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

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

Computes the normal closure of an algebraic number field.

<p><p>

<h3>
Syntax:
</h3>
<pre>O := OrderSplittingField (o);</pre>

<p>

<table>
<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>


<h3>
Description:
</h3>
Let o be an absolute order. The <tt> OrderSplittingField</tt>
function computes an equation order of the normal closure of
the quotient field of o.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Computation of an equation order O of the normal closure of
the quotient field of the absolut order o and
the factorization of the generating polynomial f for o
in O
<pre>

kash> o := Order(Z,3,2);
Generating polynomial: x^3 - 2

kash> O := OrderSplittingField(o);
Generating polynomial: x^6 - 3*x^5 + 5*x^3 - 3*x + 1
Discriminant: -34992 

kash> f := PolyMove(x^3-2, O );
x^3 - 2
kash> Factor(f);
> [ [ x + [-1, -1, 1, 0, 0, 0], 1 ], [ x + [5, -5, -10, 3, 5, -2], 1 ], 
  [ x + [-4, 6, 9, -3, -5, 2], 1 ] ]

</pre>

<p>


<hr>

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