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<p>&nbsp;<p>
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<h2><a name="RayClassFieldArtin"></a>
RayClassFieldArtin
</h2>

Given an ideal, this function computes the corresponding automorphism.

<p><p>

<h3>
Syntax:
</h3>
<pre>aut := RayClassFieldArtin(id, O);</pre>

<p>

<table>
<tr>
<td>an automorphism</td>
<td><pre>  aut  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  id  </pre></td>
<td>coprime to the defining module</td>
</tr>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td>output of <tt> RayClassFieldAuto</tt></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#RayClassFieldAuto">RayClassFieldAuto</a>, <a href="kashref.html#RayClassField">RayClassField</a>

<p>

<h3>
Description:
</h3>
This function essentially provides (\a, O/o)\inGal(O/o)
for given unramified ideals. Note, that this function won't check
if the conductor of the abelian extension is known. Therefore
it is only possible to compute automorphisms for ideals coprime
to the defining module.\par
Note, that this function won't work on an arbitraily defined abelian
extensions <tt> O</tt> of <tt> o</tt>. It is necessary to compute <tt> O</tt>
using <tt> RayClassFieldAuto</tt>.

<p><p>

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

<pre>

</pre>

<p>


<hr>

<p>
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