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<!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 (recog) - Chapter 5: After successful recognition</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="chap5" onload="jscontent()"> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a <div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a> <a href="chap0.html#con <p id="mathjaxlink" class="pcenter"><a href="chap5_mj.html">[MathJax on]</a></p> <p><a id="X851A3F04786123D5" name="X851A3F04786123D5"></a></p> <div class="ChapSects"><a href="chap5.html#X851A3F04786123D5">5 <span class="Heading">Afte <div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8 </span> <div class="ContSSBlock"> <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X82F5B37186B949BF">5 <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X87BDB89B7AAFE8AD"><c <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X858ADA3B7A684421">5 <span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X80FFBDCD816690E3">5 </div></div> </div> <h3>5 <span class=" <p>This chapter explains, what one can do with recognition nodes after a successful recognition <p>Of course, one can inspect the whole tree of recognition nodes just by looking at the stored att <p>Here is an example of a successful recognition tree:</p> <div class="example"><pre> <span class="GAPprompt">gap></span> <span class="GAPinput">g := DirectProduct(SymmetricGroup Group([ (1,2,3,4,5,6,7,8,9,10,11,12), (1,2), (13,14,15,16,17), (13,14) ]) <span class="GAPprompt">gap></span> <span class="GAPinput">ri := RecogniseGroup(g);</span> #I Finished rank 90 method "NonTransitive": success. #I Going to the image (depth=0, try=1). #I Finished rank 95 method "MovesOnlySmallPoints": success. #I Back from image (depth=0). #I Calculating preimages of nice generators. #I Creating 20 random generators for kernel. .................... #I Going to the kernel (depth=0). #I Finished rank 80 method "Giant": success. #I Back from kernel (depth=0). <recognition node NonTransitive F:<recognition node MovesOnlySmallPoints Size=120> K:<recognition node Giant Size=479001600>> </pre></div> <p>One sees that the recursive process runs, first it finds that the permutation action is not tra <p>After this, we can write arbitrary group elements in the group <code class="code">g</code> in ter <div class="example"><pre> <span class="GAPprompt">gap></span> <span class="GAPinput">x := PseudoRandom(g);</span> (1,12)(2,5,9,11,10,3,4)(7,8)(13,14,16,15,17) <span class="GAPprompt">gap></span> <span class="GAPinput">slp := SLPforElement(ri,x);</span> <straight line program> <span class="GAPprompt">gap></span> <span class="GAPinput">ResultOfStraightLineProgram(slp (1,12)(2,5,9,11,10,3,4)(7,8)(13,14,16,15,17) </pre></div> <p>Note that this example only works by using also the <strong class="pkg">recog</strong> package w <p><a id="X80EB3C7481C63B7F" name="X80EB3C7481C63B7F"></a></p> <h4>5.1 <span class="Heading">Functions and methods for recognition nodes</span></h4> <p>If you need an element explicitly written in terms of the original generators, you can use the f <p><a id="X82F5B37186B949BF" name="X82F5B37186B949BF"></a></p> <h5>5.1-1 SLPforNiceGens</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SL <p>Returns: an SLP expressing the nice generators in the original ones</p> <p>This function assembles a possibly quite large straight line program expressing the nice gen <p>You can concatenate straight line programs in the nice generators with the result of this func <p><a id="X87BDB89B7AAFE8AD" name="X87BDB89B7AAFE8AD"></a></p> <h5><code>5.1-2 \in</code></h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ \i <p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p> <p>This method tests, whether the element <var class="Arg">x</var> lies in the group recognised by t <p><a id="X858ADA3B7A684421" name="X858ADA3B7A684421"></a></p> <h5>5.1-3 Size</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Si <p>Returns: the size of the recognised group</p> <p>This method calculates the size of the recognised group by multiplying the size of the image an <p><a id="X80FFBDCD816690E3" name="X80FFBDCD816690E3"></a></p> <h5>5.1-4 DisplayCompositionFactors</h5> <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Di <p>Returns: nothing</p> <p>This function displays a composition series by using the recursive recognition tree. 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