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

Computes the group of multilinear mappings.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AbelianMultiHomGroup([g_{1}, &hellip; ,g_{n}], h);</pre>

<p>

<table>
<tr>
<td>groups</td>
<td><pre>   g_{1}, &hellip; , g_{n}, h  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Computes the group of multilinear mappings from d =
g_{1}\timescdots\times g_{n} to h.
<tt> AbelianMultiHomGroup</tt> returns a list with three entries:
<ul>
<li> group of multilinear mappings from
g_{1}\timescdots\times g_{n} to h.
<li> direct product d = g_{1}\timescdots\times g_{n}
<li> tensor product
t = g_{1}otimescdotsotimes g_{n}.
</ul>
You need d and t only if you want to create multilinear
mappings from g_{1}\timescdots\times g_{n} to h corresponding
to a given matrix using the function
\hyperlink{AbelianGroupMultiHomCreate}{<tt>AbelianGroupMultiHomCreate</tt>}.


<p><p>

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

<pre>

kash> z := AbelianGroupCreate(Mat(Z,[[0]]));;
kash> z2 := AbelianGroupCreate(Mat(Z,[[2]]));;
kash> z4 := AbelianGroupCreate(Mat(Z,[[4]]));;
kash> z8 := AbelianGroupCreate(Mat(Z,[[8]]));;
kash> l := AbelianMultiHomGroup([z,z4,z8], z2*z8);
[ Group with relations:
    [2 0]
    [0 4], Group with relations:
    [0 0 0]
    [0 4 0]
    [0 0 8], Group with relations:
    [4] ]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 mg is the group of multilinear mappings from
d = z \times z4 \times z8 to h = z2 \times z8: 
<pre>

kash> mg := l[1];
Group with relations:
[2 0]
[0 4]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 d is the direct product z \times z4 \times z8: 
<pre>

kash> d := l[2];
Group with relations:
[0 0 0]
[0 4 0]
[0 0 8]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 t is the tensor product z otimes z4 otimes z8: 
<pre>

kash> t := l[3];
Group with relations:
[4]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 elt is element of group of multilinear mappings from
d = z \times z4 \times z8 to h = z2 \times z8: 
<pre>

kash> elt := AbelianGroupEltCreate(mg, [1,0]);
[1 0]


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 f is a multilinear mapping from d = z\times z4 \times z8
to h = z2 \times z8: 
<pre>

kash> f := AbelianGroupDiscreteExp(elt);
MultiHom [ 1, 1, 1 ] from Group with relations:
[0 0 0]
[0 4 0]
[0 0 8] to Group with relations:
[2 0]
[0 8]

kash> a := AbelianGroupEltCreate(d, [1,1,1]);
[1 1 1]
kash> f * a;
> [1 0]

</pre>

<p>


<hr>

<p>
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