<?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 (IdRel) - 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" /> </head> <body> <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="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <div class="chlinkprevnexttop"> <a href="chap0.html">Top of Book</a> <a href="chap1.html">Next Chapter</a> </div> <p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p> <div class="pcenter"> <h1><strong class="pkg">IdRel</strong></h1> <h2>A package for Identities among Relators</h2> <p>Version 2.05</p> <p>November 2008</p> </div> <p><b> Anne Heyworth </b> <br />Email: <span class="URL"><a href="mailto:anne.heyworth@googlemail.com">anne.heyworth@googlemail.com</a></span> </p><p><b> Chris Wensley </b> <br />Email: <span class="URL"><a href="mailto:c.d.wensley@bangor.ac.uk">c.d.wensley@bangor.ac.uk</a></span> <br />Homepage: <span class="URL"><a href="http://www.bangor.ac.uk/~mas023/">http://www.bangor.ac.uk/~mas023/</a></span> <br />Address: <br />School of Computer Science, Bangor University,<br /> Dean Street, Bangor, Gwynedd, LL57 1UT, U.K. </p> <p><a id="X7AA6C5737B711C89" name="X7AA6C5737B711C89"></a></p> <h3>Abstract</h3> <p>The <strong class="pkg">IdRel</strong> package was originally implemented in 1999, using the <strong class="pkg">GAP</strong> 3 language, when the first author was studying for a Ph.D. in Bangor.</p> <p>This package is designed to compute a minimal set of generators for the module of the identities among relators of a group presentation. It does this using</p> <ul> <li><p>rewriting and logged rewriting: a self-contained implementation of the Knuth-Bendix process using the monoid presentation associated to the group presentation;</p> </li> <li><p>monoid polynomials: an implementation of the monoid ring;</p> </li> <li><p>module polynomials: an implementation of the right module over this monoid generated by the relators.</p> </li> <li><p>Y-sequences: used as a <em>rewriting</em> way of representing elements of a free crossed module (products of conjugates of group relators and inverse relators).</p> </li> </ul> <p>Bug reports, suggestions and comments are, of course, welcome. Please contact the second author at <span class="URL"><a href="mailto:c.d.wensley@bangor.ac.uk">c.d.wensley@bangor.ac.uk</a></span>.</p> <p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p> <h3>Copyright</h3> <p>© 2005-2008 Anne Heyworth and Chris Wensley</p> <p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p> <h3>Acknowledgements</h3> <p>This <strong class="pkg">idrel</strong> package is released under the GNU General Public License (GPL). This file is part of <strong class="pkg">idrel</strong>, though as documentation it is released under the GNU Free Documentation License (see <span class="URL"><a href="http://www.gnu.org/licenses/licenses.html#FDL">http://www.gnu.org/licenses/licenses.html#FDL</a></span>).</p> <p><strong class="pkg">idrel</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.</p> <p><strong class="pkg">idrel</strong> is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.</p> <p>You should have received a copy of the GNU General Public License along with <strong class="pkg">idrel</strong>; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.</p> <p>For more details, see <span class="URL"><a href="http://www.fsf.org/licenses/gpl.html">http://www.fsf.org/licenses/gpl.html</a></span>.</p> <p>This documentation was prepared with the <strong class="pkg">GAPDoc</strong> package of Frank L\"ubeck and Max Neunh\"offer.</p> <p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p> <div class="contents"> <h3>Contents</h3> <div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a> </div> <div class="ContChap"><a href="chap2.html#X7CA8FCFD81AA1890">2 <span class="Heading">Rewriting Systems</span></a> <div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X7C9AE9BC78CCBFAA">2.1 <span class="Heading">Identity Y-sequences</span></a> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X7875619E84157FC1">2.2 <span class="Heading">Monoid Presentations of FpGroups</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X868422B878B0C380">2.2-1 FreeRelatorGroup</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7CBE13927DFF4446">2.2-2 MonoidPresentationFpGroup</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X7A1F10597D8FC9A9">2.3 <span class="Heading">Rewriting systems for FpGroups</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X858ECE3E807C7363">2.3-1 RewritingSystemFpGroup</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X83BD6C0A80D88C2C">2.3-2 OnePassReduceWord</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7F0CD1EB7C220D40">2.3-3 OnePassKB</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X83CBF2BE8478A728">2.4 <span class="Heading">Enumerating elements</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7EDA50068207339D">2.4-1 ElementsOfMonoidPresentation</a></span> </div> </div> <div class="ContChap"><a href="chap3.html#X7B8D727485966AF8">3 <span class="Heading">Logged Rewriting Systems</span></a> <div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X797732E87F1FE197">3.1 <span class="Heading">Logged Knuth-Bendix Completion</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X80075D5180A8F1A5">3.1-1 LoggedOnePassKB</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X87D1E3A578AAAFCB">3.1-2 LoggedKnuthBendix</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X831A93087918AA5D">3.2 <span class="Heading">Logged reduction of a word</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7C5094AF784A8BA7">3.2-1 LoggedReduceWordKB</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8652CEEF7802DA46">3.2-2 LoggedRewritingSystemFpGroup</a></span> </div> </div> <div class="ContChap"><a href="chap4.html#X83B25026816C87CE">4 <span class="Heading">Monoid Polynomials</span></a> <div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X7E8CE44085FE959D">4.1 <span class="Heading">Construction of monoid polynomials</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7DE231F282DB8660">4.1-1 MonoidPolyFromCoeffsWords</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X84B1F4CC79983A94">4.2 <span class="Heading">Components of a polynomial</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X832D20E8813FBE5D">4.2-1 Terms</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X85C78946877C1FF5">4.2-2 Monic</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X82E04F1086DAAA43">4.2-3 AddTermMonoidPoly</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X832341AB7A04BA45">4.3 <span class="Heading">Monoid Polynomial Operations</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X780769238600AFD1">4.3-1 Length</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap4.html#X7A80EA5C7AEA68B1">4.4 <span class="Heading">Reduction of a Monoid Polynomial</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7979DE308676398D">4.4-1 ReduceMonoidPoly</a></span> </div> </div> <div class="ContChap"><a href="chap5.html#X7B5CEEDF82747121">5 <span class="Heading">Module Polynomials</span></a> <div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X86625AB980F24AA5">5.1 <span class="Heading">Construction of module polynomials</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7BEE34B27861ACE5">5.1-1 ModulePoly</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X83ECC2D5781DE850">5.2 <span class="Heading">Components of a module polynomial</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X832D20E8813FBE5D">5.2-1 Terms</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X7E57DFF4791C4CAA">5.3 <span class="Heading">Module Polynomial Operations</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X811C7964873E4062">5.3-1 AddTermModulePoly</a></span> </div> <div class="ContSect"><span class="nocss"> </span><a href="chap5.html#X78038BF07E998E21">5.4 <span class="Heading">Identities among relators</span></a> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X78A94CB77B98ACAA">5.4-1 IdentityYSequences</a></span> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7BEE0DBB78F9355E">5.4-2 RootIdentities</a></span> </div> </div> <br /> </div> <div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</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="chapBib.html">Bib</a> <a href="chapInd.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>