CoCalc -- Matrices.xml

GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap4r8 / pkg / MatricesForHomalg-2018.01.07 / doc / Matrices.xml
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<?xml version="1.0" encoding="UTF-8"?>
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<!-- 
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  Matrices.xml            MatricesForHomalg package documentation            Mohamed Barakat
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         Copyright (C) 2007-2009, Mohamed Barakat, RWTH-Aachen
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-->
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<Chapter Label="Matrices">
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<Heading>Matrices</Heading>
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<Section Label="Matrices:Category">
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<Heading>Matrices: Category and Representations</Heading>
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<#Include Label="IsHomalgMatrix">
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<#Include Label="IsHomalgInternalMatrixRep">
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</Section>
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<Section Label="Matrices:Constructors">
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<Heading>Matrices: Constructors</Heading>
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<#Include Label="HomalgInitialMatrix">
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<#Include Label="HomalgInitialIdentityMatrix">
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<#Include Label="HomalgZeroMatrix">
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<#Include Label="HomalgIdentityMatrix">
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<#Include Label="HomalgVoidMatrix">
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<#Include Label="HomalgMatrix">
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<#Include Label="HomalgDiagonalMatrix">
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<#Include Label="\*:MatrixBaseChange">
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</Section>
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<Section Label="Matrices:Properties">
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<Heading>Matrices: Properties</Heading>
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<#Include Label="IsZero:matrix">
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<#Include Label="IsOne:matrix">
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<#Include Label="IsUnitFree">
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<#Include Label="IsPermutationMatrix">
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<#Include Label="IsSpecialSubidentityMatrix">
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<#Include Label="IsSubidentityMatrix">
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<#Include Label="IsLeftRegular">
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<#Include Label="IsRightRegular">
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<#Include Label="IsInvertibleMatrix">
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<#Include Label="IsLeftInvertibleMatrix">
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<#Include Label="IsRightInvertibleMatrix">
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<#Include Label="IsEmptyMatrix">
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<#Include Label="IsDiagonalMatrix">
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<#Include Label="IsScalarMatrix">
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<#Include Label="IsUpperTriangularMatrix">
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<#Include Label="IsLowerTriangularMatrix">
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<#Include Label="IsStrictUpperTriangularMatrix">
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<#Include Label="IsStrictLowerTriangularMatrix">
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<#Include Label="IsUpperStairCaseMatrix">
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<#Include Label="IsLowerStairCaseMatrix">
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<#Include Label="IsTriangularMatrix">
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<#Include Label="IsBasisOfRowsMatrix">
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<#Include Label="IsBasisOfColumnsMatrix">
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<#Include Label="IsReducedBasisOfRowsMatrix">
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<#Include Label="IsReducedBasisOfColumnsMatrix">
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<#Include Label="IsInitialMatrix">
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<#Include Label="IsInitialIdentityMatrix">
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<#Include Label="IsVoidMatrix">
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</Section>
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<Section Label="Matrices:Attributes">
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<Heading>Matrices: Attributes</Heading>
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<#Include Label="NrRows">
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<#Include Label="NrColumns">
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<#Include Label="DeterminantMat">
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<#Include Label="ZeroRows">
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<#Include Label="ZeroColumns">
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<#Include Label="NonZeroRows">
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<#Include Label="NonZeroColumns">
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<#Include Label="PositionOfFirstNonZeroEntryPerRow">
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<#Include Label="PositionOfFirstNonZeroEntryPerColumn">
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<#Include Label="RowRankOfMatrix">
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<#Include Label="ColumnRankOfMatrix">
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<#Include Label="LeftInverse">
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<#Include Label="RightInverse">
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<#Include Label="CoefficientsOfUnreducedNumeratorOfHilbertPoincareSeries">
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<#Include Label="CoefficientsOfNumeratorOfHilbertPoincareSeries">
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<#Include Label="UnreducedNumeratorOfHilbertPoincareSeries">
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<#Include Label="NumeratorOfHilbertPoincareSeries">
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<#Include Label="HilbertPoincareSeries">
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<#Include Label="HilbertPolynomial">
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<#Include Label="AffineDimension">
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<#Include Label="AffineDegree">
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<#Include Label="ProjectiveDegree">
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<#Include Label="ConstantTermOfHilbertPolynomial">
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<#Include Label="MatrixOfSymbols">
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</Section>
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<Section Label="Matrices:Operations">
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<Heading>Matrices: Operations and Functions</Heading>
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<#Include Label="HomalgRing:matrix">
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<#Include Label="LeftInverse:method">
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<#Include Label="RightInverse:method">
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<#Include Label="LeftInverseLazy">
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<#Include Label="RightInverseLazy">
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<#Include Label="Involution">
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<#Include Label="CertainRows">
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<#Include Label="CertainColumns">
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<#Include Label="UnionOfRows">
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<#Include Label="UnionOfColumns">
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<#Include Label="DiagMat">
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<#Include Label="KroneckerMat">
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<#Include Label="MulMat">
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<#Include Label="AddMat">
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<#Include Label="SubMat">
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<#Include Label="Compose:matrix">
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<#Include Label="EQ:matrix">
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<#Include Label="GetColumnIndependentUnitPositions">
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<#Include Label="GetRowIndependentUnitPositions">
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<#Include Label="GetUnitPosition">
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<#Include Label="Eliminate">
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<#Include Label="BasisOfRowModule">
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<#Include Label="BasisOfColumnModule">
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<#Include Label="DecideZeroRows">
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<#Include Label="DecideZeroColumns">
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<#Include Label="SyzygiesGeneratorsOfRows">
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<#Include Label="SyzygiesGeneratorsOfColumns">
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<#Include Label="RelativeSyzygiesGeneratorsOfRows">
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<#Include Label="RelativeSyzygiesGeneratorsOfColumns">
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<#Include Label="ReducedBasisOfRowModule">
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<#Include Label="ReducedBasisOfColumnModule">
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<#Include Label="ReducedSyzygiesGeneratorsOfRows">
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<#Include Label="ReducedSyzygiesGeneratorsOfColumns">
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<#Include Label="BasisOfRowsCoeff">
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<#Include Label="BasisOfColumnsCoeff">
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<#Include Label="DecideZeroRowsEffectively">
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<#Include Label="DecideZeroColumnsEffectively">
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<#Include Label="BasisOfRows">
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<#Include Label="BasisOfColumns">
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<#Include Label="DecideZero:matrix_rel">
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<#Include Label="SyzygiesOfRows">
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<#Include Label="SyzygiesOfColumns">
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<#Include Label="ReducedSyzygiesOfRows">
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<#Include Label="ReducedSyzygiesOfColumns">
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<#Include Label="RightDivide">
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<#Include Label="LeftDivide">
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<#Include Label="RelativeRightDivide">
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<#Include Label="RelativeLeftDivide">
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<#Include Label="GenerateSameRowModule">
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<#Include Label="GenerateSameColumnModule">
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</Section>
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<!-- ############################################################ -->
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</Chapter>
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