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<h1>RingsForHomalg</h1>


<h2>Dictionaries of external rings</h2>

<p>
    2024.11-02</p>

<p>
    16 November 2024
  </p>

</div>
<p><b>
    Mohamed Barakat




  </b>
<br />Email: <span class="URL"><a href="mailto:mohamed.barakat@uni-siegen.de">mohamed.barakat@uni-siegen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://mohamed-barakat.github.io">https://mohamed-barakat.github.io</a></span>
<br />Address: <br />Walter-Flex-Str. 3<br /> 57072 Siegen<br /> Germany<br />
</p><p><b>
    Simon Görtzen




  </b>
<br />Email: <span class="URL"><a href="mailto:simon.goertzen@rwth-aachen.de">simon.goertzen@rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://www.linkedin.com/in/simongoertzen/">https://www.linkedin.com/in/simongoertzen/</a></span>
<br />Address: <br />Simon Görtzen<br /> Lehrstuhl B fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />
</p><p><b>
    Markus Kirschmer




  </b>
<br />Email: <span class="URL"><a href="mailto:markus.kirschmer@math.rwth-aachen.de">markus.kirschmer@math.rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="http://www.math.rwth-aachen.de/~Markus.Kirschmer/">http://www.math.rwth-aachen.de/~Markus.Kirschmer/</a></span>
<br />Address: <br />Markus Kirschmer<br /> Lehrstuhl D fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />
</p><p><b>
    Markus Lange-Hegermann




  </b>
<br />Email: <span class="URL"><a href="mailto:markus.lange-hegermann@hs-owl.de">markus.lange-hegermann@hs-owl.de</a></span>
<br />Homepage: <span class="URL"><a href="https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/">https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/</a></span>
<br />Address: <br />Markus Lange-Hegermann<br /> Hochschule Ostwestfalen-Lippe<br /> Liebigstraße 87<br /> 32657 Lemgo<br /> Germany<br />
</p><p><b>
    Oleksandr Motsak




  </b>
<br />Email: <span class="URL"><a href="mailto:motsak@mathematik.uni-kl.de">motsak@mathematik.uni-kl.de</a></span>
<br />Homepage: <span class="URL"><a href="http://www.mathematik.uni-kl.de/~motsak/">http://www.mathematik.uni-kl.de/~motsak/</a></span>
<br />Address: <br />Department of Mathematics<br /> University of Kaiserslautern<br /> 67653 Kaiserslautern<br /> Germany<br />
</p><p><b>
    Daniel Robertz




  </b>
<br />Email: <span class="URL"><a href="mailto:daniel@momo.math.rwth-aachen.de">daniel@momo.math.rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="http://wwwb.math.rwth-aachen.de/~daniel/">http://wwwb.math.rwth-aachen.de/~daniel/</a></span>
<br />Address: <br />Daniel Robertz<br /> Lehrstuhl B fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />
</p><p><b>
    Hans Schönemann




  </b>
<br />Email: <span class="URL"><a href="mailto:hannes@mathematik.uni-kl.de">hannes@mathematik.uni-kl.de</a></span>
<br />Homepage: <span class="URL"><a href="http://www.mathematik.uni-kl.de/~hannes/">http://www.mathematik.uni-kl.de/~hannes/</a></span>
<br />Address: <br />Department of Mathematics<br /> University of Kaiserslautern<br /> 67653 Kaiserslautern<br /> Germany<br />
</p><p><b>
    Andreas Steenpaß



  </b>
<br />Email: <span class="URL"><a href="mailto:steenpass@mathematik.uni-kl.de">steenpass@mathematik.uni-kl.de</a></span>
<br />Address: <br />Department of Mathematics<br /> University of Kaiserslautern<br /> 67653 Kaiserslautern<br /> Germany<br />
</p><p><b>
    Vinay Wagh




  </b>
<br />Email: <span class="URL"><a href="mailto:waghoba@gmail.com">waghoba@gmail.com</a></span>
<br />Homepage: <span class="URL"><a href="http://www.iitg.ernet.in/vinay.wagh/">http://www.iitg.ernet.in/vinay.wagh/</a></span>
<br />Address: <br />E-102, Department of Mathematics,<br /> Indian Institute of Technology Guwahati,<br /> Guwahati, Assam, India.<br /> PIN: 781 039.<br /> India<br />
</p>

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<h3>Copyright</h3>
<p>© 2007-2015 by Mohamed Barakat, Simon Görtzen, Markus Kirschmer, Markus Lange-Hegermann, Oleksandr Motsak, Max Neunhöffer, Daniel Robertz, and Hans Schönemann. This package may be distributed under the terms and conditions of the GNU Public License Version 2 or (at your option) any later version.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7B818AF0834AE510">1.1 <span class="Heading">Ring Constructions for Supported External Computer Algebra Systems</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X827FA5FD7CBEE73C">1.1-1 <span class="Heading">external <strong class="pkg">GAP</strong></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X840A7A5D7AE407F2">1.1-2 <span class="Heading"><strong class="pkg">Singular</strong></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X839147CF813312D6">1.1-3 <span class="Heading"><strong class="pkg">MAGMA</strong></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X83D66E0279CF39E6">1.1-4 <span class="Heading"><strong class="pkg">Macaulay2</strong></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7A9D29E187AA3F83">1.1-5 <span class="Heading"><strong class="pkg">Sage</strong></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X83E0B3C584764593">1.1-6 <span class="Heading"><strong class="pkg">Maple</strong></span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X7B7472BA86FD3177">2 <span class="Heading">Installation of the <strong class="pkg">RingsForHomalg</strong> Package</span></a>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7BE194BD79C972A3">3 <span class="Heading">The Ring Table</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7B7C37BD80727239">3.1 <span class="Heading">An Example for a Ring Table - Singular</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7CA9554E855D5032">3.1-1 BasisOfRowModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A0EDA3284F0832B">3.1-2 BasisOfRowModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A8574FE7B4DCE59">3.1-3 BasisOfColumnModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X870A963687F2867F">3.1-4 BasisOfColumnModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7834682C822FC188">3.1-5 DecideZeroRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A7ADD857AAD8158">3.1-6 DecideZeroRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8721416787B06D9B">3.1-7 DecideZeroColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X781FC1367F5A2EB7">3.1-8 DecideZeroColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X85D2A3EA86796DD5">3.1-9 SyzygiesGeneratorsOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X78551C36859F7524">3.1-10 SyzygiesGeneratorsOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X834F1AF179AE3F7F">3.1-11 SyzygiesGeneratorsOfColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7BFA32BA80762292">3.1-12 SyzygiesGeneratorsOfColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F4661FD863E3EB4">3.1-13 BasisOfRowsCoeff</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X874402C08793EDAD">3.1-14 BasisOfRowsCoeff</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X796A404D7A059D47">3.1-15 BasisOfColumnsCoeff</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A404EC486BAD561">3.1-16 BasisOfColumnsCoeff</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8009817D78CF032B">3.1-17 DecideZeroRowsEffectively</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X80A26CC279614874">3.1-18 DecideZeroRowsEffectively</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X833A271E83F7B7E6">3.1-19 DecideZeroColumnsEffectively</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F239DE47B7EEA55">3.1-20 DecideZeroColumnsEffectively</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X87131F9182FD3B1C">3.1-21 RelativeSyzygiesGeneratorsOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7BF27670874C5CE1">3.1-22 RelativeSyzygiesGeneratorsOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7FEB3B37852B72D4">3.1-23 RelativeSyzygiesGeneratorsOfColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X78370E58780C91C2">3.1-24 RelativeSyzygiesGeneratorsOfColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E533B0A8392EBC6">3.1-25 ReducedSyzygiesGeneratorsOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A6E97FA7F1FF73D">3.1-26 ReducedSyzygiesGeneratorsOfRows</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7FF049FA85A2C82E">3.1-27 ReducedSyzygiesGeneratorsOfColumns</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7AF938828299812C">3.1-28 ReducedSyzygiesGeneratorsOfColumns</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
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