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

Lifts an idempotent.

<p><p>

<h3>
Syntax:
</h3>
<pre>alpha:=IdemLift(a, p, k);</pre>

<p>

<table>
<tr>
<td>algebraic element</td>
<td><pre>  alpha  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  p  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  k  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
<tt> a</tt> is an idempotent for a prime ideal \p over <tt> p</tt>. This
function calculates the idempotent \alpha corresponding
to the ideal \p^{2^{<tt> k</tt>}}.

<p><p>

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

<pre>

kash> O:=OrderMaximal(Order(Poly(Zx,[1,0,-4,0,1])));
Generating polynomial: x^4 - 4*x^2 + 1
Discriminant: 2304 

kash> L:=Factor(5*O);
[ [ <5, [1, 1, 1, 0]>, 1 ], [ <5, [1, 4, 1, 0]>, 1 ] ]
kash> L1:=IdealIdempotents([L[1][1],L[2][1]]);
[ [-2, 0, 0, 2], [3, 0, 0, -2] ]
kash> IdemLift(L1[1],5,3);
> [-195312, 112715, 0, -22543]

</pre>

<p>


<hr>

<p>
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