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

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

Returns the floor of the Minkowski bound of the algebraic
number field which is generated by the given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>m := OrderMinkowski(O);</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  m  </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#OrderBach">OrderBach</a>

<p>

<h3>
Description:
</h3>
Returns the floor of the Minkowski bound of the algebraic
number field which is generated by the maximal order O.
Returns an error if O is not known to be maximal.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the floor of the Minkowski bound of the algebraic
number field {\Bbb Q}(\sqrt[4]{-27}). 
<pre>

kash> o := Order(Z,4,-27);
Generating polynomial: x^4 + 27

kash> O := OrderMaximal(o);
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^4 + 27
Discriminant: 432 

kash> OrderMinkowski(O);
> 3

</pre>

<p>


<hr>

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