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<?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 (Smallsemi) - 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="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 >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >Smallsemi</h1 >small semigroups</h2>div >br />Email: <span class="URL" ><a href="mailto:a.distler@tu-bs.de" >a.distler@tu-bs.de</a></span >br />Email: <span class="URL" ><a href="mailto:jdm3@st-andrews.ac.uk" >jdm3@st-andrews.ac.uk</a></span >br />Homepage: <span class="URL" ><a href="https://jdbm.me " >https://jdbm.me</a></span >br />Address : <br />Mathematical Institute<br /> North Haugh<br /> St Andrews<br /> Fife<br /> KY16 9SS<br /> Scotland<br />"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>strong class="pkg" >Smallsemi</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 3 of the license, or (at your option ) any later version.</p>strong class="pkg" >Smallsemi</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>'LICENSE' ; for the latest version see <span class="URL" ><a href="https://www.gnu.org/licenses/#GPL " >https://www.gnu.org/licenses/#GPL</a></span >.</p>strong class="pkg" >Smallsemi</strong >, though as documentation it is released under the GNU Free Documentation License (see <span class="URL" ><a href="https://www.gnu.org/licenses/#FDL " >https://www.gnu.org/licenses/#FDL</a></span >).</p>"X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>mputations in Minion <a href="chapBib.html#biBminion" >[GJM06]</a>. <br /> The first author acknowledges financial support of the University of St Andrews. The second author acknowledges support of EPSRC grant number GR/S/56085/01.</p>"X7982162280BC7A61" name="X7982162280BC7A61" ></a></p>would let us know via our issue tracker (see <span class="URL" ><a href="https://github.com/gap-packages/smallsemi/issues " >https://github.com/gap-packages/smallsemi/issues</a></span >).</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"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#X85A08CF187A6D986" >1.1 <span class="Heading" >Requirements</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X82C5588B7E8B2725" >1.1-1 <span class="Heading" >Operating System</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X78F27CCA81555251" >1.1-2 <span class="Heading" >RAM</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X87E4E0377BF1EAC6" >1.1-3 <span class="Heading" >Disk Space</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X796A04C37CB7AC04" >1.2 <span class="Heading" >Installation and Setup</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7C87C34C79B9D28D" >1.2-1 <span class="Heading" >Download and Extract <strong class="pkg" >Smallsemi</strong ></span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X86BA319E87365B5C" >1.2-2 <span class="Heading" >Contents</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X861ED1338181C66D" >1.2-3 <span class="Heading" >Loading</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X803939AE7C3565DA" >1.2-4 <span class="Heading" >Memory Issues</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7DE7E7187BE24368" >1.2-5 <span class="Heading" >Testing</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap1.html#X7B3500B984306465" >1.2-6 <span class="Heading" >Customizing</span ></a>span >div ></div >div >div class="ContChap" ><a href="chap2.html#X7E933CC381DA3D7C" >2 <span class="Heading" >The Data in the Library</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7A8F62A38080168D" >2.1 <span class="Heading" >Creation of the Semigroups</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X79038EE8873A1B4B" >2.2 <span class="Heading" >Storing the Semigroups</span ></a>span >div >div >div class="ContChap" ><a href="chap3.html#X7CDC63A27F7790AA" >3 <span class="Heading" >Extended Examples</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X80DFE0117B7A7C24" >3.1 <span class="Heading" >Lists, Enumerators and Iterators of Semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X790CB8D686E0A336" >3.1-1 <span class="Heading" >Precomputed properties</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X804593297D7EEF68" >3.1-2 <span class="Heading" >User functions</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7E4F0756878EB958" >3.1-3 <span class="Heading" >Semigroups of order 8</span ></a>span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X8772952F7B2CFDE1" >3.2 <span class="Heading" >Identifying Semigroups</span ></a>span >div >div >div class="ContChap" ><a href="chap4.html#X87F1120883F5B4D0" >4 <span class="Heading" >Functionality</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X83F5AF81859D6CBF" >4.1 <span class="Heading" >Individual Semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8538248D78185960" >4.1-1 SmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X857428A57D3FFACB" >4.1-2 IsSmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7EC241FB7985775E" >4.1-3 IsSmallSemigroupElt</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X793FF84E80B334D1" >4.1-4 RecoverMultiplicationTable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X813727FD851302B7" >4.1-5 SemigroupByMultiplicationTableNC</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X788211A07D67C282" >4.1-6 IdSmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79D38A3886C7431D" >4.1-7 EquivalenceSmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8078FC78871FA496" >4.1-8 InfoSmallsemi</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X841BB74986A73272" >4.1-9 UnloadSmallsemiData</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X78274024827F306D" >4.2 <span class="Heading" >Properties of Semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X86A4F95783A18702" >4.2-1 Annihilators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E1195927C454C8A" >4.2-2 DiagonalOfMultiplicationTable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7DCF7C368665E94D" >4.2-3 DisplaySmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X86B662117F4C4C7F" >4.2-4 IndexPeriod</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7C8DB14587D1B55A" >4.2-5 IsBand</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7EFDBA687DCDA6FA" >4.2-6 IsBrandtSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X81DE11987BB81017" >4.2-7 IsCliffordSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X843EFDA4807FDC31" >4.2-8 IsCommutativeSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7AFA23AF819FBF3D" >4.2-9 IsCompletelyRegularSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D51FD2B7AA3E8DF" >4.2-10 IsFullTransformationSemigroupCopy</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X852F29E8795FA489" >4.2-11 IsGroupAsSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X835484C481CF3DDD" >4.2-12 <span class="Heading" >IsIdempotentGenerated</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83F1529479D56665" >4.2-13 IsInverseSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E9261367C8C52C0" >4.2-14 IsLeftZeroSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79D46BAB7E327AD1" >4.2-15 IsMonogenicSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E4DEECD7CD9886D" >4.2-16 IsMonoidAsSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79FF88207AFC8330" >4.2-17 IsMultSemigroupOfNearRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83D4ED237BB929AF" >4.2-18 IsNGeneratedSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X87BF19367BA2B9ED" >4.2-19 IsNIdempotentSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X780ADE31828F0848" >4.2-20 <span class="Heading" >IsNilpotentSemigroup</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7935C476808C8773" >4.2-21 IsOrthodoxSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E9B674D781B072C" >4.2-22 IsRectangularBand</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7C4663827C5ACEF1" >4.2-23 IsRegularSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7CB099958658F979" >4.2-24 IsRightZeroSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X846FC6247EE31607" >4.2-25 IsSelfDualSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D3ACD8A7C0AB34C" >4.2-26 IsSemigroupWithClosedIdempotents</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X82D229727C6278EC" >4.2-27 IsSemigroupWithZero</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X836F4692839F4874" >4.2-28 <span class="Heading" >IsSimpleSemigroup</span ></a>span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X85A3F78C864507EB" >4.2-29 IsSingularSemigroupCopy</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X85F7E5CD86F0643B" >4.2-30 IsZeroGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X81A1882181B75CC9" >4.2-31 IsZeroSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8193A60F839C064E" >4.2-32 IsZeroSimpleSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X81D15723804771E2" >4.2-33 MinimalGeneratingSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D1C336E7B0A059C" >4.2-34 NilpotencyDegree</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X866B154E7F54AE62" >4.3 <span class="Heading" >Nilpotent semigroups by coclass</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X819BD88C78976AFD" >4.3-1 NilpotentSemigroupsByCoclass</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7D6E81E37E3AAED8" >4.4 <span class="Heading" >Starred Green's relations
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.4-1 IsStarRelation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A8059EC848E0A77" >4.4-2 RStarRelation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D30CDC386C8816A" >4.4-3 RStarClass</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83E1C16B8247ECBD" >4.4-4 RStarClass</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X82A391177D13A7E0" >4.4-5 IsStarClass</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83B9C0417C03A220" >4.4-6 RStarClasses</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X82F9C36C86006857" >4.5 <span class="Heading" >Families of Semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X81DC0FE28043C9B0" >4.5-1 AllSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X831E543E83DDFDEA" >4.5-2 EnumeratorOfSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7F8EF88E7EB417A8" >4.5-3 EnumeratorOfSmallSemigroupsByIds</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A14F5A58020DCFF" >4.5-4 ArgumentsUsedToCreate</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X814BA9F778B06D47" >4.5-5 IdsOfSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7BF0DCA5853A5C22" >4.5-6 IsEnumeratorOfSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83C27CD97895698A" >4.5-7 IsIdSmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X803366027F328BC9" >4.5-8 IsIteratorOfSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D6BFDE17A9BEEC3" >4.5-9 IteratorOfSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X867F3E967CF3AFE9" >4.5-10 Nr3NilpotentSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8257C9207DDF2451" >4.5-11 NrSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7C71885F7DF31EC4" >4.5-12 OneSmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7EACCD1F7DF9DD3C" >4.5-13 PositionsOfSmallSemigroupsIn</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7FAF09BF7CC1C265" >4.5-14 PositionsOfSmallSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79AFE7FC81C0DF37" >4.5-15 PrecomputedSmallSemisInfo</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A63356C85E45F6F" >4.5-16 RandomSmallSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83C6631B7D53AE02" >4.5-17 SizesOfSmallSemigroupsIn</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X87C50557821D4786" >4.5-18 UpToIsomorphism</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="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html >quality 97%
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