[back] [prev] [next] [index] [root]

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

Computes a normal form of the given module.

<p><p>

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

<p>

<table>
<tr>
<td>modules </td>
<td><pre>  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#Module">Module</a>

<p>

<h3>
Description:
</h3>
The module will be represented by a pseudomatrix whose matrix is
in triangular form with ones on the diagonal.

Two different algorithms are implemented. One is according to
CoDe (the default), the other one according to
BoPo (which is invoked by the string parameter <tt> PBNF</tt>).

The pseudomatrix will be either in upper triangular form which is
the default or in lower triangular form if requested by the
string parameter <tt> lower</tt>.

Modular reduction is implemented using either an integer or
an ideal.

<p><p>

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

<pre>

kash> O:=OrderMaximal(Poly(Zx,[1, 5, -6, -53, 3, 206, 244]));;
kash> IL:=List(Factor(2*O),f->f[1]);;
kash> List(IL,IdealGenerators);;
kash> EL1:=List(Factor(5*O),f->IdealGen(f[1],2));;
kash> EL2:=List(Factor(13*O),f->IdealGen(f[1],2));;
kash> EL2[3]:=IdealGen(Factor(7*O)[1][1],2);;
kash> EL3:=List(Factor(3*O),f->IdealGen(f[1],2));;
kash> EL3[3]:=IdealGen(Factor(7*O)[2][1],2);;
kash> M:=Module(IL,Mat(O,[EL1,EL2,EL3]));
{<2, [0, 2, 0, 3, 0, 2]><2, [0, 0, 3, 0, 1, 2]><2, [3, 3, 1, 2, 0, 0]>
[[12, 17, 15, 7, 9, 5] [19, 18, 15, 1, 10, 24] [4, 22, 4, 10, 23, 4]]
[[10, 8, 0, 1, 0, 0] [1, 12, 5, 1, 0, 0] [1, 1, 0, 0, 0, 0]]
[[1, 1, 0, 0, 0, 0] [1, 0, 1, 0, 0, 0] [3, 1, 0, 0, 0, 0]]
}

kash> ModuleNF(M);
> {<26236112388386371287536615054, [294144153883328, 688333593256040823590763075\
215506079571362956748104814491, 106413296427452, 30897359779322, 2714188044413\
95, 688333593256040823590763075215506079571362445884846952856]><2><2, [3, 2, 1\
, 2, 2, 0]>
[1 [-10218246369603710638941628710, 0, 1, 0, 0, 1] / 2 [7551087260070784648140\
818381, -1, 1, 1, 1, 1] / 2]
[0 1 [2, -1, -1, 1, 2, 0] / 2]
[0 0 1]
}


</pre>

<p>


<hr>

<p>
<a href="../kashref.html"><- back</a>[back] [prev] [next] [index] [root]