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

Returns a reduced representation of a group element.

<p><p>

<h3>
Syntax:
</h3>
<pre>elt2 := AbelianGroupEltReduce(elt1 [, positive]);</pre>

<p>

<table>
<tr>
<td>group element</td>
<td><pre>  elt1  </pre></td>
<td></td>
</tr>
<tr>
<td>group element</td>
<td><pre>  elt2  </pre></td>
<td>reduced representation</td>
</tr>
<tr>
<td>boolean</td>
<td><pre>  positive  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Returns the reduced representation <tt>elt2</tt> of a group element
(exponent vector) <tt>elt1</tt>.
If the second (optional) parameter is <tt>true</tt> then all
entries of <tt>elt2</tt> are non negative. Only in this case it is
sure that a good reduction is performed.


<p><p>

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

<pre>

kash> g := AbelianGroupCreate(Mat(Z, [[2,1], [1,3]]));
Group with relations:
[2 1]
[1 3]
kash> elt1 := AbelianGroupEltCreate(g, [-100, -217]);
[-100 -217]
kash> elt2 := AbelianGroupEltReduce(elt1);
[-100 -217]
kash> AbelianGroupSmithCreate(g);
Group with relations:
[5]
kash> elt2 := AbelianGroupEltReduce(elt1);
[-1  0]
kash> elt2 := AbelianGroupEltReduce(elt1, true);
> [4 0]

</pre>

<p>


<hr>

<p>
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