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

Returns a generator for the group of torsion units of
the given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>u := OrderTorsionUnit(o);</pre>

<p>

<table>
<tr>
<td>algebraic element</td>
<td><pre>  u  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
o must be an absolute order.
<tt> OrderTorsionUnit</tt> returns an algebraic element
u, which is a generator
for the group of roots of unity in the order o.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Computing generators for the groups of roots of unity
in an equation order and the corresponding maximal order. 
<pre>

kash> o := Order (Poly (Zx,[1,0,-186,0,13097,0,-412704,0, 4946176]));
Generating polynomial: x^8 - 186*x^6 + 13097*x^4 - 412704*x^2 + 4946176

kash> OrderTorsionUnit (o);
-1
kash> O := OrderMaximal (o);;
kash> OrderTorsionUnit (O);
> [15, -80, 10, -9, 10, -20, -51, 102]

</pre>

<p>


<hr>

<p>
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