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

Creates an order with LLL-reduced basis.

<p><p>

<h3>
Syntax:
</h3>
<pre>o1 := OrderLLL(O);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  o1  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Creates an overorder o|1 of the given order o
via transformation, so that the basis of the
new order o|1 is LLL-reduced.

<p><p>

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

<pre>

kash> o := Order (Poly(Zx,[1,0,73,-280,-2399]));;
kash> O1 := OrderMaximal (o);
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^4 + 73*x^2 - 280*x - 2399
Discriminant: -997975 

kash> O2 := OrderSimplify (OrderLLL (O1));
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^4 + 73*x^2 - 280*x - 2399
Discriminant: -997975 

kash> OrderBasis (O1);
[ 1, [0, 1, 0, 0], [1, 1, 1, 0] / 2, [414, 857, 795, 1] / 1646 ]
kash> OrderBasis (O2);
> [ 1, [2055, -34, 28, -1] / 1646, [-4045, 1775, 39, 28] / 1646, 
  [2055, -1680, 28, -1] / 1646 ]

</pre>

<p>


<hr>

<p>
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