Tools.xml

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  Tools.xml            MatricesForHomalg package documentation            Mohamed Barakat

         Copyright (C) 2007-2009, Mohamed Barakat, RWTH-Aachen

-->

<Appendix Label="Tool_Operations">
<Heading>The Matrix Tool Operations</Heading>

The functions listed below are components of the <C>homalgTable</C>
object stored in the ring. They are only indirectly accessible through
standard methods that invoke them.

<Section Label="ToolsNoFallBack">
<Heading>The Tool Operations <E>without</E> a Fallback Method</Heading>

There are matrix methods for which &homalg; needs a
<C>homalgTable</C> entry for non-internal rings, as it cannot provide
a suitable fallback. Below is the list of these <C>homalgTable</C>
entries.

<#Include Label="InitialMatrix:homalgTable_entry">
<#Include Label="InitialIdentityMatrix:homalgTable_entry">

<#Include Label="ZeroMatrix:homalgTable_entry">
<#Include Label="IdentityMatrix:homalgTable_entry">

<#Include Label="Involution:homalgTable_entry">
<#Include Label="CertainRows:homalgTable_entry">
<#Include Label="CertainColumns:homalgTable_entry">
<#Include Label="UnionOfRows:homalgTable_entry">
<#Include Label="UnionOfColumns:homalgTable_entry">
<#Include Label="DiagMat:homalgTable_entry">
<#Include Label="KroneckerMat:homalgTable_entry">
<#Include Label="MulMat:homalgTable_entry">
<#Include Label="AddMat:homalgTable_entry">
<#Include Label="SubMat:homalgTable_entry">
<#Include Label="Compose:homalgTable_entry">

<#Include Label="IsZeroMatrix:homalgTable_entry">
<#Include Label="NrRows:homalgTable_entry">
<#Include Label="NrColumns:homalgTable_entry">
<#Include Label="Determinant:homalgTable_entry">

</Section>

<Section Label="ToolsFallBack">
<Heading>The Tool Operations with a Fallback Method</Heading>

These are the methods for which it is recommended for performance
reasons to have a <C>homalgTable</C> entry for non-internal
rings. &homalg; only provides a generic fallback method.

<#Include Label="AreEqualMatrices:homalgTable_entry">
<#Include Label="IsIdentityMatrix:homalgTable_entry">
<#Include Label="IsDiagonalMatrix:homalgTable_entry">

<#Include Label="ZeroRows:homalgTable_entry">
<#Include Label="ZeroColumns:homalgTable_entry">

<#Include Label="GetColumnIndependentUnitPositions:homalgTable_entry">
<#Include Label="GetRowIndependentUnitPositions:homalgTable_entry">
<#Include Label="GetUnitPosition:homalgTable_entry">

<#Include Label="PositionOfFirstNonZeroEntryPerRow:homalgTable_entry">
<#Include Label="PositionOfFirstNonZeroEntryPerColumn:homalgTable_entry">

</Section>

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</Appendix>