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

Solves a unit equation.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderUnitsEquation (alpha,beta,gamma);
L := OrderUnitsEquation (alpha,beta);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic elements</td>
<td><pre>  alpha, beta, gamma  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let \alpha,\beta,\gamma be non-zero elements of a certain
order o. We denote by \U the unit group of o.
The <tt> OrderUnitsEquation</tt> function computes all
(\varepsilon_1,\varepsilon_2) \in \U\times \U satisfying
 \alpha cdot \varepsilon_1 + \beta cdot \varepsilon_2
= \gamma.

If the third argument is omitted, \gamma = 1 is used by default.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute all units \varepsilon_1,\varepsilon_2
\in Z[\sqrt[4]{5}] with 1 cdot \varepsilon_1 + 2 cdot
\varepsilon_2 = 3.
<pre>

kash> o := Order(Z,4,5);
Generating polynomial: x^4 - 5

kash> one := Elt(o,1);
1
kash> OrderUnitsEquation(one,2*one,3*one);
> [ [ 1, 1 ] ]

</pre>

<p>


<hr>

<p>
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