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

Creates the homomorphism corresponding to a matrix.

<p><p>

<h3>
Syntax:
</h3>
<pre>hom := AbelianGroupHomCreate(g1, g2, mat [, check]);
hom := AbelianGroupHomCreate(g1, g2, mat, [matinv]);</pre>

<p>

<table>
<tr>
<td>groups</td>
<td><pre>  g1, g2  </pre></td>
<td></td>
</tr>
<tr>
<td>homomorphism</td>
<td><pre>  hom  </pre></td>
<td>homomorphism from g1 to g2</td>
</tr>
<tr>
<td>boolean</td>
<td><pre>  check  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  matinv  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Creates the homomorphism from group <tt>g1</tt> to group
<tt>g2</tt> corresponding to the matrix <tt>mat</tt>.
The columns of <tt>mat</tt> are the images of the generators of
<tt>g1</tt>.
If the fourth (optional) parameter <tt>check</tt> is true then
it is checked whether the object <tt>hom</tt> is a
homomorphism, i.e. <tt>mat</tt> has the correct number of rows
and columns.
If the fourth parameter is a matrix then it has to be the
inverse of <tt>mat</tt>.


<p><p>

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

<pre>

kash> g1 := AbelianGroupCreate([[0,1,2],[5,6,0],[0,4,5]]);;
kash> g2 := AbelianGroupCreate([[0,2],[3,0]]);;
kash> mat := Mat(Z, [[-24,24],[20,-20],[-10,10]]);;
kash> hom := AbelianGroupHomCreate(g1, g2, mat);
HomMatrix =
[-24  24]
[ 20 -20]
[-10  10] 
from Group with relations:
[0 1 2]
[5 6 0]
[0 4 5] 
to Group with relations:
[0 2]
[3 0]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 If you feel insecure, you can use the fourth parameter check to
test, whether the matrix corresponds to a homomorphism: 
<pre>

kash> mat := Mat(Z, [[3,0],[3,-2],[-1,2]]);;
kash> hom := AbelianGroupHomCreate(g1, g2, mat, true);
> false

</pre>

<p>


<hr>

<p>
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