<?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" "https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >title >GAP (walrus) - 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="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 >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >walrus</h1 >div >br />Email: <span class="URL" ><a href="mailto:markus.pfeiffer@st-andrews.ac.uk" >markus.pfeiffer@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="http://www.morphism.de/~markusp/ " >http://www.morphism.de/~markusp/</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<br /> United Kingdom<br />"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X8389AD927B74BA4A" >1 <span class="Heading" >Overview</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X7A489A5D79DA9E5C" >1.1 <span class="Heading" >Examples</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DE9B0FF7EEC5D80" >1.1-1 TriangleGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7A3CD8E481C3E802" >1.1-2 TriangleCommutatorQuotient</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X78BB0EB087263795" >1.1-3 RandomTriangleQuotient</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7968AC7887291888" >1.1-4 JackButtonGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X863AAC9078647B94" >1.1-5 RandomPregroupPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1_mj.html#X7DEF4DA6781CCE1B" >1.1-6 RandomPregroupWord</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X861436A7862A92D2" >1.2 <span class="Heading" >Testing Hyperbolicity</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1_mj.html#X792204DC7B217ECC" >1.3 <span class="Heading" >The MAGMA-compatible interface</span ></a>span >div >div >div class="ContChap" ><a href="chap2_mj.html#X84CF717F7CE7F8A4" >2 <span class="Heading" >Pregroups</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7F44CAE5832B8511" >2.1 <span class="Heading" >Creating Pregroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7E37DF907C05522C" >2.1-1 PregroupByTable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8137D096798C1BC8" >2.1-2 PregroupByRedRelators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8632A365791D87B7" >2.1-3 PregroupOfFreeProduct</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8344F038858426A6" >2.1-4 PregroupOfFreeGroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7B1844C180E739B9" >2.2 <span class="Heading" >Filters and Representations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86AA05DA7B7BA64B" >2.2-1 IsPregroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78E417B3823387C2" >2.2-2 IsPregroupTableRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84F97B4D79FBAD44" >2.2-3 IsPregroupOfFreeGroupRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X82866B1A7D018BB7" >2.2-4 IsPregroupOfFreeProductRep</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X8053940287FA4077" >2.3 <span class="Heading" >Attributes, Properties, and Operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7946D406823A935B" >2.3-1 []</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X80EC827C83DB818B" >2.3-2 IntermultPairs</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C1AE0D983EF9693" >2.3-3 One</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X8761B5A57CC4DEA8" >2.3-4 MultiplicationTable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7BF3B344878B252F" >2.3-5 SetPregroupElementNames</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X82B7E2227A94AC98" >2.3-6 PregroupElementNames</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7E4700087FC3F933" >2.4 <span class="Heading" >Elements of Pregroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7CACF96A831CEB1F" >2.4-1 IsElementOfPregroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X80185F7579C23714" >2.4-2 IsElementOfPregroupRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X838ECC967A2377BA" >2.4-3 IsElementOfPregroupOfFreeGroupRep</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X784ACAE2800C3E7E" >2.4-4 PregroupOf</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84A42E6B7D542AD1" >2.4-5 IsDefinedMultiplication</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86FC5FDF87C3664A" >2.4-6 IsIntermultPair</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87004CD07832F9DB" >2.4-7 PregroupInverse</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X870A0A6A7CAE4680" >2.5 <span class="Heading" >Small Pregroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7AAEA96C79A55FB3" >2.5-1 NrSmallPregroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7FD30E6F812704C8" >2.5-2 SmallPregroup</a></span >div ></div >div >div class="ContChap" ><a href="chap3_mj.html#X7A05461687E1FA84" >3 <span class="Heading" >Pregroup Presentations</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7AFDBDC078777B90" >3.1 <span class="Heading" >Concepts</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83BEFE747F7726F5" >3.1-1 <span class="Heading" >Locations</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X87FA460D81566861" >3.1-2 <span class="Heading" >Places</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7C701DBF7BAE649A" >3.2 <span class="Heading" >Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81378EEB81DF801A" >3.2-1 IsPregroupLocation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X85EC64DC8116AF77" >3.2-2 InLetter</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E1013A1794D17DD" >3.2-3 OutLetter</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81E1F7F984EC37C2" >3.2-4 Places</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C88C1227C073A36" >3.2-5 NextLocation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83B0E7F778108E23" >3.2-6 PrevLocation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X796A41AD85E9AD40" >3.2-7 __ID</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X85C45E1578DB9E13" >3.3 <span class="Heading" >Creating Pregroup Presentations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B85A7217AF54FB1" >3.3-1 NewPregroupPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X78A45CA479E37F10" >3.3-2 PregroupPresentationFromFp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D9C7247794CA029" >3.3-3 PregroupPresentationToFpGroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7FC6BCF985E6819C" >3.4 <span class="Heading" >Filters, Attributes, and Properties</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8194DE3E7908C921" >3.4-1 IsPregroupPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84191A7B78073D28" >3.4-2 </a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7E53DCE97DEEFA7D" >3.5 <span class="Heading" >Hyperbolicity testing for pregroup presentations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C607CC18455D320" >3.5-1 RSymTestOp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83D3AC54833FF1CE" >3.5-2 RSymTest</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7DB6545987479C4B" >3.5-3 IsHyperbolic</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X801CA5197DF125C6" >3.6 <span class="Heading" >Input and Output of Pregroup Presentations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81F8BD2784FA17A5" >3.6-1 PregroupPresentationToKBMAG</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X844A431F8505219D" >3.6-2 PregroupPresentationToStream</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X86E791EB7FCD6FC7" >3.6-3 PregroupPresentationFromStream</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84B44E0580AE5C2A" >3.6-4 PregroupPresentationToSimpleStream</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B118D1D84350906" >3.6-5 PregroupPresentationToFile</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X808C30267956C4B0" >3.6-6 PregroupPresentationFromFile</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84C6E86D7D3EC053" >3.6-7 PregroupPresentationToSimpleFile</a></span >div ></div >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 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