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

Returns the representation of an object in a group.

<p><p>

<h3>
Syntax:
</h3>
<pre>a := AbelianGroupDiscreteLog(g, b);</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</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Returns the abstract representation a (exponent vector
corresponding to the generators of g) of an element b in the
group g.
For example if g represents a class group of a number field,
then a given ideal is represented by
<tt> AbelianGroupDiscreteLog(g,a)</tt> as an abstract element of this
group.


<p><p>

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

<pre>

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

kash> g := RayResidueRingToAbelianGroup(27*O, [2]);
Group with relations:
[2 0 0 0 0]
[0 9 0 0 0]
[0 0 2 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);
[-174350479000, 82373763000]
kash> a := AbelianGroupDiscreteLog(g, b);
[1 2 1 0 0]


</pre>

<p>

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

<pre>

kash> g := RayClassGroupToAbelianGroup(1*O);
RayClassGroupToAbelianGroup(<1>, [  ])
Group with relations:
[2]
kash> I := Ideal(2,Elt(O,[0,1]));
<2, [0, 1]>
kash> b := AbelianGroupDiscreteLog(g,I);
> [1]

</pre>

<p>


<hr>

<p>
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