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

Solves a special equation.

<p><p>

<h3>
Syntax:
</h3>
<pre>M := IdealCollection(I1,I2);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  M  </pre></td>
<td>two lists of two elements of the order</td>
</tr>
<tr>
<td>ideals</td>
<td><pre>  I1,I2  </pre></td>
<td>integral, over a maximal order</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let \alpha|1, \alpha|2 be two
algebraic numbers and {\goth{I}}|1, {\goth{I}}|2 two ideals
over the same order O.
The result of this function is a matrix M which satisfies
 \alpha|1 {\goth{I}}|1 + \alpha|2 {\goth{I}}|2 =
\beta|1 O + \beta|2 {\goth{I}}|1 {\goth{I}}|2 
where
 {\beta|1choose\beta|2}= {\alpha|1choose\alpha|2} M. 

<p><p>

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

<pre>

kash> O := OrderMaximal(Poly(Zx, [1, 6, 6, 6]));;
kash> I1:=Ideal(6,Elt(O,[0,0,1]));
<6, [0, 0, 1]>
kash> I2:=Ideal(3,Elt(O,[0,1,1]));
<3, [0, 1, 1]>
kash> M := IdealCollection(I1,I2);
[ [ [0, 0, 1], 0 ], [ -1, [0, 5, 1] / 6 ] ]
kash> M[1][1]*M[2][2]-M[1][2]*M[2][1];
1
kash> a1 := Elt(O,[2,1,0]);
[2, 1, 0]
kash> a2 := Elt(O,[0,1,-1]);
[0, 1, -1]
kash> b1 := a1 * M[1][1] + a2 * M[1][2];;
kash> b2 := a1 * M[2][1] + a2 * M[2][2];;
kash> a1*I1+a2*I2 = b1*O+b2*I1*I2;
> true

</pre>

<p>


<hr>

<p>
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