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

Returns a representive of the class of an algebraic element in the
multiplicative group of the ray residue ring.

<p><p>

<h3>
Syntax:
</h3>
<pre>r := EltRayResidueRingRep(elt,m0,minf);</pre>

<p>

<table>
<tr>
<td>matrix</td>
<td><pre>  r  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element </td>
<td><pre>  elt  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal </td>
<td><pre>  m0  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  minf  </pre></td>
<td>of integers/infinite primes</td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#EltCon">EltCon</a>, <a href="kashref.html#RayResidueRing">RayResidueRing</a>, <a href="kashref.html#RayResidueRingRepToElt">RayResidueRingRepToElt</a>, <a href="kashref.html#RayResidueRingCyclicFactors">RayResidueRingCyclicFactors</a>

<p>

<h3>
Description:
</h3>
Calculates a representative of an algebraic element <tt> elt</tt>
which is represented by a matrix [a_0, &hellip; ,a_k]. If
\eta_0, &hellip; ,\eta_k is a basis of the residue ring as given by
<tt> RayResidueRingCyclicFactors</tt>, <tt> elt</tt> \equiv
\eta_0^{a_0}cdots\eta_k^{a_k} mod^*
{({\goth{m}}_0 {\goth{m}}_\infty)} holds.

If the residue ring is not known yet, it will be computed.
Infinite primes are represented in the same way as for
RayResidueRing.

This function uses a mixture of the discrete logarithm algorithms
developed in Pau1,Pau2 and CDOants,CDO1.

<p><p>

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

<pre>

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

kash> m0 := 27*O;;
kash> minf := [2];;
kash> L := RayResidueRingCyclicFactors(m0,minf);
[ [ [-1, -27], 2 ], [ [1344, 388], 3 ], [ [5, 2], 9 ], [ [1612, 444], 9 ], 
  [ [1, 27], 2 ] ]
kash> elt := L[1][1];
[-1, -27]
kash> EltRayResidueRingRep(elt,m0,minf);
[1 0 0 0 0]

</pre>

<p>


<hr>

<p>
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