Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/fr/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 11.0.2024 mit Größe 53 kB image not shown  

Quelle  chap0.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/fr/doc/chap0.html


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

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<title>GAP (FR) - Contents</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap0"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap1.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap0_mj.html">[MathJax on]</a></p>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">

<h1>Functionally recursive groups</h1>


<h2>Self-similar groups</h2>

<p>Version 2.4.13</p>

<p>11/01/2024</p>

</div>
<p>
    Groups generated by automata or satisfying functional recursions
  </p>
<p><b>Laurent Bartholdi
   
   
  </b>
<br />Email: <span class="URL"><a href="mailto:laurent dot bartholdi at gmail dot com ">laurent dot bartholdi at gmail dot com </a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.uni-sb.de/ag/bartholdi/">https://www.math.uni-sb.de/ag/bartholdi/</a></span>
</p>

<p><b>Address:</b><br />
Mathematisches Institut<br /> Bunsenstraße 3-5<br /> D-37073 Göttingen<br /> Germany</p>
<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p>This document describes the package <strong class="pkg">FR</strong>, which implements in <strong class="pkg">GAP</strong> the basic objects of Mealy machines and functional recursions; and handles groups that they generate.</p>

<p>The computer algebra system <strong class="pkg">GAP</strong> is available at <span class="URL"><a href="https://www.gap-system.org">https://www.gap-system.org</a></span>.</p>

<p>This documentation for <strong class="pkg">FR</strong> is available at <span class="URL"><a href="https://docs.gap-system.org/pkg/fr/doc/manual.pdf">https://docs.gap-system.org/pkg/fr/doc/manual.pdf</a></span> in PDF format, and may be accessed online at <span class="URL"><a href="https://gap-packages.github.io/fr/">https://gap-packages.github.io/fr/</a></span>.</p>

<p>The latest release of the package may be downloaded as <span class="URL"><a href="https://github.com/gap-packages/fr/archive/2.4.13.tar.gz">https://github.com/gap-packages/fr/archive/2.4.13.tar.gz</a></span> (tar, gzipped). The latest repository version (possibly unstable) may be downloaded as <span class="URL"><a href="https://github.com/gap-packages/fr/tarball/master">https://github.com/gap-packages/fr/tarball/master</a></span> (tar, gzipped), <span class="URL"><a href="https://github.com/gap-packages/fr.git">https://github.com/gap-packages/fr.git</a></span> (git repository), or explored at <span class="URL"><a href="https://github.com/gap-packages/fr/tree/master/">https://github.com/gap-packages/fr/tree/master/</a></span>.</p>

<p>Groups defined by a recursive action on a rooted tree can be defined in <strong class="pkg">GAP</strong> via their recursion. Various algorithms are implemented to manipulate these groups and their elements.</p>

<p>For comments or questions on <strong class="pkg">FR</strong> please contact the author; this package is still under development.</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2006-2012 by Laurent Bartholdi</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>Part of this work is/was supported by the "Swiss National Fund for Scientific Research" and the "German Science Foundation".</p>

<p><a id="X7982162280BC7A61" name="X7982162280BC7A61"></a></p>
<h3>Colophon</h3>
<p>This project started in the mid-1990s, when, as a PhD student I did many calculations with groups generated by automata, and realized the similarities between all calculations; it quickly became clear that these calculations could be done much better by a computer than by a human.</p>

<p>The first routines I wrote constructed finite representations of the groups considered, so as to get insight from fast calculations within <strong class="pkg">GAP</strong>. The results then had to be proved correct within the infinite group under consideration, and this often involved guessing appropriate words in the infinite group with a given image in the finite quotient.</p>

<p>Around 2000, I had developed quite a few routines, which I assembled in a <strong class="pkg">GAP</strong> package, that dealt directly with infinite groups. This package was primitive at its core, but was extended with various routines as they became useful.</p>

<p>I decided in late 2005 to start a new package from scratch, that would encorporate as much functionality as possible in a uniform manner; that would handle semigroups as well as groups; that could be easily extended; and with a complete, understandable documentation. I hope I am not too far from these objectives.</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.html#X86DB23CC834ABD71">1 <span class="Heading">Licensing</span></a>
</div>
<div class="ContChap"><a href="chap2.html#X7ADCE68284FB4ACF">2 <span class="Heading">FR package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X80C332C686212786">2.1 <span class="Heading">A brief mathematical introduction</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X78DF4DE18260BD80">2.2 <span class="Heading">An example session</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap3.html#X7D65CA8B876E514C">3 <span class="Heading">Functionally recursive machines</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7D52F7ED83E2D153">3.1 <span class="Heading">Types of machines</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7EB36FBB78F4F26A">3.2 <span class="Heading">Products of machines</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X828640667D2E5280">3.3 <span class="Heading">Creators for <code class="code">FRMachine</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X80D310EF7FD5EA44">3.3-1 FRMachineNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X808F3BD97EDA8CE8">3.3-2 FRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C383F4383D22BFC">3.3-3 UnderlyingFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7BF186227C0ABE8D">3.3-4 AsGroupFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X78130FC97C58AFC4">3.3-5 AsGroupFRMachine</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8753FA157B2AD6DC">3.4 <span class="Heading">Attributes for <code class="code">FRMachine</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8000470D7DA7FFBD">3.4-1 StateSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7F77F5DD789FA2F4">3.4-2 GeneratorsOfFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7DBC41D4808979BC">3.4-3 Output</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7AEE87BC8393FA54">3.4-4 Transition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X82B3A8AB80B5E181">3.4-5 Transitions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D95D1498586E5D0">3.4-6 WreathRecursion</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X8158A8307CA98A3D">3.5 <span class="Heading">Operations for <code class="code">FRMachine</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8289C2F77D67EDC3">3.5-1 StructuralGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7F2703417F270341"><code>3.5-2 \+</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7857704878577048"><code>3.5-3 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C0677148107F7FE">3.5-4 TensorSumOp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8077C8A47E22FCB5">3.5-5 TensorProductOp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D248C737D29A7CC">3.5-6 DirectSumOp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81456F10820CAC87">3.5-7 DirectProductOp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A0858097AA3FBDA">3.5-8 TreeWreathProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X811B5BF17A3FE577">3.5-9 SubFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X814F53B97C3F43F5">3.5-10 ChangeFRMachineBasis</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81B382BD81B2BD34">3.5-11 Minimized</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C107A42815F91DA">3.5-12 Correspondence</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X863D82207A1320F1">4 <span class="Heading">Functionally recursive elements</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X79DE08CD7EE57360">4.1 <span class="Heading">Creators for <code class="code">FRElement</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7839813183881054">4.1-1 FRElementNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7CF5EDEB874BF9E3">4.1-2 FRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X86181654827919EE">4.1-3 FRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X80D518E2804ABF70">4.1-4 ComposeElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7CE388057DAB4802">4.1-5 VertexElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X848EB430831097E6">4.1-6 DiagonalElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7EB5DE3978840CDF">4.1-7 AsGroupFRElement</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X812C932C7E2F2885">4.2 <span class="Heading">Operations and Attributes for <code class="code">FRElement</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X78F819CF7DDBF310">4.2-1 Output</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8732D01C82999F32">4.2-2 Activity</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7CE58B2D837B2845">4.2-3 Transition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7D4248467B1B097A">4.2-4 Transitions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X84A193C67CDBDA35">4.2-5 Portrait</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X850EB66E7804BA3B">4.2-6 DecompositionOfFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X85441F1683E9D820">4.2-7 StateSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X819E3E3080297347">4.2-8 State</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7B0C97BC7C3BA20D">4.2-9 States</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X804B2E0F7E37F5B8">4.2-10 FixedStates</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X8303B36C83371FB3">4.2-11 LimitStates</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7C4076707CBBE945">4.2-12 IsFiniteStateFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X829A87E087F15194">4.2-13 NucleusOfFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X79E65E818690B4EB">4.2-14 InitialState</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X823B6E3D819432D6"><code>4.2-15 \^</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7C3CF6AF86336EDC"><code>4.2-16 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X78C19ACA78F9F067"><code>4.2-17 <span>\</span>[<span>\</span>]</code></a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5.html#X7C77EBC17DEF4CF6">5 <span class="Heading">Mealy machines and elements</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X846B89F686B50AE1">5.1 <span class="Heading">Creators for <code class="code">MealyMachine</code>s and <code class="code">MealyElement</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7EF3E00080624B70">5.1-1 MealyMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X875B8FED7FD20FA1">5.1-2 MealyMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8578657C7F4B6254">5.1-3 MealyMachineNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83BBE01884D6E315">5.1-4 AllMealyMachines</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7F673D877B205708">5.2 <span class="Heading">Operations and Attributes for <code class="code">MealyMachine</code>s and <code class="code">MealyElement</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7DF9F3AD86602DFC">5.2-1 Draw</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8395542D846FA2B9">5.2-2 Minimized</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X809F069B798ED985">5.2-3 DualMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7D5D480C782FCC0B">5.2-4 IsReversible</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8310A1C08158793C">5.2-5 IsMinimized</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7CCB79B981912CCC">5.2-6 AlphabetInvolution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X80D2545D7D0990A2">5.2-7 IsBireversible</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83364DAB825D7A0D">5.2-8 StateGrowth</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X84BE780A81CAC69C">5.2-9 Degree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X793C427084F830CE">5.2-10 IsFinitaryFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7E5E8B2C79688DC0">5.2-11 Depth</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X82F4410E85C54C7E">5.2-12 IsBoundedFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X81D4A3F27C5FAD96">5.2-13 IsPolynomialGrowthFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7ECE17387910C023">5.2-14 Signatures</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83DFDC3384EA4634">5.2-15 VertexTransformationsFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7E0CB3767CE08692">5.2-16 FixedRay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7A519D4C86CC4786">5.2-17 IsLevelTransitiveFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X79EFE2C97D2CCEEC">5.2-18 AsMealyMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X80F9A18483F98442">5.2-19 AsMealyMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7FB3F0A2878DD2CF">5.2-20 AsMealyElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7FBBBD9A839011C8">5.2-21 AsIntMealyMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8191456B7E586785">5.2-22 TopElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7A87ED9D789245E4">5.2-23 ConfinalityClasses</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X81592E3D79745A40">5.2-24 Germs</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7F76AF2D7C0279F9">5.2-25 HasOpenSetConditionFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X795017598575FCA3">5.2-26 LimitFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7F8163B5816969C8">5.2-27 NucleusMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7B29565784A591EC">5.2-28 GuessMealyElement</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X84AD415C872BFB91">6 <span class="Heading">Linear machines and elements</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X812C0F7B7A31FCEF">6.1 <span class="Heading">Methods and operations for <code class="code">LinearFRMachine</code>s and <code class="code">LinearFRElement</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7F1EB8CB87229764">6.1-1 VectorMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X825CA46481197C7A">6.1-2 AssociativeObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7F65118683209DC5">6.1-3 AlgebraMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7A19036B828BBA0C">6.1-4 Transition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X846683198081BA82">6.1-5 Transitions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X80F694298399E78D">6.1-6 NestedMatrixState</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7FCEE3BF86B02CC6">6.1-7 ActivitySparse</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8436BEA67F1C3C27">6.1-8 Activities</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7EF5B7417AE6B3F8">6.1-9 IsConvergent</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8136C21885019A4A">6.1-10 TransposedFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X796B736286CACF85">6.1-11 LDUDecompositionFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X783E8F427A23EAD1">6.1-12 GuessVectorElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X865EE2E887ECC079">6.1-13 AsLinearMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X82586DFB8458EF05">6.1-14 AsVectorMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7818245A7DABB311">6.1-15 AsAlgebraMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7BDD40B27F7541B2">6.1-16 AsVectorMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8120605981DDE434">6.1-17 AsAlgebraMachine</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7.html#X86C0E6F083DCCDC8">7 <span class="Heading">Self-similar groups, monoids and semigroups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X80A26BAA7B53C1BD">7.1 <span class="Heading">Creators for FR semigroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AE8F92383272329">7.1-1 FRGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D4A6996874A3DF3">7.1-2 NewSemigroupFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X853E3F0680C76F56">7.1-3 SCGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7F15D57A7959FEF6">7.1-4 Correspondence</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D0B8334786E2802">7.1-5 FullSCGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7DB92C34827D513F">7.1-6 FRMachineFRGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BF4AC9F830A8E1A">7.1-7 IsomorphismFRGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7DE1CAE981F2825B">7.1-8 IsomorphismMealyGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BB8DDEA83946C73">7.1-9 FRGroupByVirtualEndomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79D75A7D80DD9AD1">7.1-10 TreeWreathProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X85840A047C04BFC6">7.1-11 WeaklyBranchedEmbedding</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X84E20571841DE1E4">7.2 <span class="Heading">Operations for FR semigroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C6D7BA0818A3A3D">7.2-1 PermGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8620BEAF7957FA4D">7.2-2 PcGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X83834FF77F972912">7.2-3 TransformationMonoid</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8768C22D859BE75F">7.2-4 TransformationSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7BDC634086437315">7.2-5 EpimorphismGermGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X812242E584462766">7.2-6 GermData</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87378D53791D0B70">7.2-7 StabilizerImage</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B4CD9CA872BA368">7.2-8 LevelStabilizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C5002E683A044C1">7.2-9 IsStateClosed</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79246DB482BEAF2D">7.2-10 StateClosure</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E2F34417EBB7673">7.2-11 IsRecurrentFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X825688FD7CE96479">7.2-12 IsLevelTransitiveFRGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D95219481AEDD20">7.2-13 IsInfinitelyTransitive</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A6CB30181662C77">7.2-14 IsFinitaryFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X791BCD9D782C6237">7.2-15 Degree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FA67E4387C91BD8">7.2-16 HasOpenSetConditionFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7D870F9E82ACB54C">7.2-17 HasCongruenceProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7EAB4B5B843C0EC5">7.2-18 IsContracting</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7CA062A67C1554BB">7.2-19 NucleusOfFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8443D711796F06E4">7.2-20 NucleusMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X824A9E177F5A9753">7.2-21 AdjacencyBasesWithOne</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A874A107D4944E1">7.2-22 BranchingSubgroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78ADACCD8586D3C7">7.2-23 FindBranchingSubgroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X832D98E47ACA099C">7.2-24 IsBranched</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7A905CE87B49213F">7.2-25 IsBranchingSubgroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8404ECA782F2521A">7.2-26 BranchStructure</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8749E0797A99F531">7.2-27 TopVertexTransformations</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C56C90086070A2E">7.2-28 VertexTransformations</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7DF2D9838625CDED">7.2-29 VirtualEndomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C81CB1C7F0D7A90">7.2-30 EpimorphismFromFpGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X8740656382656D63">7.2-31 IsomorphismSubgroupFpGroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7E8485A081EBB3AA">7.3 <span class="Heading">Properties for infinite groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X840ED7D279ECAB7F">7.3-1 IsTorsionGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7914F2D68077F503">7.3-2 IsTorsionFreeGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X87E93FFC820ED40E">7.3-3 IsAmenableGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X873C0A7C8422C0C9">7.3-4 IsVirtuallySimpleGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79A3A0CF82B6F089">7.3-5 IsResiduallyFinite</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X86E1182E7EEFAADB">7.3-6 IsSQUniversal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FDAEAFF78A5E7D2">7.3-7 IsJustInfinite</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap8.html#X7DDBF6F47A2E021C">8 <span class="Heading">Algebras</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X842EE9427C63F92E">8.1 <span class="Heading">Creators for FR algebras</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X812FEA6778152E49">8.1-1 FRAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X844B890F7BF56236">8.1-2 SCAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7B8330F180BABC43">8.1-3 NucleusOfFRAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X81D8D0E886C8E143">8.1-4 BranchingIdeal</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X7EFB4F2E7E908B9F">8.2 <span class="Heading">Operations for FR algebras</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8115B018871FD364">8.2-1 MatrixQuotient</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8150FC4E84D208C6">8.2-2 ThinnedAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8572DCAE7F888DDA">8.2-3 Nillity</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X85163F29824C944D">8.2-4 DegreeOfHomogeneousElement</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap9.html#X7A489A5D79DA9E5C">9 <span class="Heading">Examples</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7AF5DEF08531AFA5">9.1 <span class="Heading">Examples of groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7D774B847D81E6DE">9.1-1 FullBinaryGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X813F53C57F41F5F5">9.1-2 BinaryKneadingGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7B8D49D079D336E8">9.1-3 BasilicaGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X8449487686E00D22">9.1-4 FornaessSibonyGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X85F4FDF787173863">9.1-5 AddingGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7A4BB24A805CDF63">9.1-6 BinaryAddingGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X78AFA63B86C94227">9.1-7 MixerGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X84C97E0687F119C0">9.1-8 SunicGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X79E3F3BE80F34590">9.1-9 GrigorchukMachines</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X85BAE48780E665A4">9.1-10 GrigorchukMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X800640597E9C707D">9.1-11 GrigorchukOverGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7E765AF77AAC21A6">9.1-12 GrigorchukTwistedTwin</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7F93EC437B5AE276">9.1-13 BrunnerSidkiVieiraGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7F8A028B799946D3">9.1-14 AleshinGroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7C286D3A84790ECE">9.1-15 AleshinGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7E024B4D7BA411B1">9.1-16 BabyAleshinGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X8108E3A8872A6FFE">9.1-17 SidkiFreeGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X82D3CB6A7C189C78">9.1-18 GuptaSidkiGroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X83E59288860EF661">9.1-19 GuptaSidkiGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X8521B4FF7BA189B2">9.1-20 NeumannGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X878D1C7080EA9797">9.1-21 FabrykowskiGuptaGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7C5ADAE77EA3876D">9.1-22 ZugadiSpinalGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7A0319827CB51ED0">9.1-23 GammaPQMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X80B617717C2887D4">9.1-24 RattaggiGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7A0BE9F57B401C5C">9.1-25 HanoiGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7C7A0EEF7EFF8B99">9.1-26 DahmaniGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7C958AB78484E256">9.1-27 MamaghaniGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X86D952E8784E4D97">9.1-28 WeierstrassGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X80D59AFF7E7D3B8B">9.1-29 StrichartzGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X86B124758135DFBD">9.1-30 FRAffineGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7CFBE31A78F2681B">9.1-31 CayleyGroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X81B82FA1811AAF8D">9.2 <span class="Heading">Examples of semigroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X87541DA582705033">9.2-1 I2Machine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7B32ED3D8715FA4B">9.2-2 I4Machine</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X803B02408573A30E">9.3 <span class="Heading">Examples of algebras</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X80E15ABC879F8EE2">9.3-1 PSZAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7D015CA5829FAA2A">9.3-2 GrigorchukThinnedAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7B66ED537D0A43AF">9.3-3 GuptaSidkiThinnedAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X86CE9A8787F69DBC">9.3-4 GrigorchukLieAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7B0B5B09878C7CEA">9.3-5 SidkiFreeAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7988B29F836BAA62">9.3-6 SidkiMonomialAlgebra</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7989134C83AF38AE">9.4 <span class="Heading">Bacher's determinant identities
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7C4A51947E1609A8">9.5 <span class="Heading">VH groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7E0071D4838B239D">9.5-1 VHStructure</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7F852A357D7E2E76">9.5-2 VerticalAction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X86B1C2F079FE8D82">9.5-3 VHGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7D1FCB877D1B96EA">9.5-4 IsIrreducibleVHGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X84DB7FA4846075A7">9.5-5 MaximalSimpleSubgroup</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap10.html#X86D6616E868AF75C">10 <span class="Heading">FR implementation details</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X79719CD17A948933">10.1 <span class="Heading">The family of FR objects</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7F5497A47F8C81DD">10.1-1 FRMFamily</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7C6A63427F6DB4C6">10.1-2 FREFamily</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7BC9CD3685C26823">10.1-3 AlphabetOfFRObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X793E0E1283BE7C73">10.1-4 AsPermutation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7B41902D87A48EDB">10.1-5 AsTransformation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X856A3AD87C93FC1F">10.2 <span class="Heading">Filters for <code class="code">FRObject</code>s</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7CC0BFD67CE7060E">10.2-1 IsGroupFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8157AE587CBA24C4">10.2-2 IsFRMachineStrRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X79C2395A7D65214B">10.2-3 IsMealyMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7C86614187606A4C">10.2-4 IsMealyElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X78E206B28015A395">10.2-5 IsMealyMachineIntRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7AE5B4257E2DB7E6">10.2-6 IsMealyMachineDomainRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8087EE9F79E8E339">10.2-7 IsVectorFRMachineRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7859869E7FEDA49F">10.2-8 IsAlgebraFRMachineRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X877B1EBD80170001">10.2-9 IsLinearFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X823F46A67D458AAD">10.2-10 IsLinearFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7966F9B982B1DFE1">10.2-11 IsFRElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X847A4BBE82C736B6">10.2-12 IsFRMealyElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X785D09F27DBDF6A8">10.2-13 IsFRObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7C22A1A28058F754">10.2-14 IsFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X83AEFB8184F4B023">10.2-15 IsInvertible</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X81D717E187305F2A">10.2-16 IsFRGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X853B16B381CB5366">10.2-17 IsFRAlgebra</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X7E97015E8153F782">10.3 <span class="Heading">Some of the algorithms implemented</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X84278D6F7AAD101F">10.3-1 FRMachineRWS</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X84B4FF607DA18152">10.3-2 <span class="Heading">Order of FR elements</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X847B4AFF809D2A56">10.3-3 <span class="Heading">Membership in semigroups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7F24533B7F846FC4">10.3-4 <span class="Heading">The conjugacy problem</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8735D8087DADCCC9">10.3-5 OrbitSignalizer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X817F734280E22447">10.3-6 FRConjugacyAlgorithm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X82A289077D4DAA03">10.3-7 FRBranchGroupConjugacyData</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7A0AC96784ACE0BE">10.3-8 <span class="Heading">Order of groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8329884F790E1542">10.3-9 <span class="Heading">Images and preimages of some groups in
  f.p. and l.p. groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7F4247367D1EBEB9">10.3-10 <span class="Heading">Comparison of FR, Mealy, vector,
  and algebra elements</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X81F95FEB7C72ABFF">10.3-11 <span class="Heading">Inverses of linear elements</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap11.html#X785C6C0B80936CC8">11 <span class="Heading">Miscellanea</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X783AA02C7BEF48A9">11.1 <span class="Heading">Generic operations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X844D3035877B5052">11.1-1 TensorSum</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X87EB0B4A852CF4C6">11.1-2 TensorProduct</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X82AD6F187B550060">11.1-3 DirectSum</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X816865747DD51C11">11.2 <span class="Heading">Periodic lists</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7E5CC87E871F35A3">11.2-1 PeriodicListsFamily</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7B401DFE817D3927">11.2-2 PeriodicList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7AFE88F37FC58083">11.2-3 CompressPeriodicList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7CA5FA3F7AF9BA3D">11.2-4 IsConfinal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X86AB4AFF7B1613E3">11.2-5 ConfinalityClass</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X84FB28807BC8A502">11.2-6 LargestCommonPrefix</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X7A336C66855E632D">11.3 <span class="Heading">Word growth</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7BFF1432803C9172">11.3-1 WordGrowth</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X791D4D398201C17D">11.4 <span class="Heading">Finding short relations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X868E478F86A10CFF">11.4-1 ShortGroupRelations</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7B9942AA84B0753E">11.4-2 ShortGroupWordInSet</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X82712E6C815DB9B2">11.5 <span class="Heading">Braid groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X84472A637B648C47">11.5-1 SurfaceBraidFpGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X87E12292861FFE79">11.5-2 CharneyBraidFpGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X814375977D2E4AD9">11.5-3 ArtinRepresentation</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X839ED1F982DB3469">11.6 <span class="Heading">Dirichlet series</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X82D4E885838CFBD6">11.6-1 DirichletSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7C8CD28D797A527F">11.6-2 DegreeDirichletSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X81EA791C7CA3C3FF">11.6-3 SpreadDirichletSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7D792C6985BF482B">11.6-4 ShiftDirichletSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X80571E4A86B38D53">11.6-5 ShrunkDirichletSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X850F072E8523EE9D">11.6-6 ZetaSeriesOfGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7F49DDBC829F18C8">11.6-7 ValueOfDirichletSeries</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X86256BD187D9A7FF">11.7 <span class="Heading">Projective representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7CE116C27EF109D1">11.7-1 IsProjectiveRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X80EEB0F58467ED68">11.7-2 ProjectiveRepresentationByFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7FC5A28278EB1E51">11.7-3 LinearRepresentationByImages</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X87BC132B815B4638">11.7-4 DegreeOfProjectiveRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X81AF3D937F219A6D">11.7-5 ProjectiveExtension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7C4E2ED57C2DDBE6">11.7-6 ProjectiveQuotient</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X785C6C0B80936CC8">11.8 <span class="Heading">Miscellanea</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7B5DD261825523A3">11.8-1 ForwardOrbit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7E4966327C37C790">11.8-2 StringByInt</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7CE65002842C0BD8">11.8-3 PositionInTower</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X856E72B180084639">11.8-4 RenameSubobjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X79016B3878B5EFAA">11.8-5 CoefficientsInAbelianExtension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X8624AFAD872509D8">11.8-6 MagmaEndomorphismByImagesNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7F7E6457877F69EC">11.8-7 MagmaHomomorphismByImagesNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7A2A9D24781AFC34">11.8-8 Draw</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X816A18137E5116E9">11.8-9 IsFIFO</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X86AC1C028093204D">11.8-10 ProductIdeal</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X794940277C9AD85C">11.8-11 DimensionSeries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X825149467C57DEFC">11.8-12 AlgebraHomomorphismByFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X837F6C2A797FFD41">11.8-13 IsFpLieAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X8692ADD581359CA1">11.8-14 JenningsLieAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7F5427847E43CD62">11.8-15 SolutionMatModN</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X80E9634283E2DF18">11.8-16 SolutionMatMod1</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7D2CEF7F845D2AF2">11.8-17 CyclotomicByArgument</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7A6CB5FE86501506">11.8-18 ArgumentOfCyclotomic</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X7ADFF37084706CEC">11.9 <span class="Heading">User settings</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X7E95AC267805E4C1">11.9-1 InfoFR</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11.html#X835FBD72853595BE">11.9-2 SEARCH@</a></span>
</div></div>
</div>
<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>
<br />
</div>

<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap1.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>

Messung V0.5
C=100 H=100 G=100

¤ Dauer der Verarbeitung: 0.16 Sekunden  ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.