLeftAcyclic}{11.3.5}
\makelabel{homalg:IsGradedObject}{11.3.6}
\makelabel{homalg:IsExactSequence}{11.3.7}
\makelabel{homalg:IsShortExactSequence}{11.3.8}
\makelabel{homalg:IsSplitShortExactSequence}{11.3.9}
\makelabel{homalg:IsTriangle}{11.3.10}
\makelabel{homalg:IsExactTriangle}{11.3.11}
\makelabel{homalg:BettiDiagram (for complexes)}{11.4.1}
\makelabel{homalg:Add (to complexes given a map)}{11.5.1}
\makelabel{homalg:Add (to complexes given a matrix)}{11.5.1}
\makelabel{homalg:ByASmallerPresentation (for complexes)}{11.5.2}
\makelabel{homalg:IsHomalgChainMap}{12.1.1}
\makelabel{homalg:IsHomalgChainSelfMap}{12.1.2}
\makelabel{homalg:IsChainMapOfFinitelyPresentedObjectsRep}{12.1.3}
\makelabel{homalg:IsCochainMapOfFinitelyPresentedObjectsRep}{12.1.4}
\makelabel{homalg:HomalgChainMap (constructor for chain maps given a map)}{12.2.1}
\makelabel{homalg:IsMorphism (for chain maps)}{12.3.1}
\makelabel{homalg:IsGeneralizedMorphism (for chain maps)}{12.3.2}
\makelabel{homalg:IsGeneralizedEpimorphism (for chain maps)}{12.3.3}
\makelabel{homalg:IsGeneralizedMonomorphism (for chain maps)}{12.3.4}
\makelabel{homalg:IsGeneralizedIsomorphism (for chain maps)}{12.3.5}
\makelabel{homalg:IsIdentityMorphism (for chain maps)}{12.3.6}
\makelabel{homalg:IsMonomorphism (for chain maps)}{12.3.7}
\makelabel{homalg:IsEpimorphism (for chain maps)}{12.3.8}
\makelabel{homalg:IsSplitMonomorphism (for chain maps)}{12.3.9}
\makelabel{homalg:IsSplitEpimorphism (for chain maps)}{12.3.10}
\makelabel{homalg:IsIsomorphism (for chain maps)}{12.3.11}
\makelabel{homalg:IsAutomorphism (for chain maps)}{12.3.12}
\makelabel{homalg:IsGradedMorphism (for chain maps)}{12.3.13}
\makelabel{homalg:IsQuasiIsomorphism (for chain maps)}{12.3.14}
\makelabel{homalg:Source (for chain maps)}{12.4.1}
\makelabel{homalg:Range (for chain maps)}{12.4.2}
\makelabel{homalg:ByASmallerPresentation (for chain maps)}{12.5.1}
\makelabel{homalg:IsHomalgBicomplex}{13.1.1}
\makelabel{homalg:IsBicomplexOfFinitelyPresentedObjectsRep}{13.1.2}
\makelabel{homalg:IsBicocomplexOfFinitelyPresentedObjectsRep}{13.1.3}
\makelabel{homalg:HomalgBicomplex (constructor for bicomplexes given a complex of complexes)}{13.2.1}
\makelabel{homalg:IsBisequence}{13.3.1}
\makelabel{homalg:IsBicomplex}{13.3.2}
\makelabel{homalg:IsTransposedWRTTheAssociatedComplex}{13.3.3}
\makelabel{homalg:TotalComplex}{13.4.1}
\makelabel{homalg:SpectralSequence (for bicomplexes)}{13.4.2}
\makelabel{homalg:UnderlyingComplex}{13.5.1}
\makelabel{homalg:ByASmallerPresentation (for bicomplexes)}{13.5.2}
\makelabel{homalg:IsHomalgBigradedObject}{14.1.1}
\makelabel{homalg:IsHomalgBigradedObjectAssociatedToAnExactCouple}{14.1.2}
\makelabel{homalg:IsHomalgBigradedObjectAssociatedToAFilteredComplex}{14.1.3}
\makelabel{homalg:IsHomalgBigradedObjectAssociatedToABicomplex}{14.1.4}
\makelabel{homalg:IsBigradedObjectOfFinitelyPresentedObjectsRep}{14.1.5}
\makelabel{homalg:HomalgBigradedObject (constructor for bigraded objects given a bicomplex)}{14.2.1}
\makelabel{homalg:AsDifferentialObject (for homalg bigraded objects stemming from a bicomplex)}{14.2.2}
\makelabel{homalg:DefectOfExactness (for homalg differential bigraded objects)}{14.2.3}
\makelabel{homalg:IsEndowedWithDifferential}{14.3.1}
\makelabel{homalg:IsStableSheet}{14.3.2}
\makelabel{homalg:ByASmallerPresentation (for bigraded objects)}{14.4.1}
\makelabel{homalg:IsHomalgSpectralSequence}{15.1.1}
\makelabel{homalg:IsHomalgSpectralSequenceAssociatedToAnExactCouple}{15.1.2}
\makelabel{homalg:IsHomalgSpectralSequenceAssociatedToAFilteredComplex}{15.1.3}
\makelabel{homalg:IsHomalgSpectralSequenceAssociatedToABicomplex}{15.1.4}
\makelabel{homalg:IsSpectralSequenceOfFinitelyPresentedObjectsRep}{15.1.5}
\makelabel{homalg:IsSpectralCosequenceOfFinitelyPresentedObjectsRep}{15.1.6}
\makelabel{homalg:HomalgSpectralSequence (constructor for spectral sequences given a bicomplex)}{15.2.1}
\makelabel{homalg:HomalgSpectralSequence (constructor for spectral sequences without a special sheet given a bicomplex)}{15.2.1}
\makelabel{homalg:HomalgSpectralSequence (constructor for spectral sequences without bound given a bicomplex)}{15.2.1}
\makelabel{homalg:HomalgSpectralSequence (constructor for spectral sequences without bound and without a special sheet given a bicomplex)}{15.2.1}
\makelabel{homalg:GeneralizedEmbeddingsInTotalObjects}{15.3.1}
\makelabel{homalg:GeneralizedEmbeddingsInTotalDefects}{15.3.2}
\makelabel{homalg:ByASmallerPresentation (for spectral sequences)}{15.4.1}
\makelabel{homalg:IsHomalgFunctor}{16.1.1}
\makelabel{homalg:IsHomalgFunctorRep}{16.1.2}
\makelabel{homalg:CreateHomalgFunctor (constructor for functors)}{16.2.1}
\makelabel{homalg:InsertObjectInMultiFunctor (constructor for functors given a multi-functor and an object)}{16.2.2}
\makelabel{homalg:RightSatelliteOfCofunctor (constructor of the right satellite of a contravariant functor)}{16.2.3}
\makelabel{homalg:LeftSatelliteOfFunctor (constructor of the left satellite of a covariant functor)}{16.2.4}
\makelabel{homalg:RightDerivedCofunctor (constructor of the right derived functor of a contravariant functor)}{16.2.5}
\makelabel{homalg:LeftDerivedFunctor (constructor of the left derived functor of a covariant functor)}{16.2.6}
\makelabel{homalg:ComposeFunctors (constructor for functors given two functors)}{16.2.7}
\makelabel{homalg:Genesis}{16.3.1}
\makelabel{homalg:functorCokernel}{16.4.1}
\makelabel{homalg:Cokernel}{16.4.2}
\makelabel{homalg:functorImageModule}{16.4.3}
\makelabel{homalg:ImageModule}{16.4.4}
\makelabel{homalg:functorKernel}{16.4.5}
\makelabel{homalg:Kernel (for maps)}{16.4.6}
\makelabel{homalg:functorDefectOfExactness}{16.4.7}
\makelabel{homalg:DefectOfExactness}{16.4.8}
\makelabel{homalg:FunctorHom}{16.4.9}
\makelabel{homalg:Hom}{16.4.10}
\makelabel{homalg:FunctorTensorProduct}{16.4.11}
\makelabel{homalg:TensorProduct}{16.4.12}
\makelabel{homalg:\* (TensorProduct)}{16.4.12}
\makelabel{homalg:FunctorExt}{16.4.13}
\makelabel{homalg:Ext}{16.4.14}
\makelabel{homalg:FunctorTor}{16.4.15}
\makelabel{homalg:Tor}{16.4.16}
\makelabel{homalg:FunctorRHom}{16.4.17}
\makelabel{homalg:RHom}{16.4.18}
\makelabel{homalg:FunctorLTensorProduct}{16.4.19}
\makelabel{homalg:LTensorProduct}{16.4.20}
\makelabel{homalg:FunctorHomHom}{16.4.21}
\makelabel{homalg:FunctorLHomHom}{16.4.22}
\makelabel{homalg:NameOfFunctor}{16.7.1}
\makelabel{homalg:InstallFunctor}{16.7.2}
\makelabel{homalg:InstallDeltaFunctor}{16.7.3}
\makelabel{homalg:ZeroMatrix (homalgTable entry for initial matrices)}{D.1.1}
\makelabel{homalg:IdentityMatrix (homalgTable entry for initial identity matrices)}{D.1.2}
\makelabel{homalg:ZeroMatrix (homalgTable entry)}{D.1.3}
\makelabel{homalg:IdentityMatrix (homalgTable entry)}{D.1.4}
\makelabel{homalg:Involution (homalgTable entry)}{D.1.5}
\makelabel{homalg:CertainRows (homalgTable entry)}{D.1.6}
\makelabel{homalg:CertainColumns (homalgTable entry)}{D.1.7}
\makelabel{homalg:UnionOfRows (homalgTable entry)}{D.1.8}
\makelabel{homalg:UnionOfColumns (homalgTable entry)}{D.1.9}
\makelabel{homalg:DiagMat (homalgTable entry)}{D.1.10}
\makelabel{homalg:KroneckerMat (homalgTable entry)}{D.1.11}
\makelabel{homalg:MulMat (homalgTable entry)}{D.1.12}
\makelabel{homalg:AddMat (homalgTable entry)}{D.1.13}
\makelabel{homalg:SubMat (homalgTable entry)}{D.1.14}
\makelabel{homalg:Compose (homalgTable entry)}{D.1.15}
\makelabel{homalg:IsZeroMatrix (homalgTable entry)}{D.1.16}
\makelabel{homalg:NrRows (homalgTable entry)}{D.1.17}
\makelabel{homalg:NrColumns (homalgTable entry)}{D.1.18}
\makelabel{homalg:Determinant (homalgTable entry)}{D.1.19}
\makelabel{homalg:AreEqualMatrices (homalgTable entry)}{D.2.1}
\makelabel{homalg:IsIdentityMatrix (homalgTable entry)}{D.2.2}
\makelabel{homalg:IsDiagonalMatrix (homalgTable entry)}{D.2.3}
\makelabel{homalg:ZeroRows (homalgTable entry)}{D.2.4}
\makelabel{homalg:ZeroColumns (homalgTable entry)}{D.2.5}
\makelabel{homalg:GetColumnIndependentUnitPositions (homalgTable entry)}{D.2.6}
\makelabel{homalg:GetRowIndependentUnitPositions (homalgTable entry)}{D.2.7}
\makelabel{homalg:GetUnitPosition (homalgTable entry)}{D.2.8}
\makelabel{homalg:DegreesOfEntries (homalgTable entry)}{D.2.9}
\makelabel{homalg:Eval (for matrices created with HomalgInitialMatrix)}{E.4.1}
\makelabel{homalg:Eval (for matrices created with HomalgInitialIdentityMatrix)}{E.4.2}
\makelabel{homalg:Eval (for matrices created with HomalgZeroMatrix)}{E.4.3}
\makelabel{homalg:Eval (for matrices created with HomalgIdentityMatrix)}{E.4.4}
\makelabel{homalg:Eval (for matrices created with Involution)}{E.4.5}
\makelabel{homalg:Eval (for matrices created with CertainRows)}{E.4.6}
\makelabel{homalg:Eval (for matrices created with CertainColumns)}{E.4.7}
\makelabel{homalg:Eval (for matrices created with UnionOfRows)}{E.4.8}
\makelabel{homalg:Eval (for matrices created with UnionOfColumns)}{E.4.9}
\makelabel{homalg:Eval (for matrices created with DiagMat)}{E.4.10}
\makelabel{homalg:Eval (for matrices created with KroneckerMat)}{E.4.11}
\makelabel{homalg:Eval (for matrices created with MulMat)}{E.4.12}
\makelabel{homalg:Eval (for matrices created with AddMat)}{E.4.13}
\makelabel{homalg:Eval (for matrices created with SubMat)}{E.4.14}
\makelabel{homalg:Eval (for matrices created with Compose)}{E.4.15}
\makelabel{homalg:Eval (for matrices created with LeftInverse)}{E.4.16}
\makelabel{homalg:Eval (for matrices created with RightInverse)}{E.4.17}
\makelabel{homalg:BasisOfRowModule (ResidueClassRing)}{F.1.1}
\makelabel{homalg:BasisOfColumnModule (ResidueClassRing)}{F.1.2}
\makelabel{homalg:DecideZeroRows (ResidueClassRing)}{F.1.3}
\makelabel{homalg:DecideZeroColumns (ResidueClassRing)}{F.1.4}
\makelabel{homalg:SyzygiesGeneratorsOfRows (ResidueClassRing)}{F.1.5}
\makelabel{homalg:SyzygiesGeneratorsOfColumns (ResidueClassRing)}{F.1.6}
\makelabel{homalg:BasisOfRowsCoeff (ResidueClassRing)}{F.1.7}
\makelabel{homalg:BasisOfColumnsCoeff (ResidueClassRing)}{F.1.8}
\makelabel{homalg:DecideZeroRowsEffectively (ResidueClassRing)}{F.1.9}
\makelabel{homalg:DecideZeroColumnsEffectively (ResidueClassRing)}{F.1.10}
\makelabel{homalg:RelativeSyzygiesGeneratorsOfRows (ResidueClassRing)}{F.1.11}
\makelabel{homalg:RelativeSyzygiesGeneratorsOfColumns (ResidueClassRing)}{F.1.12}
\makelabel{homalg:ZeroMatrix (ResidueClassRing)}{F.2.1}
\makelabel{homalg:IdentityMatrix (ResidueClassRing)}{F.2.2}
\makelabel{homalg:Involution (ResidueClassRing)}{F.2.3}
\makelabel{homalg:CertainRows (ResidueClassRing)}{F.2.4}
\makelabel{homalg:CertainColumns (ResidueClassRing)}{F.2.5}
\makelabel{homalg:UnionOfRows (ResidueClassRing)}{F.2.6}
\makelabel{homalg:UnionOfColumns (ResidueClassRing)}{F.2.7}
\makelabel{homalg:DiagMat (ResidueClassRing)}{F.2.8}
\makelabel{homalg:KroneckerMat (ResidueClassRing)}{F.2.9}
\makelabel{homalg:MulMat (ResidueClassRing)}{F.2.10}
\makelabel{homalg:AddMat (ResidueClassRing)}{F.2.11}
\makelabel{homalg:SubMat (ResidueClassRing)}{F.2.12}
\makelabel{homalg:Compose (ResidueClassRing)}{F.2.13}
\makelabel{homalg:IsZeroMatrix (ResidueClassRing)}{F.2.14}
\makelabel{homalg:NrRows (ResidueClassRing)}{F.2.15}
\makelabel{homalg:NrColumns (ResidueClassRing)}{F.2.16}
\makelabel{homalg:Determinant (ResidueClassRing)}{F.2.17}
\makelabel{homalg:AreEqualMatrices (ResidueClassRing)}{F.3.1}
\makelabel{homalg:IsIdentityMatrix (ResidueClassRing)}{F.3.2}
\makelabel{homalg:IsDiagonalMatrix (ResidueClassRing)}{F.3.3}
\makelabel{homalg:ZeroRows (ResidueClassRing)}{F.3.4}
\makelabel{homalg:ZeroColumns (ResidueClassRing)}{F.3.5}
\makelabel{homalg:homalgMode}{G.2.1}
