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

Creates an absolute extension from a simple relative extension
and tries to find a "good" primitive polynomial for the given
order.

<p><p>

<h3>
Syntax:
</h3>
<pre>Oa := OrderShortAbs(O);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  Oa  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Given a simple relative order O - the coefficient ring
(<tt> OrderCoefOrder</tt>) of the coefficient ring of
O is {\Bbb Z} -
this function computes an absolute equation order O|a
with quotient field isomorphic to the quotient field of
O over Q.

At the same time this algorithm tries to find a polynomial for which
the corresponding equation order is of small index.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
The following example creates the absolute extension of a relative
extension: 
<pre>

kash> o:=OrderMaximal(x^2 + 19*x + 11);
Generating polynomial: x^2 + 19*x + 11
Discriminant: 317 

kash> ox:=PolyAlg(o);
Univariate Polynomial Ring in x over Generating polynomial: x^2 + 19*x + 11
Discriminant: 317 

kash> O:=Order(Poly(ox,[1,-18,-6]));
      F[1]
        /
       /
   E1[1]
  /
 /
Q
F  [ 1]     x^2 - 18*x - 6
E 1[ 1]     x^2 + 19*x + 11

kash> Oa:=OrderShortAbs(O);
>    F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^4 - 2*x^3 - 331*x^2 + 332*x - 23


</pre>

<p>


<hr>

<p>
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