Gedichte Musik Bilder Quellcodebibliothek Diashow Normaldarstellung
Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/circle/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 25.1.2023 mit Größe 9 kB image not shown  

Quelle  chap0_mj.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/circle/doc/chap0_mj.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>
<script type="text/javascript"
  src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (Circle) - 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_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap0.html">[MathJax off]</a></p>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">

<h1><strong class="pkg">Circle</strong></h1>


<h2>Adjoint groups of finite rings</h2>

<p>Version 1.6.6</p>

<p>25 February 2023</p>

</div>
<p><b>Olexandr Konovalov
          
       
           
  </b>
<br />Email: <span class="URL"><a href="mailto:obk1@st-andrews.ac.uk">obk1@st-andrews.ac.uk</a></span>
<br />Homepage: <span class="URL"><a href="https://alex-konovalov.github.io/">https://alex-konovalov.github.io/</a></span>
<br />Address: <br />School of Computer Science<br /> University of St Andrews<br /> Jack Cole Building, North Haugh,<br /> St Andrews, Fife, KY16 9SX, Scotland
</p><p><b>Panagiotis Soules
          
                  
  </b>
<br />Email: <span class="URL"><a href="mailto:psoules@math.uoa.gr">psoules@math.uoa.gr</a></span>
<br />Address: <br />Department of Mathematics<br /> National and Capodistrian University of Athens<br /> Panepistimioupolis, GR-15784, Athens, Greece
</p>

<p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p>
<h3>Abstract</h3>
<p>The <strong class="pkg">GAP</strong>4 package <strong class="pkg">Circle</strong> extends the <strong class="pkg">GAP</strong> functionality for computations in adjoint groups of associative rings. It provides functionality to construct circle objects that will respect the circle multiplication <span class="SimpleMath">\( r \cdot s = r + s + rs \)</span>, and to compute adjoint semigroups and adjoint groups of finite rings. Also it may serve as an example of extending the <strong class="pkg">GAP</strong> system with new multiplicative objects.</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2006-2023 by Olexandr Konovalov and Panagiotis Soules</p>

<p><strong class="pkg">Circle</strong> is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the FSF's own site https://www.gnu.org/licenses/gpl.html.



<p>If you obtained <strong class="pkg">Circle</strong>, we would be grateful for a short notification sent to one of the authors.</p>

<p>If you publish a result which was partially obtained with the usage of <strong class="pkg">Circle</strong>, please cite it in the following form:</p>

<p>O. Konovalov, P. Soules. <em>Circle --- Adjoint groups of finite rings, Version 1.6.6;</em> 2023 (<span class="URL"><a href="https://gap-packages.github.io/circle/">https://gap-packages.github.io/circle/</a></span>).</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>We acknowledge very much Alexander Hulpke and James Mitchell for their helpful comments and advices, and the referee for testing the package and useful suggestions.</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#X8557083378F2A3B2">1.1 <span class="Heading">General aims</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7DB566D5785B7DBC">1.2 <span class="Heading">Installation and system requirements</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X8404D6997A466953">2 <span class="Heading">Implementing circle objects</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X86492955868108EC">2.1 <span class="Heading">First attempts</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X852C1F3281137DD6">2.2 <span class="Heading">Defining circle objects</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X85B1413E7FBC8ACB">2.3 <span class="Heading">Installing operations for circle objects</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X81CE94FA8343B1D8">3 <span class="Heading"><strong class="pkg">Circle</strong> functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7E25EF1786B5F87C">3.1 <span class="Heading">Circle objects</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F5C18AA7B433BDD">3.1-1 CircleObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X874B2B2A7F5A9A78">3.1-2 UnderlyingRingElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X810FB77F860F888D">3.1-3 IsCircleObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8469C7F67A8864B3">3.1-4 IsPositionalObjectOneSlotRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F88A0017DC2E878">3.1-5 CircleFamily</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X85ECB0B482AB3170">3.2 <span class="Heading">Operations with circle objects</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8129A6877FFD804B">3.2-1 One</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X82EC4F49877D6EB1">3.2-2 InverseOp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X85CBFBAE78DE72E8">3.2-3 IsUnit</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7CE7866F7CD00709">3.2-4 IsCircleUnit</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X86F80DD8823966F7">3.3 <span class="Heading">Construction of the adjoint semigroup and adjoint group</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X83993FD0848D0C80">3.3-1 AdjointSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X868FAC7E87D11137">3.3-2 AdjointGroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X80DFB24F8289C323">3.4 <span class="Heading">Service functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A24C0997AC7C6A3">3.4-1 InfoCircle</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X803553D8849F6D7A">4 <span class="Heading">A sample computation with <strong class="pkg">Circle</strong></span></a>
</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>
<br />
</div>

<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

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

100%


¤ Dauer der Verarbeitung: 0.21 Sekunden  (vorverarbeitet)  ¤

*© 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 ist noch experimentell.