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

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

Computes of the given Abelian extension.

<p><p>

<h3>
Syntax:
</h3>
<pre>aut := OrderAutomorphismsAbel(o);</pre>

<p>

<table>
<tr>
<td>logical</td>
<td><pre>  aut  </pre></td>
<td>IsAbelian</td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td>the given order</td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#EltAutomorphism">EltAutomorphism</a>, <a href="kashref.html#OrderAutomorphisms">OrderAutomorphisms</a>, <a href="kashref.html#OrderAutomorphismsNormal">OrderAutomorphismsNormal</a>

<p>

<h3>
Description:
</h3>
This function computes the automorphisms of the given Abelian
extension. The automorphisms are represented by algebraic
numbers which are zeros of the generating polynomials of the
given extension. They can be applied to algebraic numbers
with the function <tt> EltAutomorphism</tt>.

The computation of automorphisms is only possible for
absolute Abelian extensions. In the case that an extension
is Abelian the function will return <tt> true</tt> otherwise
<tt> false</tt>. Using the function <tt> OrderAutomorphisms</tt>
one gets the explicit automorphisms.
The algorithms are described in Kl2,AcKl1.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the automorphisms:
<pre>

kash> o := Order(x^4-4*x^2+1);;
kash> OrderAutomorphismsAbel(o);
> true

</pre>

<p>


<hr>

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