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

missing shortdoc

<p><p>

<h3>
Syntax:
</h3>
<pre>g := IdealGen(I, i);</pre>

<p>

<table>
<tr>
<td>algebraic element</td>
<td><pre>  g  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
<tr>
<td>small integer</td>
<td><pre>  i  </pre></td>
<td>{\in{1,2}}</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Any ideal <tt> I</tt> of a maximal order o may be generated using
two elements g_1 and g_2 (i.e. <tt> I</tt> = g_1o + g_2o).
This functions returns g_i (i\in{1,2}) after computing
suitable generators if necessary.

The restriction to maximal orders is only necessary to compute the
generators. Note that the generators are not unique! In fact
since the algorithm is probabilistic, they may change
between two sessions.

<p><p>

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

<pre>

kash> O := Order(Poly(Zx, [1, 6, 6, 6]));;
kash> alpha := Elt(O, [0, 1, 0]);;
kash> I := Ideal(6, alpha);
<6, [0, 1, 0]>
kash> IdealGen(I, 1);
6
kash> IdealGen(I, 2);
> [0, 1, 0]

</pre>

<p>


<hr>

<p>
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