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<a name="Functions-and-Variables-for-Groups"></a>
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<p>
Previous: <a href="maxima_150.html#Groups" accesskey="p" rel="previous">Groups</a>, Up: <a href="maxima_150.html#Groups" accesskey="u" rel="up">Groups</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Functions-and-Variables-for-Groups-1"></a>
<h3 class="section">31.1 Functions and Variables for Groups</h3>
<a name="todd_005fcoxeter"></a><a name="Item_003a-Groups_002fdeffn_002ftodd_005fcoxeter"></a><dl>
<dt><a name="index-todd_005fcoxeter"></a>Function: <strong>todd_coxeter</strong> <em><br> <tt>todd_coxeter</tt> (<var>relations</var>, <var>subgroup</var>) <br> <tt>todd_coxeter</tt> (<var>relations</var>)</em></dt>
<dd>
<p>Find the order of G/H where G is the Free Group modulo <var>relations</var>, and
H is the subgroup of G generated by <var>subgroup</var>. <var>subgroup</var> is an optional
argument, defaulting to []. In doing this it produces a
multiplication table for the right action of G on G/H, where the
cosets are enumerated [H,Hg2,Hg3,...]. This can be seen internally in
the variable <code>todd_coxeter_state</code>.
</p>
<p>Example:
</p>
<div class="example">
<pre class="example">(%i1) symet(n):=create_list(
if (j - i) = 1 then (p(i,j))^^3 else
if (not i = j) then (p(i,j))^^2 else
p(i,i) , j, 1, n-1, i, 1, j);
<3>
(%o1) symet(n) := create_list(if j - i = 1 then p(i, j)
<2>
else (if not i = j then p(i, j) else p(i, i)), j, 1, n - 1,
i, 1, j)
(%i2) p(i,j) := concat(x,i).concat(x,j);
(%o2) p(i, j) := concat(x, i) . concat(x, j)
(%i3) symet(5);
<2> <3> <2> <2> <3>
(%o3) [x1 , (x1 . x2) , x2 , (x1 . x3) , (x2 . x3) ,
<2> <2> <2> <3> <2>
x3 , (x1 . x4) , (x2 . x4) , (x3 . x4) , x4 ]
(%i4) todd_coxeter(%o3);
Rows tried 426
(%o4) 120
(%i5) todd_coxeter(%o3,[x1]);
Rows tried 213
(%o5) 60
(%i6) todd_coxeter(%o3,[x1,x2]);
Rows tried 71
(%o6) 20
</pre></div>
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Categories:<a href="maxima_424.html#Category_003a-Group-theory">Group theory</a>
·</div></dd></dl>
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