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<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">
<h1>Functionally recursive groups</h1>
<h2>Self-similar groups</h2>
<p>Version 0.857142p8</p>
<p>$Date: 2008/12/02 12:04:31 $</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="http://www.uni-math.gwdg.de/laurent/">http://www.uni-math.gwdg.de/laurent/</a></span>
</p>
<p><b>Address:</b><br />
Mathematisches Institut, Bunsenstraße 3-5, D-37073 Göttingen<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="http://gap-system.org">http://gap-system.org</a></span>.</p>
<p>This documentation for <strong class="pkg">FR</strong> is available at <span class="URL"><a href="http://www.uni-math.gwdg.de/laurent/FR/manual.pdf">http://www.uni-math.gwdg.de/laurent/FR/manual.pdf</a></span> in PDF format, and may be accessed online at <span class="URL"><a href="http://www.uni-math.gwdg.de/laurent/FR/">http://www.uni-math.gwdg.de/laurent/FR/</a></span>.</p>
<p>The latest source of the package may be downloaded as <span class="URL"><a href="http://www.uni-math.gwdg.de/laurent/FR/fr.tar.gz">http://www.uni-math.gwdg.de/laurent/FR/fr.tar.gz</a></span> (tar, gzipped) and <span class="URL"><a href="http://www.uni-math.gwdg.de/laurent/FR/fr.zoo">http://www.uni-math.gwdg.de/laurent/FR/fr.zoo</a></span> (zoo).</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>© 2006-2008 by Laurent Bartholdi</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>Part of this work is supported by the "Swiss National Fund for Scientific Research"</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</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="nocss"> </span><a href="chap2.html#X80C332C686212786">2.1 <span class="Heading">A brief mathematical introduction</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap2.html#X78DF4DE18260BD80">2.2 <span class="Heading">An example session</span></a>
</div>
</div>
<div class="ContChap"><a href="chap3.html#X7D65CA8B876E514C">3 <span class="Heading">Functionally recursive machines</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X7D52F7ED83E2D153">3.1 <span class="Heading">Types of machines</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap3.html#X7EB36FBB78F4F26A">3.2 <span class="Heading">Products of machines</span></a>
</div>
<div class="ContSect"><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 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#X814F53B97C3F43F5">3.3-5 ChangeFRMachineBasis</a></span>
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<div class="ContSect"><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 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#X80B52A8A7F30878E">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#X7D95D1498586E5D0">3.4-5 WreathRecursion</a></span>
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<div class="ContSect"><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 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">3.5-2 \+</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7857704878577048">3.5-3 \*</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#X81B382BD81B2BD34">3.5-10 Minimized</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7C107A42815F91DA">3.5-11 Correspondence</a></span>
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</div>
<div class="ContChap"><a href="chap4.html#X863D82207A1320F1">4 <span class="Heading">Functionally recursive elements</span></a>
<div class="ContSect"><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 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>
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<div class="ContSect"><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 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#X84A193C67CDBDA35">4.2-4 Portrait</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X850EB66E7804BA3B">4.2-5 DecompositionOfFRElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X85441F1683E9D820">4.2-6 StateSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X819E3E3080297347">4.2-7 State</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7B0C97BC7C3BA20D">4.2-8 States</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X804B2E0F7E37F5B8">4.2-9 FixedStates</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8303B36C83371FB3">4.2-10 LimitStates</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7C4076707CBBE945">4.2-11 IsFiniteStateFRElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X79E65E818690B4EB">4.2-12 InitialState</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X823B6E3D819432D6">4.2-13 \^</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7C3CF6AF86336EDC">4.2-14 \*</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X78C19ACA78F9F067">4.2-15 \[\]</a></span>
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</div>
<div class="ContChap"><a href="chap5.html#X7C77EBC17DEF4CF6">5 <span class="Heading">Mealy machines and elements</span></a>
<div class="ContSect"><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 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 class="ContSect"><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 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#X828C167B7D7691E9">5.2-17 IsLevelTransitive</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#X82308064814FEA51">5.2-26 LimitMachine</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>
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<div class="ContChap"><a href="chap6.html#X84AD415C872BFB91">6 <span class="Heading">Linear machines and elements</span></a>
<div class="ContSect"><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 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#X7F65118683209DC5">6.1-2 AlgebraMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A19036B828BBA0C">6.1-3 Transition</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X846683198081BA82">6.1-4 Transitions</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X80F694298399E78D">6.1-5 NestedMatrixState</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7FCEE3BF86B02CC6">6.1-6 ActivitySparse</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8436BEA67F1C3C27">6.1-7 Activities</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EF5B7417AE6B3F8">6.1-8 IsConvergent</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8136C21885019A4A">6.1-9 TransposedFRElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X796B736286CACF85">6.1-10 LDUDecompositionFRElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X783E8F427A23EAD1">6.1-11 GuessVectorElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X865EE2E887ECC079">6.1-12 AsLinearMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X82586DFB8458EF05">6.1-13 AsVectorMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7818245A7DABB311">6.1-14 AsAlgebraMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7BDD40B27F7541B2">6.1-15 AsVectorMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8120605981DDE434">6.1-16 AsAlgebraMachine</a></span>
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<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="nocss"> </span><a href="chap7.html#X80A26BAA7B53C1BD">7.1 <span class="Heading">Creators for FR semigroups</span></a>
<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#X853E3F0680C76F56">7.1-2 SCGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F15D57A7959FEF6">7.1-3 Correspondence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7D0B8334786E2802">7.1-4 FullSCGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7DB92C34827D513F">7.1-5 FRMachineFRGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7BF4AC9F830A8E1A">7.1-6 IsomorphismFRGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7DE1CAE981F2825B">7.1-7 IsomorphismMealyGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7BB8DDEA83946C73">7.1-8 FRGroupByVirtualEndomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X79D75A7D80DD9AD1">7.1-9 TreeWreathProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X85840A047C04BFC6">7.1-10 WeaklyBranchedEmbedding</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap7.html#X84E20571841DE1E4">7.2 <span class="Heading">Operations for FR semigroups</span></a>
<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#X79B8CFEA79987E12">7.2-3 TransMonoid</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X82BF1F2579A02C5E">7.2-4 TransSemigroup</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#X87378D53791D0B70">7.2-6 StabilizerImage</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7B4CD9CA872BA368">7.2-7 LevelStabilizer</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F65F07F85034B3B">7.2-8 IsStateClosedFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X79246DB482BEAF2D">7.2-9 StateClosure</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7E2F34417EBB7673">7.2-10 IsRecurrentFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7FBF56737D9063F4">7.2-11 IsLevelTransitive</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7D95219481AEDD20">7.2-12 IsInfinitelyTransitive</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A6CB30181662C77">7.2-13 IsFinitaryFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X791BCD9D782C6237">7.2-14 Degree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7FA67E4387C91BD8">7.2-15 HasOpenSetConditionFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7EAB4B5B843C0EC5">7.2-16 IsContracting</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7CA062A67C1554BB">7.2-17 NucleusOfFRSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8443D711796F06E4">7.2-18 NucleusMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A874A107D4944E1">7.2-19 BranchingSubgroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X78ADACCD8586D3C7">7.2-20 FindBranchingSubgroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X832D98E47ACA099C">7.2-21 IsBranched</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A905CE87B49213F">7.2-22 IsBranchingSubgroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8749E0797A99F531">7.2-23 TopVertexTransformations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7C56C90086070A2E">7.2-24 VertexTransformations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7DF2D9838625CDED">7.2-25 VirtualEndomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7C81CB1C7F0D7A90">7.2-26 EpimorphismFromFpGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8740656382656D63">7.2-27 IsomorphismSubgroupFpGroup</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap7.html#X7E8485A081EBB3AA">7.3 <span class="Heading">Properties for infinite groups</span></a>
<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 class="ContChap"><a href="chap8.html#X7DDBF6F47A2E021C">8 <span class="Heading">Algebras</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap8.html#X842EE9427C63F92E">8.1 <span class="Heading">Creators for FR algebras</span></a>
<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#X81D8D0E886C8E143">8.1-3 BranchingIdeal</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap8.html#X7EFB4F2E7E908B9F">8.2 <span class="Heading">Operations for FR algebras</span></a>
<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>
</div>
</div>
<div class="ContChap"><a href="chap9.html#X798DE1297EC58F59">9 <span class="Heading">Iterated monodromy groups</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap9.html#X7CA23C95828C2A3E">9.1 <span class="Heading">Creators and operations for IMG FR machines</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X79C411167D97F0F9">9.1-1 IMGFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7BCE03F2827DAA0A">9.1-2 IMGRelator</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7AB029AE8590964E">9.1-3 Mating</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7D71EBDA7D7C3474">9.1-4 PolynomialFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X82F0B23486F2E3AC">9.1-5 DBRationalIMGGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7A32EC907B726CF7">9.1-6 ValueRational</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X789111E786DF284D">9.1-7 CriticalValuesQuadraticRational</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7EA768B886A5C7F2">9.1-8 CanonicalQuadraticRational</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X8365719F7E03B7C3">9.1-9 PostCriticalMachine</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap9.html#X7C73C74D87428A33">9.2 <span class="Heading">Spiders</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7CC0BBAD807D1A45">9.2-1 RationalFunction</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7ED04E0884385D54">9.2-2 IMGFRMachine</a></span>
</div>
</div>
<div class="ContChap"><a href="chap10.html#X7A489A5D79DA9E5C">10 <span class="Heading">Examples</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X7AF5DEF08531AFA5">10.1 <span class="Heading">Examples of groups</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7D774B847D81E6DE">10.1-1 FullBinaryGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X813F53C57F41F5F5">10.1-2 BinaryKneadingGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7B8D49D079D336E8">10.1-3 BasilicaGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X85F4FDF787173863">10.1-4 AddingGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7A4BB24A805CDF63">10.1-5 BinaryAddingGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X78AFA63B86C94227">10.1-6 MixerGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X84C97E0687F119C0">10.1-7 SunicGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X79E3F3BE80F34590">10.1-8 GrigorchukMachines</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X85BAE48780E665A4">10.1-9 GrigorchukMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X800640597E9C707D">10.1-10 GrigorchukOverGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7C58F33D825A473A">10.1-11 GrigorchukEvilTwin</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7F93EC437B5AE276">10.1-12 BrunnerSidkiVieiraGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7F8A028B799946D3">10.1-13 AleshinGroups</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7C286D3A84790ECE">10.1-14 AleshinGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7E024B4D7BA411B1">10.1-15 BabyAleshinGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X8108E3A8872A6FFE">10.1-16 SidkiFreeGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X82D3CB6A7C189C78">10.1-17 GuptaSidkiGroups</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X83E59288860EF661">10.1-18 GuptaSidkiGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X8521B4FF7BA189B2">10.1-19 NeumannGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X878D1C7080EA9797">10.1-20 FabrykowskiGuptaGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X864A87957D1E1AF6">10.1-21 OtherSpinalGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7A0319827CB51ED0">10.1-22 GammaPQMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7A0BE9F57B401C5C">10.1-23 HanoiGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7C7A0EEF7EFF8B99">10.1-24 DahmaniGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7C958AB78484E256">10.1-25 MamaghaniGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X86D952E8784E4D97">10.1-26 WeierstrassGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X86B124758135DFBD">10.1-27 FRAffineGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7CFBE31A78F2681B">10.1-28 CayleyGroup</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X81B82FA1811AAF8D">10.2 <span class="Heading">Examples of semigroups</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X87541DA582705033">10.2-1 I2Machine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7B32ED3D8715FA4B">10.2-2 I4Machine</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X803B02408573A30E">10.3 <span class="Heading">Examples of algebras</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X80E15ABC879F8EE2">10.3-1 PSZAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7D015CA5829FAA2A">10.3-2 GrigorchukThinnedAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7B66ED537D0A43AF">10.3-3 GuptaSidkiThinnedAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7B0B5B09878C7CEA">10.3-4 SidkiFreeAlgebra</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X7989134C83AF38AE">10.4 <span class="Heading">Bacher's determinant identities</span></a>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap10.html#X7C4A51947E1609A8">10.5 <span class="Heading">VH groups</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7E0071D4838B239D">10.5-1 VHStructure</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7F852A357D7E2E76">10.5-2 VerticalAction</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X86B1C2F079FE8D82">10.5-3 VHGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7D1FCB877D1B96EA">10.5-4 IsIrreducibleVHGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X84DB7FA4846075A7">10.5-5 MaximalSimpleSubgroup</a></span>
</div>
</div>
<div class="ContChap"><a href="chap11.html#X86D6616E868AF75C">11 <span class="Heading">FR implementation details</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap11.html#X79719CD17A948933">11.1 <span class="Heading">The family of FR objects</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7F5497A47F8C81DD">11.1-1 FRMFamily</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7C6A63427F6DB4C6">11.1-2 FREFamily</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7BC9CD3685C26823">11.1-3 AlphabetOfFRObject</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X793E0E1283BE7C73">11.1-4 AsPermutation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7B41902D87A48EDB">11.1-5 AsTransformation</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap11.html#X856A3AD87C93FC1F">11.2 <span class="Heading">Filters for <code class="code">FRObject</code>s</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7CC0BFD67CE7060E">11.2-1 IsGroupFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X8157AE587CBA24C4">11.2-2 IsFRMachineStrRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X79C2395A7D65214B">11.2-3 IsMealyMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7C86614187606A4C">11.2-4 IsMealyElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X78E206B28015A395">11.2-5 IsMealyMachineIntRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7AE5B4257E2DB7E6">11.2-6 IsMealyMachineDomainRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X8087EE9F79E8E339">11.2-7 IsVectorFRMachineRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7859869E7FEDA49F">11.2-8 IsAlgebraFRMachineRep</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X877B1EBD80170001">11.2-9 IsLinearFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X823F46A67D458AAD">11.2-10 IsLinearFRElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7966F9B982B1DFE1">11.2-11 IsFRElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X785D09F27DBDF6A8">11.2-12 IsFRObject</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7C22A1A28058F754">11.2-13 IsFRMachine</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X83AEFB8184F4B023">11.2-14 IsInvertible</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X81D717E187305F2A">11.2-15 IsFRGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X853B16B381CB5366">11.2-16 IsFRAlgebra</a></span>
</div>
<div class="ContSect"><span class="nocss"> </span><a href="chap11.html#X7E97015E8153F782">11.3 <span class="Heading">Some of the algorithms implemented</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X84278D6F7AAD101F">11.3-1 FRMachineRWS</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X84B4FF607DA18152">11.3-2 <span class="Heading">Order of FR elements</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X847B4AFF809D2A56">11.3-3 <span class="Heading">Membership in semigroups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7A0AC96784ACE0BE">11.3-4 <span class="Heading">Order of groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X8329884F790E1542">11.3-5 <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="chap11.html#X7F4247367D1EBEB9">11.3-6 <span class="Heading">Comparison of FR, Mealy, vector,
and algebra elements</span></a>
</span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X81F95FEB7C72ABFF">11.3-7 <span class="Heading">Inverses of linear elements</span></a>
</span>
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<div class="ContChap"><a href="chap12.html#X785C6C0B80936CC8">12 <span class="Heading">Miscellanea</span></a>
<div class="ContSect"><span class="nocss"> </span><a href="chap12.html#X7E665607810488EE">12.1 <span class="Heading">Helpers</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7AF592A57A86A158">12.1-1 maybe</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7FFD58887FB6D36D">12.1-2 ReturnMaybe</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X844D3035877B5052">12.1-3 TensorSum</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X868A30347924CEDF">12.1-4 TensorProductX</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X82AD6F187B550060">12.1-5 DirectSum</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7B401DFE817D3927">12.1-6 PeriodicList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7AFE88F37FC58083">12.1-7 CompressPeriodicList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7CA5FA3F7AF9BA3D">12.1-8 IsConfinal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X86AB4AFF7B1613E3">12.1-9 ConfinalityClass</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X84FB28807BC8A502">12.1-10 LargestCommonPrefix</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7BFF1432803C9172">12.1-11 WordGrowth</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X868E478F86A10CFF">12.1-12 ShortGroupRelations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7B9942AA84B0753E">12.1-13 ShortGroupWordInSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X84472A637B648C47">12.1-14 SurfaceBraidFpGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X87E12292861FFE79">12.1-15 CharneyBraidFpGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X814375977D2E4AD9">12.1-16 ArtinRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7E4966327C37C790">12.1-17 StringByInt</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7979A86E781759F0">12.1-18 PositionTower</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X79016B3878B5EFAA">12.1-19 CoefficientsInAbelianExtension</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X8624AFAD872509D8">12.1-20 MagmaEndomorphismByImagesNC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7F7E6457877F69EC">12.1-21 MagmaHomomorphismByImagesNC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7D44289E861E3343">12.1-22 NewFIFO</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X86AC1C028093204D">12.1-23 ProductIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X794940277C9AD85C">12.1-24 DimensionSeries</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7CA512F481AADD38">12.1-25 Trans</a></span>
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<div class="ContSect"><span class="nocss"> </span><a href="chap12.html#X7ADFF37084706CEC">12.2 <span class="Heading">User settings</span></a>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7E95AC267805E4C1">12.2-1 InfoFR</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap12.html#X7DBA334C83DE0619">12.2-2 FR_SEARCH</a></span>
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