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

Solves an index form equation.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderIndexFormEquation(o,index);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  index  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let o be an order over Z. We say that algebraic integers
a, b \in o are Z-equivalent iff a - b or a + b is
a rational integer. The <tt> OrderIndexFormEquation</tt>
function computes a full set of pairwise inequivalent
\alpha \in o such that the module index
(o:Z[\alpha]) equals <tt> index</tt>. Note that this set
is always finite due to a result of K.~Gy\H{o}ry.\medskip

At present, the <tt> OrderIndexFormEquation</tt> function can
only handle cubic and quartic fields. Algorithms are taken
from GaPePo1,GaPePo2,GaSch.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute - up to Z-equivalence - all generators of power
integral bases of
Z[\sqrt[3]{2}] : 
<pre>

kash> o := Order(Z,3,2);
Generating polynomial: x^3 - 2

kash> OrderIndexFormEquation(o,1);
> [ [0, 1, 0], [0, 1, 1] ]

</pre>

<p>


<hr>

<p>
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