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

Given a congruence module, this function computes generating
polynomials for the class fields belonging to the cyclic
factors of the corresponding ray class group.

<p><p>

<h3>
Syntax:
</h3>
<pre>c := RayClassField( o | a [, [inf | inf, deg | mat] | deg | mat ] );</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  c  </pre></td>
<td>containg polynomials of <tt> o[x]</tt></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td>for Hilbert class field computations</td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  a  </pre></td>
<td>used as (part of) an congruence module as for <tt> RayClassGroup</tt></td>
</tr>
<tr>
<td>list</td>
<td><pre>  inf  </pre></td>
<td>of infinite places as for <tt> RayClassGroup</tt></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  deg  </pre></td>
<td>if your interesed only in the <tt> deg</tt> part of the class field</td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  mat  </pre></td>
<td>rows of <tt> mat</tt> define a factorgroup of the RayClassGroup</td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#RayClassGroup">RayClassGroup</a>, <a href="kashref.html#RayDiscSig">RayDiscSig</a>, <a href="kashref.html#ImQuadRayField">ImQuadRayField</a>, <a href="kashref.html#RayConductor">RayConductor</a>, <a href="kashref.html#RayConductorTest">RayConductorTest</a>

<p>

<h3>
Description:
</h3>
Using the methods of Fi2, this function computes
generating polynomials for the class fields belonging to the
cyclic factors of a decomposition of the corresponding ray class
group as into factors of prime power order.

For each cyclic factor this function will first construct a field
containing certain roots of unity. Since this field may have
a very large degree, computation may be very lengthy. So
be careful if the ray class group has large cyclic factors.

<p><p>

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

<pre>

</pre>

<p>


<hr>

<p>
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