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

Returns an ideal which can be used for reduction.

<p><p>

<h3>
Syntax:
</h3>
<pre>a := ModuleModul(M)</pre>

<p>

<table>
<tr>
<td>ideal </td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>module </td>
<td><pre>  M  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let R be a Dedekind ring, n \in \N, M \subset
Q(R)^n be a module of degree n over the ring
R. The ideal \a guarantees \a R^n \subset M
where R^n denotes the 1-module of degree n over R.

It is computed as follows: Let d be the denominator of
M, \a := frac{1}{d}\det(dM).

<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> M:=IdealBasis(IdealMove(L[2]*L[6]/2, o));
{<5, [4, 1, 2] / 2><1, [2, 3, 2] / 2><1 / 2>
[1 -2 -1]
[0 1 1]
[0 0 1]
}

kash> I := ModuleModul(M);
<
[20  6  4]
[ 0  1  0]
[ 0  0  1]
/16>

kash> I*ModuleId(O,3) < M;
> false

</pre>

<p>


<hr>

<p>
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