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

<!-- 

  Basic.xml            MatricesForHomalg package documentation            Mohamed Barakat

         Copyright (C) 2007-2009, Mohamed Barakat, RWTH-Aachen

-->

<Appendix Label="Basic_Operations">
<Heading>The Basic Matrix Operations</Heading>

These are the operations used to solve one-sided (in)homogeneous
linear systems <M>XA=B</M> resp. <M>AX=B</M>.

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

<Section Label="Main">
<Heading>Main</Heading>

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

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

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

</Section>

<Section Label="Effective">
<Heading>Effective</Heading>

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

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

</Section>

<Section Label="Relative">
<Heading>Relative</Heading>

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

</Section>

<Section Label="Reduced">
<Heading>Reduced</Heading>

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

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

</Section>

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

</Appendix>

