[back] [prev] [next] [index] [root]

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

Computes data to get the splitting field of the Ray Class Field.

<p><p>

<h3>
Syntax:
</h3>
<pre>sg := RayClassFieldSplittingField(G, l);</pre>

<p>

<table>
<tr>
<td>AbelianGroup</td>
<td><pre>  sg  </pre></td>
<td></td>
</tr>
<tr>
<td>AbelianGroup</td>
<td><pre>  G  </pre></td>
<td>quotient of RayClassGroupToAbelianGroup</td>
</tr>
<tr>
<td>list</td>
<td><pre>  l  </pre></td>
<td>of automorphisms. Must be complete, not just generators.</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
<i>no detailed description available yet</i>

<p><p>

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

<pre>

kash> o := OrderMaximal(Z, 2, 10);
Generating polynomial: x^2 - 10
Discriminant: 40 

kash> OrderAutomorphisms(o);
[ [0, 1], [0, -1] ]
kash> p3 := Factor(3*o)[2][1];
<3, [2, 1]>
kash> G1 := RayClassGroupToAbelianGroup(p3, [2]);
RayClassGroupToAbelianGroup(<3, [2, 1]>, [ 2 ])
Group with relations:
[4]
kash> G2 := RayClassFieldSplittingField(G1);
Group with relations:
[4 0]
[0 2]
[4 0]
[0 2]
kash> RayClassFieldIsNormal(G1);
false
kash> RayClassFieldIsNormal(G2);
true
kash> O1 := RayClassField(G1);
[ x^4 + [8, 4]*x^2 + [28, 8] ]
kash> Galois(OrderAbs(Order(O1[1])));
> "1/2[2^3]E(4)"

</pre>

<p>


<hr>

<p>
<a href="../kashref.html"><- back</a>[back] [prev] [next] [index] [root]