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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="OrderClassGroupCyclicFactors"></a>
OrderClassGroupCyclicFactors
</h2>

Returns a list with the generators of the cyclic factors.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderClassGroupCyclicFactors(O);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#OrderClassGroup">OrderClassGroup</a>, <a href="kashref.html#OrderClassGroupCyclicFactorsPrincipal">OrderClassGroupCyclicFactorsPrincipal</a>

<p>

<h3>
Description:
</h3>
Returns a list with the generators of the cyclic factors
of the class group together with their orders in the
class group. The list contains sublists and each
sublist contains two items. The first is an ideal, and
the second item is the order of this ideal in the class group.

This function does not compute the class group so that
<tt> OrderClassGroup</tt> has to be called in advance.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the class group structure of {\Bbb Q}(\sqrt[4]{-65}). 
<pre>

kash> O := OrderMaximal(Z,4,-65);;
kash> OrderClassGroup (O, 100);
[ 128, [ 2, 4, 4, 4 ] ]
kash> OrderClassGroupCyclicFactors (O);
> [ [ <30, [885, 896, 0, 899]>, 2 ], [ <3, [2, 1, 0, 0]>, 4 ], 
  [ <3, [1, 0, 1, 0]>, 4 ], [ <2, [1, 1, 0, 0]>, 4 ] ]

</pre>

<p>


<hr>

<p>
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