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

Calculates an element of given norm.

<p><p>

<h3>
Syntax:
</h3>
<pre>elt := OrderRelNormEq(O,n [, "true"]);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  elt  </pre></td>
<td>list of elements in O</td>
</tr>
<tr>
<td>element</td>
<td><pre>  n  </pre></td>
<td>element in coefficient ring of O</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let o be the coefficient order of O and O a simple
relative extension. This means that o is an absolute
extension. (Thus not Z!)
Let f and F be the quotient fields of o and O. This
function computes for a given n \in o an element
elt \in O with N^{F/f}(elt) = n.
If no such element exists an empty list is returned.
If "true" is set we try to find an integral element.
Sometimes two solutions are returned. That is if the reduced version
is different from the non-reduced version.

<p><p>

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

<pre>

kash> o:= Order(Z, 2, 2);
Generating polynomial: x^2 - 2

kash> O:= Order(o, 2, 3);
      F[1]
        /
       /
   E1[1]
  /
 /
Q
F  [ 1]     x^2 - 3
E 1[ 1]     x^2 - 2

kash> n := Elt(o, [-3856938, 1576756]);
[-3856938, 1576756]
kash> elt := OrderRelNormEq(O,n);
> [ [[-3961, -4022], [3679, 1372]], [[-449, 140], [361, -786]] ]

</pre>

<p>


<hr>

<p>
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