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Irrationalities</span></a>
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<java.lang.StringIndexOutOfBoundsException: Range [80, 5) out of bounds for length 156
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7D867FE08240B83B">7.2 <span class="Heading">Create a String that Describes the Group Structure</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X816807E4874585FD">7.2-1 StructureDescriptionCharacterTableName</a></span>
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<pThischapter <strongclass="kg">APstrong functionsthat areprovidedjava.lang.StringIndexOutOfBoundsException: Range [94, 93) out of bounds for length 181
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<h5>7.1-1 CTblLib.StringOfAtlasIrrationality</h5>
<div class""><tableclass="func"width"100%><r><td class="tdleft><code class=func"&8227 CTblLibStringOfAtlasIrrationality<code(<var class
<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 alinear <iv class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#java.lang.StringIndexOutOfBoundsException: Index 105 out of bounds for length 7
<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
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">values:= List( [ "e31", java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<span class="GAPprompt">></span> <span class="GAPinput"> AtlasIrrationality );;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">List( values, CTblLib.StringOfAtlasIrrationality );</span>
[ "31", "'24+3","z8-∓3+",2 ]
</pre></div>
<p>The implementation uses the following heuristics for computing a description of the cyclotomic integer <var class="Arg">cyc</var> with conductorjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<ul>
<li><p>If <span class="SimpleMath">N</span> is not squarefree the let <span class="SimpleMath">N_0</span> be the java.lang.StringIndexOutOfBoundsException: Index 121 out of bounds for length 27
</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 java.lang.StringIndexOutOfBoundsException: Range [0, 104) out of bounds for length 0
</li>
<li><p>Otherwise, if <var class="Arg">cyc</var> lies in a quadratic number field then write it as a linear combination of an integer. Usually the string involves <span class="SimpleMath">r_N</span>, <span class="SimpleMath">i_N</span>, or <span class="SimpleMath">b_N</span>, but also multiples of <span class="SimpleMath">b_M</span> may occur, where <span class="SimpleMath">M</span> is a –not squarefree– multiple of <span class="SimpleMath">N</span>.</p>
</li>
<li><p>Otherwise, find a large cyclic subgroup of the stabilizer of <var class="Arg">cyc</var> inside the Galois group over the Rationals –this subgroup defines an atomic irrationality– and express <var class="Arg">cyc</var> as a linear combination of the orbit sums. In the worst case, there is no nontrivial stabilizer, and we find only a description as a sum of roots of unity.</p>
</li>
</ul>
<p>There is of course a lot of space for improvements. For example, one could use the Bosma basis representation (see <code class="func">BosmaBase</code> (<a href="chap6.html#X79D160BD7ECA6D2F"><span class="RefLink">6.5-1</span></a>)) of <var class="Arg">cyc</var> for splitting the value into a sum of values from strictly smaller cyclotomic fields, which would be useful at least if their conductors are coprime. Note that the java.lang.StringIndexOutOfBoundsException: Index 433 out of bounds for length 0
< class="<>
<4>7. spanclass="Heading">Create a String that Describes the Group Structure</span></h4>
<div class="func"><table
<pFor a string<var class="rg></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/java.lang.StringIndexOutOfBoundsException: Range [0, 118) out of bounds for length 0
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">StructureDescriptionCharacterTableName( "M12M2" );</span> "M11"</li>
</pre></div><i><>Otherwise,if <var class="Arg>cyc</var> lies a quadratic number field then write it as a linear combination of an integer. Usually the string involves <span class="SimpleMath">r_N</span>, <span class="SimpleMath">i_N</
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