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

Computes extension fields which contain the given ones.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderMerge(o1,o2);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>return value</td>
</tr>
<tr>
<td>order</td>
<td><pre>  o1  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o2  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
This function computes fields which contain the given ones.
It is possible to get more than one field (see example).
The output is a list of generating polynomials for these fields.

Let \alpha|i, \beta|j be the zeroes of the defining polynomials
of o|1 and o|2. After a substitution of the form
\beta|i \mapsto \beta|i+s, s\in\N appropriate,
all \alpha|i + \beta|j are pairwise distinct.
The polynomial f := \prod|{i,j} (x-\alpha|i - \beta|j) is computed,
and the irreducible factors are returned.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the following splitting field. 
<pre>

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

kash> L:=OrderMerge(o,o);
> [ Generating polynomial: x^3 - 54
    , Generating polynomial: x^6 + 108
     ]

</pre>

<p>


<hr>

<p>
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