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

Tests Quo(<tt> o</tt>|1)\subseteq Quo(<tt> o</tt>|2).

<p><p>

<h3>
Syntax:
</h3>
<pre>OrderIsSubfield(o1, o2);</pre>

<p>

<table>
<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 checks whether
Quo(<tt> o</tt>|1)\subseteq Quo(<tt> o</tt>|2)
and returns
true or false. If true is returned, a homomorphism between
<tt> o</tt>|1 and <tt> o</tt>|2 is saved (globally) for further
usage in, say, moving elements from <tt> o</tt>|1 and <tt> o</tt>|2.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Check a certain subfield. 
<pre>

kash> o1 := Order (Z,2,3);
Generating polynomial: x^2 - 3

kash> o2 := Order (o1, 2, 2);
      F[1]
        /
       /
   E1[1]
  /
 /
Q
F  [ 1]     x^2 - 2
E 1[ 1]     x^2 - 3

kash> M := EltRepMat (Elt (o2,[[0,1], 1]),Z)[2];
[0 3 2 0]
[1 0 0 2]
[1 0 0 3]
[0 1 1 0]
kash> o3 := Order (MatMinPoly (M));
Generating polynomial: x^4 - 10*x^2 + 1

kash> EltMove (Elt (o1,[0,1]), o3);
[0, -11, 0, 1] / 2
kash> OrderIsSubfield (o1, o3);
> true

</pre>

<p>


<hr>

<p>
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