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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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  Basic.xml            ToolsForHomalg 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="Basic_Operations">

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<Heading>The Basic Matrix Operations</Heading>

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These are the operations used to solve one-sided (in)homogeneous

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linear systems <M>XA=B</M> resp. <M>AX=B</M>.

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<!--

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(&see; Appendix <Ref Chap="homalg-Idea"/>)

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-->

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<Section Label="Main">

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<Heading>Main</Heading>

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<List>

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  <Item><Ref Oper="BasisOfRowModule" Label="for matrices"/></Item>

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  <Item><Ref Oper="BasisOfColumnModule" Label="for matrices"/></Item>

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</List>

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<List>

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  <Item><Ref Oper="DecideZeroRows" Label="for pairs of matrices"/></Item>

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  <Item><Ref Oper="DecideZeroColumns" Label="for pairs of matrices"/></Item>

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</List>

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<List>

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  <Item><Ref Oper="SyzygiesGeneratorsOfRows" Label="for matrices"/></Item>

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  <Item><Ref Oper="SyzygiesGeneratorsOfColumns" Label="for matrices"/></Item>

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</List>

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</Section>

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<Section Label="Effective">

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<Heading>Effective</Heading>

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<List>

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  <Item><Ref Oper="BasisOfRowsCoeff" Label="for matrices"/></Item>

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  <Item><Ref Oper="BasisOfColumnsCoeff" Label="for matrices"/></Item>

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</List>

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<List>

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  <Item><Ref Oper="DecideZeroRowsEffectively" Label="for pairs of matrices"/></Item>

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  <Item><Ref Oper="DecideZeroColumnsEffectively" Label="for pairs of matrices"/></Item>

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</List>

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</Section>

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<Section Label="Relative">

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<Heading>Relative</Heading>

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<List>

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  <Item><Ref Oper="SyzygiesGeneratorsOfRows" Label="for pairs of matrices"/></Item>

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  <Item><Ref Oper="SyzygiesGeneratorsOfColumns" Label="for pairs of matrices"/></Item>

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</List>

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</Section>

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<Section Label="Reduced">

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<Heading>Reduced</Heading>

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<List>

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  <Item><Ref Oper="ReducedBasisOfRowModule" Label="for matrices"/></Item>

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  <Item><Ref Oper="ReducedBasisOfColumnModule" Label="for matrices"/></Item>

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</List>

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<List>

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  <Item><Ref Oper="ReducedSyzygiesGeneratorsOfRows" Label="for matrices"/></Item>

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  <Item><Ref Oper="ReducedSyzygiesGeneratorsOfColumns" Label="for matrices"/></Item>

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</List>

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</Section>

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

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</Appendix>

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