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

Returns a canonical representative of an element of the
multiplicative group of the residue class ring of a congruence
module.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := RayResidueRingRepToElt( r, m0, minf);</pre>

<p>

<table>
<tr>
<td>algebraic element</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix </td>
<td><pre>  r  </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#RayResidueRing">RayResidueRing</a>, <a href="kashref.html#RayResidueRingCyclicFactors">RayResidueRingCyclicFactors</a>, <a href="kashref.html#EltRayResidueRingRep">EltRayResidueRingRep</a>

<p>

<h3>
Description:
</h3>
This is the inverse to <tt> EltRayResidueRingRep</tt>. The function will
compute the following product:
\prod|{i=1}^l a|i^{<tt> r</tt>|i}
with a|i the multiplicative basis for (o/{\goth{m}}_0)^* as
returned by <tt> RayResidueRingCyclicFactors</tt>.

<p><p>

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

<pre>

kash> O := OrderMaximal(Order(Poly(Zx,[1,3,-4,7])));;
kash> m0 := 15*O;;
kash> a := Elt(O,[7,1,8]);;
kash> r := EltRayResidueRingRep(a,m0);
[20 65]
kash> b := RayResidueRingRepToElt(r,m0);
[7, 1, 8]

</pre>

<p>


<hr>

<p>
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