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

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

Computes the determinant of a row normal form of an integral matrix.

<p><p>

<h3>
Syntax:
</h3>
<pre>n := MatIndex(m);</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  n  </pre></td>
<td>index</td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  m  </pre></td>
<td>over Z</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Suppose we have Z modules M|1\subset M|2 given via a basis of M|2
and a set of elements generating M|1. Furthermore let m be the
matrix which rows contain the aforementioned generators. <tt> MatIndex</tt>(m)
will compute the index of M|1 in M|2. If the index is not finite, a 0
will be returned.

<p><p>

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

<pre>

kash> m := RandomMatrix(Z, 3);
[ 19  11   5]
[ -6 -18  -6]
[ 17  18   5]
kash> MatIndex(m);
540
kash> m := m{[1..2]};IsMat(m);
[ 19  11   5]
[ -6 -18  -6]
true
kash> MatIndex(m);
0
kash> m := Concatenation(m, RandomMatrix(Z, 3));IsMat(m);
[ [19 11  5], [ -6 -18  -6], [-16  -1 -16], [-4 -3 13], [17 11 -9] ]
true
kash> MatIndex(m);
> 1

</pre>

<p>


<hr>

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