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

Computes a representation of the ideal class over the
cyclic generators of the class group.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := IdealClassRep(I);
L := IdealClassRep(I, "gen");</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#OrderClassGroup">OrderClassGroup</a>, <a href="kashref.html#IdealIsPrincipal">IdealIsPrincipal</a>, <a href="kashref.html#IdealRayClassRep">IdealRayClassRep</a>

<p>

<h3>
Description:
</h3>
If {\goth{a}}|1,  &hellip; , {\goth{a}}|k are the cyclic generators
of the class group as returned by {\tt
OrderClassGroupCyclicFactors}, for an ideal \goth{b}
this function computes a representation of the form
 {\goth{b}} = \alpha \prod|{i=1}^k {\goth{a}}|i^{s|i}  with
 \alpha  an algebraic element. The result is stored in a
list of the form { \alpha, { {\goth{a}}|1 , s|1 },  &hellip; ,
{ {\goth{a}}|k, s|k } }, where  \alpha  is omitted when the
second parameter "gen" is not given.

<p><p>

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

<pre>

kash> o := OrderMaximal(Order(x^3-117));;
kash> OrderClassGroup(o, euler);
[ 3, [ 3 ] ]
kash> OrderClassGroupCyclicFactors(o);
[ [ <2, [1, 1, 3]>, 3 ] ]
kash> p := Factor(1021*o)[1][1];
<1021, [499, 1, 0]>
kash> L := IdealClassRep(p, "gen");
[ [287, 59, 36] / 2, [ <2, [1, 1, 3]>, 1 ] ]
kash> alpha := L[1];
[287, 59, 36] / 2
kash> a1 := L[2][1];
<2, [1, 1, 3]>
kash> s1 := L[2][2];
1
kash> alpha*a1^s1/p;
> <
[1 0 0]
[0 1 0]
[0 0 1]
>


</pre>

<p>


<hr>

<p>
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