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

Computes the intersection of two modules.

<p><p>

<h3>
Syntax:
</h3>
<pre>M :=ModuleIntersection(M1, M2 [,d | I] [,"PBNF"] [,"lower"] );</pre>

<p>

<table>
<tr>
<td>modules </td>
<td><pre>  M, M1, M2  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  d  </pre></td>
<td>used for reduction</td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td>used for reduction</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This function computes the intersetion M_1 cap M_2 of the
given modules. Both modules must be of full rank.

The additional parameters control the normal form algorithm
application. For their description see <tt> ModuleNF</tt>.

The algorithm computes the dual module of the sum of
the dual moduls of the input, it is described in
Hop1.

<p><p>

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

<pre>
kash>  O:=OrderMaximal(Poly(Zx, [1,-10,-3,-2]));;
kash> o:=OrderMaximal(O,3,3);;
kash> Oa:=OrderMaximal(OrderAbs(o));;
kash> L:=List(Factor(10*Oa),i->i[1]);;
kash> M1:=IdealBasis(IdealMove(L[2]*L[6], o));
{<10, [26, 1, 0]><2, [0, 0, 1]><1>
[1 -2 -1]
[0 1 1]
[0 0 1]
}

kash> M2:=IdealBasis(IdealMove(L[1]*L[6], o));
{<10, [-12714, -20615, -67306]><1><1>
[1 3 1]
[0 1 0]
[0 0 1]
}

kash> ModuleIntersection(M1,M2);
> {<10, [88, 2, 99]><2, [0, 2, 1]><2, [2, 2, 1]>
[1 -2 -1]
[0 1 1]
[0 0 1]
}


</pre>

<p>


<hr>

<p>
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