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

Returns a list of the generators of
the cyclic factors of the class group to the power
of their orders.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderClassGroupCyclicFactorsPrincipal(O, ["raw"]);</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#OrderClassGroupCyclicFactors">OrderClassGroupCyclicFactors</a>

<p>

<h3>
Description:
</h3>
This function computes the generating elements of the powers
of the cyclic factors of the class group to their orders
(which are principal integral ideals). Given a second string
parameter <tt> "raw"</tt> a power product representation is returned.

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> L1 := 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 ] ]
kash> L2 := OrderClassGroupCyclicFactorsPrincipal(O);
[ [5, 0, -1, 0], [-2, -1, 0, 0], [4, 0, 1, 0], 2 ]
kash> L1[2][1]^4/L2[2] = 1*O;
> true

</pre>

<p>


<hr>

<p>
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