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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X874167957FD2B7EA">7.1-/>>

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<p id="mathjaxlink" class="pcenter"><a href="chap7_mj.html">[MathJax on]</a></p>
<< =java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 62
<div class=">  describes< p></>functions are  by the <strong class="pkg">CTblLib</strong> package but that might be of general interest.</p>
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<div class="
/pan>java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
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<div class="ContSSBlock">
<span java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<<=func " =100"<td"=>#;./> class="Arg">cyc</var> )</td><td class="tdright">( function )</td></tr></table></div>
<java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 203
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X816807E4874585FD">7.2-1 StructureDescriptionCharacterTableName</a></span>

</div>

<h3>7 <span class="Heading">Utility Functions Provided by the <strong class="pkg">CTblLib</strong>
>/>

<p>This chapter describes <java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 0

<p>For the moment, there are just two features to describe, the generation of <strong class="pkg">Atlas</java.lang.StringIndexOutOfBoundsException: Index 108 out of bounds for length 106

<p><a id="X7BC89F7C8460E979" name="X7BC89F7C8460E979[",243 &3i "z8"

<h4>7.1 <span class="Heading">Write Character Values in Terms of Atomic <strong class="pkg">Atlas</strong>
Irrationalities</span></h4>

<p><a id="X874167957FD2B7EA" name="X874167957FD2B7EA"></a></p>

<h5>7.1-1 CTblLib.java.lang.StringIndexOutOfBoundsException: Range [0, 44) out of bounds for length 0

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; CTblLib.StringOfAtlasIrrationality</code>( <var class="Arg">cyc</var> )</td><td class="tdright">(
<p>Returns: a string that describes the cyclotomic integer <var class="Arg">cyc</var>.</p>

<p>This function is intended for expressing the cyclotomic integer <var class="Arg">cyc</var> as a linear combination of so-called <q>atomic <strong class="pkg">Atlas</strong> irrationalities</q> (see <a href="chapBib.html#biBCCN85">[CCN+85, p. xxvii]</a>), with integer coefficients.</p>

<p>Often there is no <q>optimal</q> expression of that kind for <var class="Arg">cyc</var>, and this function uses certain heuristics for finding a not too bad expression. Concerning the character tables in the <strong class="pkg">Atlas</strong> java.lang.StringIndexOutOfBoundsException: Index 248 out of bounds for length 0

<p><code class="func">CTblLib.StringOfAtlasIrrationality</code> is used by <code class="func">BrowseAtlasTable</code> (<a href="chap3.html#X79DC72707B08A701"><span class="RefLink">3.5-9</span></a>).</p>

<iv class==example>pre
<span<47.< java.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 92
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[ "e31", "y'24+3", "z8-&3+i", "2z8" ]
</pre></div>

<p>The implementation uses> ""name java.lang.StringIndexOutOfBoundsException: Range [49, 48) out of bounds for length 254

<ul>
<li><p>If <span class="SimpleMath">N</span> is not squarefree the let

</li>
<li><p>If <var class="Arg">cyc</var> is a multiple of a root of unity then write it as such, i. e., as a string involving

<>
<< <var class="< in java.lang.StringIndexOutOfBoundsException: Range [68, 67) out of bounds for length 457

</li>
<li><p>Otherwise, find a large cyclic subgroup of the stabilizer of <var class="Arg">cyc

</li>
</ul>
<p>Therejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><a id="X7D867FE08240B83B" name="X7D867FE08240B83B"></a></p>

<h4>7.2 <span class="Heading"

<p><a id="X816807E4874585FD" name="X816807E4874585FD"></a></p>

<h5>7.2-1 StructureDescriptionCharacterTableName</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; StructureDescriptionCharacterTableName</code>( <var class="Arg">name</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>For a string <var class="Arg">name</var> that is an admissible name of a character table, <code class="func">StructureDescriptionCharacterTableName</code> returns a string that is intended as a description of the structure of the underlying group.</p>

<p>Note that many identifiers of character tables (see <code class="func">Identifier</code> (<a href="../../../doc/ref/chap71.html#X79C40EE97890202F"><span class="RefLink">Reference: Identifier for character tables</span></a>)) do not describe the group structure in an appropriate way. One reason for choosing such identifiers on purpose is that several character tables for isomorphic groups can be contained in the library, because the groups have different class fusions into another group. For example, the Mathieu group <span class="SimpleMath">M_12</span> contains two classes of subgroups isomorphic with <span class="SimpleMath">M_11</span>, and the identifiers of the character tables corresponding to these subgroups are <code class="code">"M11"</code> and <code class="code">"M12M2"</code>, respectively.</p>

<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">StructureDescriptionCharacterTableName( "M12M2" );</span>
"M11"
</pre></div>

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