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

Returns elements of the comaximal ideals which sum to 1.

<p><p>

<h3>
Syntax:
</h3>
<pre>E := IdealIdempotents(L)</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of integral ideals over the same order</td>
</tr>
<tr>
<td>false or list</td>
<td><pre>  E  </pre></td>
<td>of algebraic elements over the same order</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let L be the list of ideals [ I|1,  &hellip;  ,I|n ].

This function tries to find algebraic elements a|i in I|i such that:
\sum a|i = 1.
The function will return false
if this in not possible
(iff I|1,  &hellip;  ,I|n are NOT comaximal).

Otherwise it returns the list [ a|1,  &hellip;  ,a|n ]
of elements which sum to one.
Each entry of E is an
element of the ideal in L with the same index.

Fractional ideals are allowed and considered as the biggest integral
ideal which contains the fractional ideal, i.e. disregarding the
denominator.

<p><p>

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

<pre>

kash> O := OrderMaximal(Order(Z,2,- 45));;
kash> L := List( Factor(210*O), x->x[1]);
[ <2, [1, 3]>, <3, [1, 2]>, <3, [7, 7]>, <5, [0, 3]>, <7, [2, 3]>, 
  <7, [5, 3]> ]
kash> E := IdealIdempotents([L[2]*L[6]*L[3],L[2]*L[4],L[1]*L[4]*L[6]]);
> [ 966, -1035, 70 ]

</pre>

<p>


<hr>

<p>
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