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

<!-- 

  ResidueClassRingForHomalg.xml     MatricesForHomalg package documentation            Mohamed Barakat

         Copyright (C) 2007-2009, Mohamed Barakat, Universität des Saarlandes

-->

<Appendix Label="ResidueClassRingForHomalg">
<Heading>The subpackage &ResidueClassRingForHomalg; as a sample ring package</Heading>

<Section Label="ResidueClassRingForHomalg:BasicNoFallBack">
<Heading>The Mandatory Basic Operations</Heading>

<#Include Label="BasisOfRowModule:ResidueClassRing">
<#Include Label="BasisOfColumnModule:ResidueClassRing">
<#Include Label="DecideZeroRows:ResidueClassRing">
<#Include Label="DecideZeroColumns:ResidueClassRing">
<#Include Label="SyzygiesGeneratorsOfRows:ResidueClassRing">
<#Include Label="SyzygiesGeneratorsOfColumns:ResidueClassRing">
<#Include Label="BasisOfRowsCoeff:ResidueClassRing">
<#Include Label="BasisOfColumnsCoeff:ResidueClassRing">
<#Include Label="DecideZeroRowsEffectively:ResidueClassRing">
<#Include Label="DecideZeroColumnsEffectively:ResidueClassRing">
<#Include Label="RelativeSyzygiesGeneratorsOfRows:ResidueClassRing">
<#Include Label="RelativeSyzygiesGeneratorsOfColumns:ResidueClassRing">

</Section>

<Section Label="ResidueClassRingForHomalg:ToolsNoFallBack">
<Heading>The Mandatory Tool Operations</Heading>

Here we list those matrix operations for which &homalg; provides no
fallback method.

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

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

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

<#Include Label="IsZeroMatrix:ResidueClassRing">
<#Include Label="NumberRows:ResidueClassRing">
<#Include Label="NumberColumns:ResidueClassRing">
<#Include Label="Determinant:ResidueClassRing">

</Section>

<Section Label="ResidueClassRingForHomalg:ToolsFallBack">
<Heading>Some of the Recommended Tool Operations</Heading>

Here we list those matrix operations for which &homalg; does provide a
fallback method. But specifying the below <C>homalgTable</C> functions
increases the performance by replacing the fallback method.

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

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

</Section>

<!-- ############################################################ -->

</Appendix>