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

Computes the modular upper column Hermite normal form
of an integer matrix.

<p><p>

<h3>
Syntax:
</h3>
<pre>H := MatHermiteColModUpper(k, M);</pre>

<p>

<table>
<tr>
<td>matrix</td>
<td><pre>  H  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  k  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  M  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let <tt> M</tt> \in {\Bbb Z}^{m \times n}. The
<tt> MatHermiteColModUpper</tt>
routine computes the upper column Hermite normal form of the matrix
 (<tt> M</tt> | <tt> k</tt> cdot I|m) \in {\Bbb Z}^{m\times(n+m)} 
and returns the rightmost n columns of the Hermite normal form.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the upper modular column Hermite normal form of
\left(\begin{array}{ccc}3 & 7 & 10 20 & 25 & 40 47 & 61 & 90
\end{array}right)
with respect to the modulus 5. 
<pre>

kash> M := Mat(Z,[[3,7,10],[20,25,40],[47,61,90]]);
[ 3  7 10]
[20 25 40]
[47 61 90]
kash> MatHermiteColModUpper(5,M);
> [1 0 0]
[0 5 0]
[0 0 1]

</pre>

<p>


<hr>

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