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<h2><a name="RayCantoneseRemainder"></a>
RayCantoneseRemainder
</h2>

missing shortdoc

<p><p>

<h3>
Syntax:
</h3>
<pre>elt := RayCantoneseRemainder(m0,minf,elt0,sig);</pre>

<p>

<table>
<tr>
<td>ideal </td>
<td><pre>  m0  </pre></td>
<td></td>
</tr>
<tr>
<td>list of integers/infinite primes</td>
<td><pre>  minf  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic number </td>
<td><pre>  elt0  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  sig  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic number </td>
<td><pre>  elt  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Returns an algebraic number <tt> elt</tt>, which is congruent
to <tt> elt0</tt> \pmod {<tt> m0</tt>} and
whose real conjugates have the signature as chosen by <tt> sig</tt>
at the
places of <tt> minf</tt>. The algorithm is described in Pau1.
<tt> sig</tt> is a vector/matrix, which consists of 0's and 1's.
A 1 in the i'th position means that elt has
a negative conjugate at the i'th
place of <tt> minf</tt> (which must be sorted!), a 0 means that it
has positive conjugate.

<p><p>

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

<pre>

kash> O := OrderMaximal(Z,4,5);
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^4 - 5
Discriminant: -2000 

kash> m0 := 12*O;; minf := [1,2];;
kash> elt0 := Elt(O,[1,2,3,4]);;sig := [1,0];;IsMat(sig);;
kash> elt := RayCantoneseRemainder(m0,minf,elt0,sig);
[5029, -2590, 3591, -2300]
kash> elt mod m0;
[1, 2, 3, 4]
kash> EltCon(elt);
> [-5910.979315905677215736970806158202922913622694351555 12964.7430748579057138\
0121401249028054286746099661 640.118120523885750967878396833961190023080848871\
131 - 1747.347688152938188731912066849790464428137141477991*i 640.118120523885\
750967878396833961190023080848871131 + 1747.3476881529381887319120668497904644\
28137141477991*i]

</pre>

<p>


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