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

Returns the index of the given order relative to its suborder.

<p><p>

<h3>
Syntax:
</h3>
<pre>I := OrderIndex(o);</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  I  </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#OrderDisc">OrderDisc</a>

<p>

<h3>
Description:
</h3>
This function returns the index of the suborder o|1 of
o in o. The index equals
\sqrt{disc(o|1) / disc(o)}.
In the absolute case the index is a rational integer, otherwise
it is an ideal.
If o has no suborder 1 resp. the ideal generated
by the coefficient order is returned.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Computing and checking the index of a maximal order. 
<pre>

kash> o := Order (Poly (Zx,[1,0,-186,0,13097,0,-412704,0,4946176]));
Generating polynomial: x^8 - 186*x^6 + 13097*x^4 - 412704*x^2 + 4946176

kash> OrderIndex (o);
1
kash> O := OrderMaximal (o);
   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> OrderIndex (O);
117012089012224
kash> OrderDisc (o) / OrderDisc (O) - OrderIndex (O)^2;
> 0

</pre>

<p>


<hr>

<p>
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