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

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

Excluding impossible Galois groups by cycle types.

<p><p>

<h3>
Syntax:
</h3>
<pre>GaloisModulo(o, b);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  b  </pre></td>
<td>bound</td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#Galois">Galois</a>, <a href="kashref.html#GaloisBlocks">GaloisBlocks</a>, <a href="kashref.html#GaloisGroupsPossible">GaloisGroupsPossible</a>, <a href="kashref.html#GaloisTree">GaloisTree</a>

<p>

<h3>
Description:
</h3>
This function computes cycle types of the Galois group
by factoring the generating polynomial modulo some prime
numbers up to a given bound. Transitive groups without
the cycle types are excluded from the list of possible
Galois groups and the list is returned.

<p><p>

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

<pre>

kash> o := Order(Z, 8, 2);
Generating polynomial: x^8 - 2

kash> GaloisGroupsPossible(o);
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 
  22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 
  41, 42, 43, 44, 45, 46, 47, 48, 49, 50 ]
kash> GaloisModulo(o, 100);
> [ 6, 8, 15, 23, 26, 27, 35, 40, 43, 44, 47, 50 ]

</pre>

<p>


<hr>

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