Quelle Matrices.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>



<Chapter Label="Matrices">
<Heading>Matrices</Heading>

<Section Label="Matrices:Category">
<Heading>Matrices: Category and Representations</Heading>

<#Include Label="IsHomalgMatrix">

<#Include Label="IsHomalgInternalMatrixRep">

</Section>

<Section Label="Matrices:Constructors">
<Heading>Matrices: Constructors</Heading>

<#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">

</Section>

<Section Label="Matrices:Properties">
<Heading>Matrices: Properties</Heading>

<#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">

</Section>

<Section Label="Matrices:Attributes">
<Heading>Matrices: Attributes</Heading>

<#Include Label="NumberRows">
<#Include Label="NumberColumns">
<#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">

</Section>

<Section Label="Matrices:Operations">
<Heading>Matrices: Operations and Functions</Heading>

<#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="SafeRightDivide">
<#Include Label="SafeLeftDivide">
<#Include Label="UniqueRightDivide">
<#Include Label="UniqueLeftDivide">

<#Include Label="GenerateSameRowModule">
<#Include Label="GenerateSameColumnModule">

<#Include Label="SimplifyHomalgMatrixByLeftAndRightMultiplicationWithInvertibleMatrices">
<#Include Label="SimplifyHomalgMatrixByLeftMultiplicationWithInvertibleMatrix">
<#Include Label="SimplifyHomalgMatrixByRightMultiplicationWithInvertibleMatrix">

<#Include Label="CoefficientsWithGivenMonomials">

</Section>



</Chapter>

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