Matrices
Matrices: Category and Representations <#Include Label="IsHomalgMatrix"> <#Include Label="IsHomalgInternalMatrixRep">
Matrices: Constructors <#Include Label="HomalgInitialMatrix"> <#Include Label="HomalgInitialIdentityMatrix"> <#Include Label="HomalgZeroMatrix"> <#Include Label="HomalgIdentityMatrix"> <#Include Label="HomalgVoidMatrix"> <#Include Label="HomalgMatrix"> <#Include Label="HomalgMatrixListList"> <#Include Label="HomalgRowVector"> <#Include Label="HomalgColumnVector"> <#Include Label="HomalgDiagonalMatrix"> <#Include Label="\*:MatrixBaseChange"> <#Include Label="CoercedMatrix">
Matrices: Properties <#Include Label="IsZero:matrix"> <#Include Label="IsOne:matrix"> <#Include Label="IsUnitFree"> <#Include Label="IsPermutationMatrix"> <#Include Label="IsSpecialSubidentityMatrix"> <#Include Label="IsSubidentityMatrix"> <#Include Label="IsLeftRegular"> <#Include Label="IsRightRegular"> <#Include Label="IsInvertibleMatrix"> <#Include Label="IsLeftInvertibleMatrix"> <#Include Label="IsRightInvertibleMatrix"> <#Include Label="IsEmptyMatrix"> <#Include Label="IsDiagonalMatrix"> <#Include Label="IsScalarMatrix"> <#Include Label="IsUpperTriangularMatrix"> <#Include Label="IsLowerTriangularMatrix"> <#Include Label="IsStrictUpperTriangularMatrix"> <#Include Label="IsStrictLowerTriangularMatrix"> <#Include Label="IsUpperStairCaseMatrix"> <#Include Label="IsLowerStairCaseMatrix"> <#Include Label="IsTriangularMatrix"> <#Include Label="IsBasisOfRowsMatrix"> <#Include Label="IsBasisOfColumnsMatrix"> <#Include Label="IsReducedBasisOfRowsMatrix"> <#Include Label="IsReducedBasisOfColumnsMatrix"> <#Include Label="IsInitialMatrix"> <#Include Label="IsInitialIdentityMatrix"> <#Include Label="IsVoidMatrix">
Matrices: Attributes <#Include Label="NrRows"> <#Include Label="NrColumns"> <#Include Label="DeterminantMat"> <#Include Label="ZeroRows"> <#Include Label="ZeroColumns"> <#Include Label="NonZeroRows"> <#Include Label="NonZeroColumns"> <#Include Label="PositionOfFirstNonZeroEntryPerRow"> <#Include Label="PositionOfFirstNonZeroEntryPerColumn"> <#Include Label="RowRankOfMatrix"> <#Include Label="ColumnRankOfMatrix"> <#Include Label="LeftInverse"> <#Include Label="RightInverse"> <#Include Label="CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries"> <#Include Label="CoefficientsOfNumeratorOfHilbertPoincareSeries"> <#Include Label="UnreducedNumeratorOfHilbertPoincareSeries"> <#Include Label="NumeratorOfHilbertPoincareSeries"> <#Include Label="HilbertPoincareSeries"> <#Include Label="HilbertPolynomial"> <#Include Label="AffineDimension"> <#Include Label="AffineDegree"> <#Include Label="ProjectiveDegree"> <#Include Label="ConstantTermOfHilbertPolynomial"> <#Include Label="MatrixOfSymbols">
Matrices: Operations and Functions <#Include Label="HomalgRing:matrix"> <#Include Label="LeftInverse:method"> <#Include Label="RightInverse:method"> <#Include Label="LeftInverseLazy"> <#Include Label="RightInverseLazy"> <#Include Label="Involution"> <#Include Label="TransposedMatrix"> <#Include Label="CertainRows"> <#Include Label="CertainColumns"> <#Include Label="UnionOfRows"> <#Include Label="UnionOfColumns"> <#Include Label="ConvertRowToMatrix"> <#Include Label="ConvertColumnToMatrix"> <#Include Label="ConvertMatrixToRow"> <#Include Label="ConvertMatrixToColumn"> <#Include Label="DiagMat"> <#Include Label="KroneckerMat"> <#Include Label="DualKroneckerMat"> <#Include Label="MulMat"> <#Include Label="AddMat"> <#Include Label="SubMat"> <#Include Label="Compose:matrix"> <#Include Label="EQ:matrix"> <#Include Label="GetColumnIndependentUnitPositions"> <#Include Label="GetRowIndependentUnitPositions"> <#Include Label="GetUnitPosition"> <#Include Label="Eliminate"> <#Include Label="BasisOfRowModule"> <#Include Label="BasisOfColumnModule"> <#Include Label="DecideZeroRows"> <#Include Label="DecideZeroColumns"> <#Include Label="SyzygiesGeneratorsOfRows"> <#Include Label="SyzygiesGeneratorsOfColumns"> <#Include Label="RelativeSyzygiesGeneratorsOfRows"> <#Include Label="RelativeSyzygiesGeneratorsOfColumns"> <#Include Label="ReducedBasisOfRowModule"> <#Include Label="ReducedBasisOfColumnModule"> <#Include Label="ReducedSyzygiesGeneratorsOfRows"> <#Include Label="ReducedSyzygiesGeneratorsOfColumns"> <#Include Label="BasisOfRowsCoeff"> <#Include Label="BasisOfColumnsCoeff"> <#Include Label="DecideZeroRowsEffectively"> <#Include Label="DecideZeroColumnsEffectively"> <#Include Label="BasisOfRows"> <#Include Label="BasisOfColumns"> <#Include Label="DecideZero:matrix_rel"> <#Include Label="SyzygiesOfRows"> <#Include Label="SyzygiesOfColumns"> <#Include Label="ReducedSyzygiesOfRows"> <#Include Label="ReducedSyzygiesOfColumns"> <#Include Label="RightDivide"> <#Include Label="LeftDivide"> <#Include Label="RelativeRightDivide"> <#Include Label="RelativeLeftDivide"> <#Include Label="GenerateSameRowModule"> <#Include Label="GenerateSameColumnModule"> <#Include Label="SimplifyHomalgMatrixByLeftAndRightMultiplicationWithInvertibleMatrices"> <#Include Label="SimplifyHomalgMatrixByLeftMultiplicationWithInvertibleMatrix"> <#Include Label="SimplifyHomalgMatrixByRightMultiplicationWithInvertibleMatrix"> <#Include Label="CoefficientsWithGivenMonomials">