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

Computes "the next" element of an abelian group.

<p><p>

<h3>
Syntax:
</h3>
<pre>flag := AbelianGroupEnumNext(s);</pre>

<p>

<table>
<tr>
<td>boolean</td>
<td><pre>  flag  </pre></td>
<td><tt> true</tt> iff there is a valid element in <tt> s</tt></td>
</tr>
<tr>
<td>record</td>
<td><pre>  s  </pre></td>
<td>generated by <tt> AbelianGroupEnumInit</tt></td>
</tr>
<tr>
<td>AbelianGroupElt</td>
<td><pre>  s.elt  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
<i>no detailed description available yet</i>

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
We'll produce an ideal in every ray modulo 9 in Q(\sqrt {10}):
<pre>

kash> o := OrderMaximal(Z, 2, 10);
Generating polynomial: x^2 - 10
Discriminant: 40 

kash> G := RayClassGroupToAbelianGroup(9*o);
RayClassGroupToAbelianGroup(<9>, [  ])
Group with relations:
[2 0]
[0 3]
kash> s := AbelianGroupEnumInit(G);
Record of type AbelianGroupEnum

kash> while AbelianGroupEnumNext(s) do
> Print(s.elt, "\t", AbelianGroupDiscreteExp(s.elt), "\n");
> od;
> [0 0]	<1>
[1 1]	<[818, 168], [840, 409]>
[0 2]	<[409, 84]>
[1 0]	<[14, 12], [60, 7]>
[0 1]	<[7, 6]>
[1 2]	<[15806, 6084], [30420, 7903]>

</pre>

<p>


<hr>

<p>
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