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<h1>Polenta</h1>


<h2>Polycyclic presentations for matrix groups</h2>

<p>
    1.3.11</p>

<p>
    10 April 2025
  </p>

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<p><b>
    Björn Assmann

  </b>
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<h3>Copyright</h3>
<p>© 2003-2007 by Björn Assmann</p>

<p>The <strong class="pkg">Polenta</strong> package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>

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<h3>Acknowledgements</h3>
<p>We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by <strong class="pkg">GAP</strong> users and developers.</p>

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

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X79DE59997FDCF767">1.1 <span class="Heading">The package</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X86007B0083F60470">1.2 <span class="Heading">Polycyclic groups</span></a>
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<div class="ContChap"><a href="chap2.html#X829BA50B82FEC109">2 <span class="Heading">Methods for matrix groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X826C51B3825A2789">2.1 <span class="Heading">Polycyclic presentations of matrix groups</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7A1BC4437FD92201">2.1-1 PcpGroupByMatGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8771540F7A235763">2.1-2 IsomorphismPcpGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X85ADB89B7C8DD7D0">2.1-3 ImagesRepresentative</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X809C78D5877D31DF">2.1-4 IsSolvableGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7EE01C207C214C1F">2.1-5 IsTriangularizableMatGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7D7456077D3D1B86">2.1-6 IsPolycyclicGroup</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X80D1E9E07DB87F97">2.2 <span class="Heading">Module series</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X84472FDC863322BD">2.2-1 RadicalSeriesSolvableMatGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8524F992828B6A71">2.2-2 HomogeneousSeriesAbelianMatGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X87D9F67C7CBB1499">2.2-3 HomogeneousSeriesTriangularizableMatGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X86FB6E9B801A37D4">2.2-4 CompositionSeriesAbelianMatGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X78DE110C7E2A493C">2.2-5 CompositionSeriesTriangularizableMatGroup</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7BA181CA81D785BB">2.3 <span class="Heading">Subgroups</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X79273B8581D15356">2.3-1 SubgroupsUnipotentByAbelianByFinite</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7A489A5D79DA9E5C">2.4 <span class="Heading">Examples</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7C7C3EFA7E49F932">2.4-1 PolExamples</a></span>
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<div class="ContChap"><a href="chap3.html#X81CAD2F27B2066C4">3 <span class="Heading">An example application</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7DAC33E37B977087">3.1 <span class="Heading">Presentation for rational matrix groups</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X79CF643081B3FB26">3.2 <span class="Heading">Modules series</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7BA34CD28059D6CD">3.3 <span class="Heading">Triangularizable subgroups</span></a>
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<div class="ContChap"><a href="chap4.html#X8360C04082558A12">4 <span class="Heading">Installation</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X81746D7285808409">4.1 <span class="Heading">Installing this package</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X802ED64A87AA11DC">4.2 <span class="Heading">Loading the <strong class="pkg">Polenta</strong> package</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X796DF52483B61C74">4.3 <span class="Heading">Running the test suite</span></a>
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<div class="ContChap"><a href="chap5.html#X85677704855596EB">5 <span class="Heading">Information Messages</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7EBFC26F83EB9F72">5.1 <span class="Heading">Info Class</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X809F2CFB87393CE0">5.1-1 InfoPolenta</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X85861B017AEEC50B">5.2 <span class="Heading">Example</span></a>
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<div class="ContChap"><a href="chapBib.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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