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

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

Returns the trace matrix of the order.

<p><p>

<h3>
Syntax:
</h3>
<pre>M := OrderTraceMat(o);</pre>

<p>

<table>
<tr>
<td>Matrix</td>
<td><pre>  M  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
<tt> OrderTraceMat</tt> returns the the trace matrix of the
given order o. Let o be given by a (pseudo) basis
omega|1,  &hellip; , omega|n (we ignore the coefficient
ideals here). The <tt> OrderTraceMat</tt>
M = (\Tr(omega|i omega|j))_{i,j}.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Extracting the equation order of an arbitrary order. 
<pre>

kash> O := OrderMaximal(Poly (Zx,[1,0,-186,0,13097,0,-412704,0,4946176]));
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^8 - 186*x^6 + 13097*x^4 - 412704*x^2 + 4946176
Discriminant: 60050488100625 

kash> M := OrderTraceMat(O);
> [      8       0     186       4    1120     657     774     387]
[      0     372     186    2426     186   24657       0    5304]
[    186     186    4294    1306   24471   26711   16664   10984]
[      4    2426    1306   15364    1773  147638     387   32097]
[   1120     186   24471    1773  133394   91728   89382   47343]
[    657   24657   26711  147638   91728 1282603   53410  298835]
[    774       0   16664     387   89382   53410   59566   29783]
[    387    5304   10984   32097   47343  298835   29783   74701]

</pre>

<p>


<hr>

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