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

Computes the modular row Hermite normal form
of an integer matrix.

<p><p>

<h3>
Syntax:
</h3>
<pre>H := MatHermiteRowMod(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> MatHermiteRowMod</tt>
routine computes the row Hermite normal form of the matrix
\left(\begin{array}{c} <tt> M</tt> <tt> k</tt>
cdot I_n \end{array}right) \in {\Bbb Z}^{(m+n)\times n}

and returns the upper m rows of the Hermite Normal form.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the row Hermite normal form of
 \left(\begin{array}{ccc}3 & 7 & 10 20 & 25 & 40
\end{array}right)

with respect to the modulus 5.
<pre>

kash> M := Mat(Z,[[3,7,10],[20,25,40]]);
[ 3  7 10]
[20 25 40]
kash> MatHermiteRowMod(5,M);
> [1 4 0]
[0 5 0]
[0 0 5]

</pre>

<p>


<hr>

<p>
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