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

Solves a Thue equation.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := ThueSolve(t,a [,"exact"|"abs"]);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>Thue object</td>
<td><pre>  t  </pre></td>
<td></td>
</tr>
<tr>
<td>int</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#Solve">Solve</a>, <a href="kashref.html#Thue">Thue</a>, <a href="kashref.html#ThueEval">ThueEval</a>

<p>

<h3>
Description:
</h3>
Let f(X,Y) \in Z[X,Y] be the homogeneous polynomial
of the <sf> Thue</sf> object <sf> t</sf> generated by the <sf> KASH</sf>
function <tt> Thue</tt>. The <tt> ThueSolve</tt> function determines all
x,y \in Z such that f(x,y) = a. \smallskip

If the third argument equals <tt> "abs"</tt> the <tt> ThueSolve</tt>
function will compute all x,y \in Z with |f(x,y)|=a.
The calling sequence <tt> ThueSolve(t,a,"exact")</tt> is
tantamount to <tt> ThueSolve(t,a)</tt>. \smallskip

The implementation of the <tt> ThueSolve</tt> function in {\sf
KASH} bases on the algorithm of Y.Bilu and G.Hanrot
BiHa.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute all x,y \in {Z} with
x^3 + x^2 y - 6 x y^2 + 2 y^3 = 2. 
<pre>

kash> t := Thue([1,1,-6,2]);
X^3 + X^2 Y - 6 X Y^2 + 2 Y^3
kash> ThueSolve(t,2);
> [ [ -724, -411 ], [ -4, -11 ], [ -3, 1 ], [ -1, -1 ], [ 0, 1 ], [ 2, 1 ] ]

</pre>

<p>


<hr>

<p>
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