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

Returns the denominator of the given module.

<p><p>

<h3>
Syntax:
</h3>
<pre>den := ModuleDen(M);</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  den  </pre></td>
<td></td>
</tr>
<tr>
<td>module </td>
<td><pre>  M  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
The denominator of a module M is defined as the smallest
natural number d that the module dM is an integral
module. An integral module over the Dedekind ring R is a
subset of R^n where n is the degree of the module.

<p><p>

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

<pre>
kash>  O := OrderMaximal(Poly(Zx,[1, 5, -6, -53, 3, 206, 244]));;
kash> Ids:=[ Ideal(5, Elt(O,[-27, 1, -2, 1, -3, 15])),
> Ideal(1, Elt(O,[-18, 0, -3, 3, -1, 0]/5)) ];
[ <5, [-27, 1, -2, 1, -3, 15]>, <1, [-18, 0, -3, 3, -1, 0] / 5> ]
kash> M := Module(Ids,Mat(O,[[1,2],[2,1]])/15);
{<5, [-27, 1, -2, 1, -3, 15]><1, [-18, 0, -3, 3, -1, 0] / 5>
[1 / 15 2 / 15]
[2 / 15 1 / 15]
}

kash> ModuleDen(M);
> 75

</pre>

<p>


<hr>

<p>
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