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

Returns current root ordering.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := GaloisRoots(o);
L := GaloisRoots(o,k);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>int</td>
<td><pre>  k  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of list of roots and permutation</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This function returns a list of the roots
of the generating polynomial in the current ordering
and a permutation giving this ordering in view of the
standard ordering as returned by <tt> Solve()</tt>. After
computation by <tt> Galois()</tt> the action of the Galois group
on this root ordering is equivalent to the computed
transitive permutation group as classified in GAP GAP.
Is the second parameter k used, the roots are returned with
precision k for the complex case and p^k in p-adic case.

<p><p>

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

<pre>

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

kash> Galois(o);
"2D_8(8)"
kash> GaloisRoots(o);
> [ [ -171, [1171, -5618], [0, -384], [1171, 5618], 171, [-1171, 5618], 
      [0, 384], [-1171, -5618] ], (2,5)(4,6,7) ]

</pre>

<p>


<hr>

<p>
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