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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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

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<!-- 

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  ResidueClassRingForHomalg.xml     MatricesForHomalg package documentation            Mohamed Barakat

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

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-->

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<Appendix Label="ResidueClassRingForHomalg">

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<Heading>The subpackage &ResidueClassRingForHomalg; as a sample ring package</Heading>

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<Section Label="ResidueClassRingForHomalg:BasicNoFallBack">

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<Heading>The Mandatory Basic Operations</Heading>

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<#Include Label="BasisOfRowModule:ResidueClassRing">

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<#Include Label="BasisOfColumnModule:ResidueClassRing">

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<#Include Label="DecideZeroRows:ResidueClassRing">

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<#Include Label="DecideZeroColumns:ResidueClassRing">

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<#Include Label="SyzygiesGeneratorsOfRows:ResidueClassRing">

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<#Include Label="SyzygiesGeneratorsOfColumns:ResidueClassRing">

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<#Include Label="BasisOfRowsCoeff:ResidueClassRing">

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<#Include Label="BasisOfColumnsCoeff:ResidueClassRing">

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<#Include Label="DecideZeroRowsEffectively:ResidueClassRing">

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<#Include Label="DecideZeroColumnsEffectively:ResidueClassRing">

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<#Include Label="RelativeSyzygiesGeneratorsOfRows:ResidueClassRing">

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<#Include Label="RelativeSyzygiesGeneratorsOfColumns:ResidueClassRing">

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</Section>

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<Section Label="ResidueClassRingForHomalg:ToolsNoFallBack">

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<Heading>The Mandatory Tool Operations</Heading>

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

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fallback method.

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<#Include Label="InitialMatrix:ResidueClassRing">

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<#Include Label="InitialIdentityMatrix:ResidueClassRing">

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<#Include Label="ZeroMatrix:ResidueClassRing">

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<#Include Label="IdentityMatrix:ResidueClassRing">

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<#Include Label="Involution:ResidueClassRing">

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<#Include Label="CertainRows:ResidueClassRing">

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<#Include Label="CertainColumns:ResidueClassRing">

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<#Include Label="UnionOfRows:ResidueClassRing">

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<#Include Label="UnionOfColumns:ResidueClassRing">

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<#Include Label="DiagMat:ResidueClassRing">

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<#Include Label="KroneckerMat:ResidueClassRing">

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<#Include Label="MulMat:ResidueClassRing">

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<#Include Label="AddMat:ResidueClassRing">

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<#Include Label="SubMat:ResidueClassRing">

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<#Include Label="Compose:ResidueClassRing">

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<#Include Label="IsZeroMatrix:ResidueClassRing">

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<#Include Label="NrRows:ResidueClassRing">

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<#Include Label="NrColumns:ResidueClassRing">

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<#Include Label="Determinant:ResidueClassRing">

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</Section>

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<Section Label="ResidueClassRingForHomalg:ToolsFallBack">

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<Heading>Some of the Recommended Tool Operations</Heading>

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Here we list those matrix operations for which &homalg; does provide a

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fallback method. But specifying the below <C>homalgTable</C> functions

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increases the performance by replacing the fallback method.

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<#Include Label="AreEqualMatrices:ResidueClassRing">

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<#Include Label="IsIdentityMatrix:ResidueClassRing">

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<#Include Label="IsDiagonalMatrix:ResidueClassRing">

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<#Include Label="ZeroRows:ResidueClassRing">

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<#Include Label="ZeroColumns:ResidueClassRing">

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</Section>

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

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</Appendix>

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