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

Chinese Remainder Theorem for number fields

<p><p>

<h3>
Syntax:
</h3>
<pre>beta := IdealChineseRemainder(a1, a2, alpha1, alpha2)</pre>

<p>

<table>
<tr>
<td>ideals </td>
<td><pre>  a1, a2  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic numbers </td>
<td><pre>  alpha1, alpha2  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic number</td>
<td><pre>  beta  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Computes an algebraic number \beta in the order o, such that
\alpha|i - \beta
is contained in the ideal \a|i, i = 1,2.

<p><p>

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

<pre>

kash> O := OrderMaximal (Order (Poly(Zx,[1,0,73,-280,-2399])));;
kash> a1 := Factor (2*O)[1][1];
<2, [1, 2, 0, 1]>
kash> a2 := Factor (NextPrime (4343343)*O)[1][1];
<4343357, [1353610, 1860090, 2, 0]>
kash> beta := IdealChineseRemainder (a1, a2, Elt (O,[1,2,3,5]), Elt (O, 4));
[4, 4343357, 0, 0]
kash> Valuation (a1, beta - Elt (O,[1,2,3,5]));
2
kash> Valuation (a2, beta - Elt (O,4));
> 1

</pre>

<p>


<hr>

<p>
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