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

Calculates the conductor of the ray class group modulo a congruence
module.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := RayConductor(m0 [, minf] [, rels]);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </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>
<tr>
<td>matrix</td>
<td><pre>  rels  </pre></td>
<td>relation matrix over Z</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Calculates the minimal ideal and the minimal set of infinite primes
with the same ray class group as the given congruence module. The
conductor is represented by a list of an ideal and a list of primes
at infinity -- the numbers correspond to the real embeddings of the
order.

This is done by a careful analysis of the structure of the ray class
group as described in Pau1,Pau2.

<p><p>

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

<pre>

kash> O := OrderMaximal(Order(x^3+9*x^2-8*x-9));;
kash> m0 := 94*O;;
kash> minf:= [1,2];;
kash> L := RayConductor(m0,minf);
[ <47>, [  ] ]
kash> OrderClassGroup(O,500,euler,fast);
[ 1, [ 1 ] ]
kash> RayClassGroup(m0,minf);
[ 23, [ 23 ] ]
kash> RayClassGroup(L[1],L[2]);
> [ 23, [ 23 ] ]

</pre>

<p>


<hr>

<p>
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