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

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

Discriminant of a module.

<p><p>

<h3>
Syntax:
</h3>
<pre>d := EltListAbsDisc (L);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of algebraic elements</td>
</tr>
<tr>
<td>integer</td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Computes the (absolute) discriminant of the module
M = o cdot L[1] + cdots + o cdot L[n], where o is
the defining order of the elements of L and n is the
number of elements in L. The discriminant is computed as the
determinant of (Tr_{o/Q}(L[i]L[j])).

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Discriminant of {\Bbb Q}(\sqrt{10},\sqrt{5}). 
<pre>

kash> F := OrderMaximal (Order (Z,2,10));;
kash> E := Order (F,2,5);
      F[1]
        /
       /
   E1[1]
  /
 /
Q
F  [ 1]     x^2 - 5
E 1[ 1]     x^2 - 10

kash> EltListAbsDisc (OrderKextGenAbs (E));
0
kash> OrderDisc (OrderMaximal (OrderAbs (E)));
> 1600

</pre>

<p>


<hr>

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