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

Lifts an algebraic element with the Newton lifting method.

<p><p>

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

<p>

<table>
<tr>
<td>algebraic element</td>
<td><pre>  alpha  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>polynomial</td>
<td><pre>  f  </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>
Given an algebraic element <tt> a</tt> with
<tt> f</tt>(<tt> a</tt>) \equiv 0 \bmod <tt> p o</tt>,
this function calculates an algebraic element \alpha with
<tt> f</tt>(\alpha) \equiv 0 \bmod <tt> p</tt>^{2^{<tt> k</tt>}}<tt> o</tt>.

<p><p>

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

<pre>

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

kash> f:=Poly(Zx,[1,40,596,3920,9601]);
x^4 + 40*x^3 + 596*x^2 + 3920*x + 9601
kash> a:=Elt(o,[0,4,0,0]);
[0, 4, 0, 0]
kash> b:=EltNewtonLift(o,a,f,5,2);
[-10, -1, 0, 0]
kash> Eval(f, b);
> 0

</pre>

<p>


<hr>

<p>
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