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

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

Creates a multilinear mapping.

<p><p>

<h3>
Syntax:
</h3>
<pre>f := AbelianGroupMultiHomCreate(d, g, t, mat);</pre>

<p>

<table>
<tr>
<td>group</td>
<td><pre>  d, g, t  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix or list of lists</td>
<td><pre>  mat  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Creates a multilinear mapping from a direct product of groups d to
a group g.
This multilinear mapping corresponds to the homomorphism from
the tensor product t of the groups to the group g with the
matrix <tt>mat</tt>.
It is recommended to use the second and third entry returned by
<tt>AbelianMultiHomGroup</tt> (see example).
It is checked if <tt>mat</tt> corresponds to a homomorphism.
For a second possibility to create multilinear mappings see
\hyperlink{AbelianMultiHomGroup}{<tt>AbelianMultiHomGroup</tt>}.


<p><p>

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

<pre>

kash> g1 := AbelianGroupCreate(Mat(Z,[[2]]));;
kash> g2 := AbelianGroupCreate(Mat(Z,[[4]]));;
kash> h := AbelianGroupCreate(Mat(Z,[[8,0],[0,2]]));;
kash> l := AbelianMultiHomGroup([g1,g2], h);
[ Group with relations:
    [2 0]
    [0 2], Group with relations:
    [2 0]
    [0 4], Group with relations:
    [2] ]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 direct product d = g1\times g2: 
<pre>

kash> d := l[2];
Group with relations:
[2 0]
[0 4]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 tensor product t = g1otimes g2: 
<pre>

kash> t := l[3];
Group with relations:
[2]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 create the multilinear mapping: 
<pre>

kash> f := AbelianGroupMultiHomCreate(d, h, t, [[0,1]]);
MultiHom [ 1, 1 ] from Group with relations:
[2 0]
[0 4] to Group with relations:
[8 0]
[0 2]

kash> elt := AbelianGroupEltCreate(d, [1,1]);
[1 1]
kash> AbelianGroupEltReduce(f*elt, true);
[0 1]
kash> f := AbelianGroupMultiHomCreate(d, h, t, [[1,0]]);
false
kash> AbelianGroupPrintLevel := 1;
1
kash> f := AbelianGroupMultiHomCreate(d, h, t, [[1,0]]);
false
kash> AbelianGroupPrintLevel := 0;
> 0

</pre>

<p>


<hr>

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