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

Returns the order defined by the given arguments.

<p><p>

<h3>
Syntax:
</h3>
<pre>o1 := Order (f);
o1 := Order (o,d,alpha);
o1 := Order (o,T,d);
o1 := Order (o,T,L);
o1 := Order (o,L);</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>
<tr>
<td>polynomial</td>
<td><pre>  f  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  T  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  alpha  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
In the following o may be an arbitrary order or the
ring of rational integers Z. At the moment there
are no checks to ensure that the created module is a ring.
So it is possible that a module is returned
which is not a ring. In this case the representation of
the module can be used as
a representation of the defined number field. Basic
arithmetic with the elements of this number field is
supported.
But be careful when using this module as an argument in functions
which require an order.
Usually these functions do not check this, so it may lead to
an error or even to wrong results
(for example calling <tt> OrderMaximal</tt>).

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Creation of {\Bbb Q}(\sqrt{2})(\sqrt[3]{3}) by polynomials. 
<pre>

kash> o := Order (Poly (Zx,[1,0,-2]));
Generating polynomial: x^2 - 2

kash> ox := PolyAlg (o);
Univariate Polynomial Ring in x over Generating polynomial: x^2 - 2

kash> zero := Elt (o,0);
0
kash> o1 := Order (Poly (ox,[Elt(o,1),zero,zero,Elt (o,-3)]));
>       F[1]
        /
       /
   E1[1]
  /
 /
Q
F  [ 1]     x^3 - 3
E 1[ 1]     x^2 - 2


</pre>

<p>


<hr>

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