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

Returns the relative discriminant and the absolute signature of
the ray class field belonging to a congruence module.

<p><p>

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

<p>

<table>
<tr>
<td>ideal </td>
<td><pre>  m0  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  minf  </pre></td>
<td>of integer/infinite primes</td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  rels  </pre></td>
<td>relation matrix over Z</td>
</tr>
<tr>
<td>list </td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
A list which contains the relative discriminant and the signature
in the form [r1,r2] is returned.

If the units of the maximal order or the multiplicative group of the
residue ring modulo the ideal or the class group of the order are
not known, they will be calculated. The algorithm is based on the
formulas for the discriminant and the signature in
CDOants,CDO1.

<p><p>

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

<pre>

kash> O := OrderMaximal(Order(x^3+9*x^2-8*x-9));
Generating polynomial: x^3 + 9*x^2 - 8*x - 9
Discriminant: 42953 

kash> m0 := 3*O;
<3>
kash> minf:= [1,2];
[ 1, 2 ]
kash> RayDiscSig(m0,minf);
> [ <
    [27  0  9]
    [ 0 27  0]
    [ 0  0  9]
    >
    , [ 8, 2 ] ]

</pre>

<p>


<hr>

<p>
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