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

Handling of possible Galois groups.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := GaloisGroupsPossible(o);
GaloisGroupsPossible(o, G, flag);
GaloisGroupsPossible(o, L, flag);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  G  </pre></td>
<td>representing transitive group in T-notation</td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of integers G</td>
</tr>
<tr>
<td>boolean</td>
<td><pre>  flag  </pre></td>
<td>whether to add or remove groups</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This function is intended for use before calling
<tt> Galois()</tt>. At the beginning of an Galois group computation
there
is a set of possible Galois groups which will be reduced
by computing possible cycle types or block systems for the
Galois group. This function either returns the list of current
possible Galois groups or is able to remove from or add groups
to the list.

<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> GaloisGroupsPossible(o, 49, false);
kash> GaloisGroupsPossible(o, [1, 2, 3, 4, 5], false);
kash> GaloisGroupsPossible(o);
> [ 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, 50 ]

</pre>

<p>


<hr>

<p>
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