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

Returns a basis of a finite abelian group.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AbelianGroupBasis(g [, exp]);</pre>

<p>

<table>
<tr>
<td>group</td>
<td><pre>  g  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>list of basis elements of g</td>
</tr>
<tr>
<td>boolean</td>
<td><pre>  exp  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Returns a list of basis elements of the group g. If the second
(optional) parameter exp is <tt>true</tt> then the discrete exp is
applied.


<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the basis of a ray class group: 
<pre>

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

kash> g := RayClassGroupToAbelianGroup(3*O, [1, 2]);
RayClassGroupToAbelianGroup(<3>, [ 1, 2 ])
Group with relations:
[4 0]
[0 2]
kash> l := AbelianGroupBasis(g);
[ [0 1], [1 0] ]
kash> l := AbelianGroupBasis(g, true);
> [ <2, [0, 1]>, <[1, -3]> ]

</pre>

<p>


<hr>

<p>
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