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

Computes automorphisms of the given normal extension.

<p><p>

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

<p>

<table>
<tr>
<td>list</td>
<td><pre>  aut  </pre></td>
<td>list of automorphisms</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#OrderAutomorphismsAbel">OrderAutomorphismsAbel</a>

<p>

<h3>
Description:
</h3>
This function computes the automorphisms of the given normal
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
normal extensions. In the case that an extension is normal
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. If it is known that the
given extension is Abelian it is strongly recommended to use
the function <tt> OrderAutomorphismsAbel</tt> which is much faster.

<p><p>

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

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

</pre>

<p>


<hr>

<p>
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