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         LocalizeRingForHomalg package documentation             Mohamed Barakat
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                                                                        Markus Lange-Hegermann
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         Copyright (C) 2009, Mohamed Barakat, Universität des Saarlandes
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                      Markus Lange-Hegermann, RWTH-Aachen University
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-->
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<Appendix Label="FileOverview">
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<Heading>Overview of the &LocalizeRingForHomalg; Package Source Code</Heading>
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  This appendix is included in the documentation to shine some light
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  on the mathematical backgrounds of this Package. Neither is it
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  needed to work with this package nor should the methods presented
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  here be called directly. The functions documented here are entries
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  of the so called ring table and not to be called directly. There are
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  higher level methods in declared and installed in
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  &MatricesForHomalg;, which call this functions
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  (&see; <C>?MatricesForHomalg:The Basic Matrix Operations</C>).
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  <P/>We only present the simpler procedures, where no transformation
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  matrices are computed, since the computation of transformation
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  matrices carries no further mathematical ideas.
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  <Section Label="HomalgTable:Generic">
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     <Heading>The generic Methods</Heading>
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     There are some methods in localized rings, where homalg is able
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     to fall back on procedures of the corresponding global
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     ring. Furthermore these methods work quite good together with
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     Mora's algorithm as implemented in Singular, since we can treat
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     it like a global ring.
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     We will present some methods as an example, to show the idea:
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     <#Include Label="BasisOfRowModule">
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     <#Include Label="DecideZeroRows:generic">
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     <#Include Label="SyzygiesGeneratorsOfRows">
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  </Section>
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  <Section Label="HomalgTable:DecideZero">
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    <Heading>The Local Decide Zero trick</Heading>
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    <#Include Label="DecideZeroRows">
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  </Section>
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  <Section Label="LocalizeRing:Tools">
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    <Heading>Tools</Heading>
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    The package &LocalizeRingForHomalg; also implements tool
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    functions. These are referred to from &MatricesForHomalg;
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    automatically. We list the implemented methods here are and refer
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    to the &MatricesForHomalg; documentation
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    (&see; <C>?MatricesForHomalg: The Matrix Tool Operations</C>
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    and <C>?MatricesForHomalg:RingElement</C>) for details. All tools
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    functions from &MatricesForHomalg; not listed here are also
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    supported by fallback tools.
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    <List>
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        <Item>IsZero</Item>
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        <Item>IsOne</Item>
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        <Item>Minus</Item>
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        <Item>DivideByUnit</Item>
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        <Item>IsUnit</Item>
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        <Item>Sum</Item>
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        <Item>Product</Item>
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        <Item>ShallowCopy</Item>
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        <Item>ZeroMatrix</Item>
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        <Item>IdentityMatrix</Item>
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        <Item>AreEqualMatrices</Item>
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        <Item>Involution</Item>
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        <Item>CertainRows</Item>
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        <Item>CertainColumns</Item>
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        <Item>UnionOfRows</Item>
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        <Item>UnionOfColumns</Item>
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        <Item>DiagMat</Item>
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        <Item>KroneckerMat</Item>
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        <Item>MulMat</Item>
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        <Item>AddMat</Item>
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        <Item>SubMat</Item>
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        <Item>Compose</Item>
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        <Item>NrRows</Item>
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        <Item>NrColumns</Item>
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        <Item>IsZeroMatrix</Item>
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        <Item>IsDiagonalMatrix</Item>
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        <Item>ZeroRows</Item>
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        <Item>ZeroColumns</Item>
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    </List>
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  </Section>
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</Appendix>
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