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

Creates a <sf> thue</sf> object for solving Thue equations.

<p><p>

<h3>
Syntax:
</h3>
<pre>t := Thue(o);
t := Thue(L);
t := Thue(f);</pre>

<p>

<table>
<tr>
<td>Thue object</td>
<td><pre>  t  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>polynomial</td>
<td><pre>  f  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
One classical object of number theory is the Diophantine
equation of Thue
 f(X,Y) = a, 
where f(X,Y) \in {Z}[X,Y] is a homogeneous
polynomial of degree n  &lt;=  3 and a is an integer. \smallskip

Before solving a Thue equation in <sf> KASH</sf> the form f
on the left side has to be created by invoking the {\tt
Thue} function. \bigskip

<tt> Thue(o)</tt>
takes the coefficients of the form from the polynomial defining
the order <tt> o</tt>.\medskip

<tt> Thue(L)</tt>
takes the coefficients from the list <tt> L</tt>.\medskip

<tt> Thue(f)</tt>
takes the coefficients from the polynomial <tt> f</tt>.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Create the <sf> Thue</sf> object corresponding to the form
f(X,Y) = X^3 + X^2 Y - 6 X Y^2 + 2 Y^3. 
<pre>

kash> o := Order(Poly(Zx,[1,1,-6,2]));
Generating polynomial: x^3 + x^2 - 6*x + 2

kash> t := Thue(o);
X^3 + X^2 Y - 6 X Y^2 + 2 Y^3
kash> L := [1,1,-6,2];
[ 1, 1, -6, 2 ]
kash> t := Thue(L);
X^3 + X^2 Y - 6 X Y^2 + 2 Y^3
kash> f := Poly(Zx,[1,1,-6,2]);
x^3 + x^2 - 6*x + 2
kash> t := Thue(f);
> X^3 + X^2 Y - 6 X Y^2 + 2 Y^3

</pre>

<p>


<hr>

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