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

Returns generators (and their orders) for the multiplicative
group of the residue class ring of an ideal or a congruence module,
as computed by <tt> RayResidueRing</tt>.


<p><p>

<h3>
Syntax:
</h3>
<pre>L := RayResidueRingCyclicFactors(m0 [,minf]);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </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#IdealRayClassRep">IdealRayClassRep</a>, <a href="kashref.html#OrderClassGroup">OrderClassGroup</a>, <a href="kashref.html#RayClassGroup">RayClassGroup</a>

<p>

<h3>
Description:
</h3>
A list containing generators and their orders is computed.
This structure can be used to solve multiplicative
congruences which may involve infinite places.

<p><p>

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

<pre>

kash> O := OrderMaximal(Order(Z,2,10));;
kash> m0 := 7^3*O;; minf := [1,2];;
kash> L := RayResidueRingCyclicFactors(m0,minf);
[ [ [243657, 43632], 48 ], [ 15, 49 ], [ [48021, 357], 49 ], [ [1, 343], 2 ], 
  [ [1, -343], 2 ] ]
kash> EltRayResidueRingRep(L[1][1],m0,minf);
[1 0 0 0 0]
kash> EltCon(L[1][1]);
[105680.50113153327298622427686931162493674837016097 381633.498868466727013775\
72313068837506325162983903]
kash> EltRayResidueRingRep(L[2][1]^2*L[3][1],m0,minf);
[0 2 1 0 0]
kash> EltRayResidueRingRep(L[4][1],m0,minf);
[0 0 0 1 0]
kash> L[4][1] mod m0;
1
kash> EltRayResidueRingRep(L[2][1]^2*L[3][1]*L[4][1],m0,minf);
> [0 2 1 1 0]

</pre>

<p>


<hr>

<p>
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