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

Lifts an algebraic element with the Newton lifting method.

<p><p>

<h3>
Syntax:
</h3>
<pre>beta := PolyNewtonLift(f, alpha, k);
beta := PolyNewtonLift(f, alpha, k, a);</pre>

<p>

<table>
<tr>
<td>algebraic element</td>
<td><pre>  alpha  </pre></td>
<td></td>
</tr>
<tr>
<td>integer (0 if omitted)</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>  k  </pre></td>
<td></td>
</tr>
<tr>
<td>polynomial</td>
<td><pre>  beta  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Given an algebraic element <tt> alpha</tt> with
<tt> f</tt>(<tt> alpha</tt>) \equiv 0 \bmod <tt> (t-a)</tt>,
this function calculates an algebraic element \beta\in o[t] with
<tt> f</tt>(\beta) \equiv 0 \bmod <tt> (t-a)</tt>^<tt> k</tt>.

<p><p>

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

<pre>

kash> AlffInit(Q,"t","X");
"Defining global variables: k, w, kt, ktf, ktX, t, X, AlffGlobals"
kash> f:=X^4-2+t;
X^4 + t - 2
kash> o:=Order(Z,4,2);
Generating polynomial: x^4 - 2

kash> alpha:=OrderBasis(o)[2];
[0, 1, 0, 0]
kash> beta:=PolyNewtonLift(f,alpha,5);
> [0, -77, 0, 0] / 32768*t^4 + [0, -7, 0, 0] / 1024*t^3 + [0, -3, 0, 0] / 128*t^\
2 + [0, -1, 0, 0] / 8*t + [0, 1, 0, 0]

</pre>

<p>


<hr>

<p>
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