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

Returns the object corresponding to a representation in a group.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := AbelianGroupDiscreteExp(a);</pre>

<p>

<table>
<tr>
<td>group</td>
<td><pre>  g  </pre></td>
<td></td>
</tr>
<tr>
<td>group element</td>
<td><pre>  a  </pre></td>
<td>representation of b in the abstract group g</td>
</tr>
<tr>
<td>object or boolean</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Returns the concrete object b corresponding to the abstact
representation of a in g. For example, if the abstract group g
represents a concrete class group of a number field, then
<tt> AbelianGroupDiscreteExp(a)</tt> calculates an Ideal <tt> b</tt>,
that is representing a class of ideals in the class group.
If g is the dual group of a given group, a \in g, then
b:=<tt> AbelianGroupDiscreteExp(a)</tt> is the homomorphism
represented by a. In this form it can directly be used to
evaluate element of the original group, to witch g is dual.

If no element is found, false is returned.


<p><p>

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

<pre>

kash> O := OrderMaximal(x^2-2*x-5);
Generating polynomial: x^2 - 2*x - 5
Discriminant: 24 

kash> g := RayResidueRingToAbelianGroup(27*O, [2]);
Group with relations:
[2 0 0 0 0]
[0 3 0 0 0]
[0 0 9 0 0]
[0 0 0 9 0]
[0 0 0 0 2]
kash> a := AbelianGroupEltCreate(g, [1, 2, 3, 0, 0]);
[1 2 3 0 0]
kash> b := AbelianGroupDiscreteExp(a);
[-337479530000, -232975502000]
kash> a := AbelianGroupDiscreteLog(g, b);
> [1 2 3 0 0]

</pre>

<p>


<hr>

<p>
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