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

Returns a representive of the class of an ideal in the
ray class group.

<p><p>

<h3>
Syntax:
</h3>
<pre>r := IdealRayClassRep(I,m0,minf);</pre>

<p>

<table>
<tr>
<td>matrix</td>
<td><pre>  r  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal </td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal </td>
<td><pre>  m0  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  minf  </pre></td>
<td>of integers/infinite primes</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Decomposes an ideal, or more exactly, the class of this ideal
(that need to be coprime to {\goth{m}}_0)
into a power product of the
classes generating the whole ray class group.

Based on the solutions for the discrete logarithm problem for
class groups (He1) and for ray residue rings
(see <tt> EltRayResidueRingRep</tt>), an exponent vector relative to
the generators is computed.


<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> O := OrderMaximal(Order(x^2-2*x-5));
Generating polynomial: x^2 - 2*x - 5
Discriminant: 24 

kash> OrderClassGroup(O,500,"euler","fast");
[ 1, [ 1 ] ]
kash> m0 := 27*O;;
kash> minf := [2];;
kash> L := RayClassGroupCyclicFactors(m0,minf);
[ [ <[1344, 388]>, 3 ], [ <[1612, 444]>, 9 ] ]
kash> I := L[1][1];
<[1344, 388]>
kash> IdealRayClassRep(I,m0,minf);
[1 0]

</pre>

<p>


<hr>

<p>
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