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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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  appendix.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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<Appendix Label="FileOverview">

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<Heading>Overview of the &MatricesForHomalg; Package Source Code</Heading>

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<Section Label="RingsMapsMatrices">

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<Heading>Rings, Ring Maps, Matrices, Ring Relations</Heading>

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<Table Align="l|l">

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<Caption><E>The &MatricesForHomalg; package files</E></Caption>

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<Row><Item>Filename <F>.gd</F>/<F>.gi</F></Item><Item>Content</Item></Row>

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<HorLine/>

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<Row>

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  <Item><F>homalg</F></Item>

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  <Item>definitions of the basic &GAP4; categories</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>and some tool functions (e.g. <C>homalgMode</C>)</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>homalgTable</F></Item>

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  <Item>dictionaries between &MatricesForHomalg;</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>and the computing engines</Item>

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</Row>

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<Row>

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  <Item><F>HomalgRing</F></Item>

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  <Item>internal and external rings</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>HomalgRingMap</F></Item>

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  <Item>ring maps</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>HomalgMatrix</F></Item>

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  <Item>internal and external matrices</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>HomalgRingRelations</F></Item>

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  <Item>a set of ring relations</Item>

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</Row>

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</Table>

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</Section>

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<Section Label="Low Level Algorithms">

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<Heading>The Low Level Algorithms</Heading>

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In the following CAS or CASystem mean computer algebra systems.

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<Table Align="l|l">

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<Caption><E>The &MatricesForHomalg; package files (continued)</E></Caption>

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<Row><Item>Filename <F>.gd</F>/<F>.gi</F></Item><Item>Content</Item></Row>

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<HorLine/>

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<Row>

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  <Item><F>Tools</F></Item>

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  <Item>the elementary matrix operations that can be</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>overwritten using the homalgTable</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>(and hence delegable even to other CASystems)</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>Service</F></Item>

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  <Item>the three operations: basis, reduction, and syzygies;</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>they can also be overwritten using the homalgTable</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>(and hence delegable even to other CASystems)</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>Basic</F></Item>

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  <Item>higher level operations for matrices</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>(cannot be overwritten using the homalgTable)</Item>

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</Row>

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</Table>

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</Section>

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<Section Label="Logical Implications">

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<Heading>Logical Implications for &MatricesForHomalg; Objects</Heading>

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<Table Align="l|l">

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<Caption><E>The &MatricesForHomalg; package files (continued)</E></Caption>

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<Row><Item>Filename <F>.gd</F>/<F>.gi</F></Item><Item>Content</Item></Row>

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<HorLine/>

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<Row>

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  <Item><F>LIRNG</F></Item>

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  <Item>logical implications for rings</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>LIMAP</F></Item>

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  <Item>logical implications for ring maps</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>LIMAT</F></Item>

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  <Item>logical implications for matrices</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>COLEM</F></Item>

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  <Item>clever operations for lazy evaluated matrices</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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</Table>

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</Section>

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<Section Label="ResidueClassRingForHomalg_subpackage">

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<Heading>The subpackage &ResidueClassRingForHomalg;</Heading>

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<Table Align="l|l">

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<Caption><E>The &MatricesForHomalg; package files (continued)</E></Caption>

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<Row><Item>Filename <F>.gd</F>/<F>.gi</F></Item><Item>Content</Item></Row>

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<HorLine/>

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<Row>

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  <Item><F>ResidueClassRingForHomalg</F></Item>

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  <Item>some global variables</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>ResidueClassRing</F></Item>

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  <Item>residue class rings, their elements, and matrices,</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>together with their constructors and operations</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>ResidueClassRingTools</F></Item>

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  <Item>the elementary matrix operations for matrices</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>over residue class rings</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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<Row>

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  <Item><F>ResidueClassRingBasic</F></Item>

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  <Item>the three operations: basis, reduction, and syzygies</Item>

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</Row>

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<Row>

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  <Item></Item>

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  <Item>for matrices over residue class rings</Item>

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</Row>

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<Row><Item></Item><Item></Item></Row>

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</Table>

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</Section>

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<Section Label="The built-in rings">

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<Heading>The homalgTable for &GAP4; built-in rings</Heading>

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For the purposes of &homalg;, the ring of integers is, at least up

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till now, the only ring which is properly supported in &GAP4;. The

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&GAP4; built-in cababilities for polynomial rings (also univariate)

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and group rings do not statisfy the minimum requirements of

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&homalg;. The &GAP4; package &Gauss; enables &GAP; to fullfil the

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&homalg; requirements for prime fields, and <M>&ZZ; / p^n</M>.

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<Table Align="l|l">

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<Caption><E>The &MatricesForHomalg; package files (continued)</E></Caption>

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<Row><Item>Filename .gi</Item><Item>Content</Item></Row>

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<HorLine/>

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<Row>

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  <Item><F>Integers</F></Item>

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  <Item>the homalgTable for the ring of integers</Item>

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</Row>

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</Table>

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</Section>

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</Appendix>

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