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

Computes the union of two modules.

<p><p>

<h3>
Syntax:
</h3>
<pre>M :=ModuleUnion(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>
The result of this function is the union or sum of the two modules
in normal form.

For a detailed description of the parameters for the modular normal
form computation see <tt> ModuleNF</tt>.
This function is basically a <tt> ModuleConcat</tt> of the modules and
a <tt> ModuleNF</tt> on the result.

The operator '+' on modules is identical to <tt> ModuleUnion</tt>
except the additionsl parameters for the normal form computation.

<p><p>

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

<pre>
kash>  O:=OrderMaximal(Poly(Zx, [1,-10,-3,-2]));;
kash> o:=OrderMaximal(Order(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> ModuleUnion(M1,M2);
> {<5, [0, 2, 2]><1><1>
[1 -2 1]
[0 1 0]
[0 0 1]
}


</pre>

<p>


<hr>

<p>
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