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

Returns a basis whose elements are elements of the given order with
a denominator.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderBasis(o);
L := OrderBasis(o, O);</pre>

<p>

<table>
<tr>
<td>list of algebraic elements</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </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#OrderCoefIdeals">OrderCoefIdeals</a>

<p>

<h3>
Description:
</h3>
If the second order is omitted, the basis returned consists of
elements of the equation order. Otherwise the elements are moved
into the second order. In the relative case the basis elements
of the pseudo basis are returned.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
A basis of the maximal order of  x^4 + 73x^2 - 280x - 2399
represented in the equation order and in the maximal order itself. 
<pre>

kash> O := OrderMaximal (Poly (Zx,[1,0, 73, -280, -2399]));
   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 (O);
[ 1, [0, 1, 0, 0], [1, 1, 1, 0] / 2, [414, 857, 795, 1] / 1646 ]
kash> OrderBasis (O, O);
> [ 1, [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] ]

</pre>

<p>


<hr>

<p>
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