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

Calculates subfields with specified block systems.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderSubfieldSub(o, p);
L := OrderSubfieldSub(o, p, d);
L := OrderSubfieldSub(o, p, d, L1);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  p  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L1  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#OrderSubfield">OrderSubfield</a>

<p>

<h3>
Description:
</h3>
This function calculates non-trivial subfields
of Quo(<tt> o</tt>) using a special prime number <tt> p</tt>,
which may not divide the discriminant of the
equation order of <tt> o</tt>.
If <tt> d</tt> is specified, only subfields of relative
degree <tt> d</tt> are calculated. <tt> L1</tt> is a potential
block system of the form [block|1, &hellip; ,block|r].

The computation time is dependent on the cycle
decomposition corresponding to the prime <tt> p</tt>.
It is very difficult to choose a "good" prime. In some
cases it is better to use this function instead of
<tt> OrderSubfield</tt>.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> o:=Order(Poly(Zx,[1,0,-4,0,1]));
Generating polynomial: x^4 - 4*x^2 + 1

kash> OrderSubfieldSub(o,5);
[ Generating polynomial: x^2 - 4*x - 2
    , Generating polynomial: x^2 - 2
    , Generating polynomial: x^2 + 4*x + 1
     ]
kash> o:=Order(Poly(Zx,[1,0,-4,0,1]));
Generating polynomial: x^4 - 4*x^2 + 1

kash> OrderSubfieldSub(o,5);
> [ Generating polynomial: x^2 - 4*x - 2
    , Generating polynomial: x^2 - 2
    , Generating polynomial: x^2 + 4*x + 1
     ]

</pre>

<p>


<hr>

<p>
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