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

Initializes an environment to enumerate certain subgroups

<p><p>

<h3>
Syntax:
</h3>
<pre>s := FindQuotientOfShapeEnumInit(G, L);</pre>

<p>

<table>
<tr>
<td>record</td>
<td><pre>  s  </pre></td>
<td></td>
</tr>
<tr>
<td>AbelianGroup</td>
<td><pre>  G  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of integers describing the shape of the subgroup</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
<i>no detailed description available yet</i>

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Let G := C^2|8\times C|6^2\times C|2. We'll enumerate all quotients Q=G/U of G
such that Qcong C|4\times C|2:
<pre>

kash> G := AbelianGroupCreate(MatDiag(Z, [8, 8, 6, 6, 2]));
Group with relations:
[8 0 0 0 0]
[0 8 0 0 0]
[0 0 6 0 0]
[0 0 0 6 0]
[0 0 0 0 2]
kash> s := FindQuotientOfShapeEnumInit(G, [4, 2]);
Record of type FindQuotientOfShapeEnum

kash> while FindQuotientOfShapeEnumNext(s) and s.no <3 do
> Print("Number ", s.no, "\n", s.elt, "\n");
> l := AbelianQuotientGroup(G, AbelianSubGroup(G, s.elt));
> gs := AbelianGroupEnumInit(l);
> l := [];
> while AbelianGroupEnumNext(gs) do Add(l, gs.elt); od;
> Apply(l, x->AbelianGroupEltMove(x, G));
> Print("Containing: ", l, "\n");
> od;
Number 1
[2 0 4 0 1]
[6 0 1 0 0]
[2 4 4 3 0]
[0 2 0 4 0]
[4 0 2 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
Containing: [ [0 0 0 0 0], [6 7 0 5 0], [1 0 0 0 0], [7 7 0 5 0], 
  [2 0 0 0 0], [0 7 0 5 0], [3 0 0 0 0], [1 7 0 5 0] ]
Number 2
[0 0 0 0 1]
[6 0 1 0 0]
[2 4 4 3 0]
[0 2 0 4 0]
[4 0 2 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
[0 0 0 0 0]
Containing: [ [0 0 0 0 0], [6 7 0 5 0], [1 0 0 0 0], [7 7 0 5 0], 
  [2 0 0 0 0], [0 7 0 5 0], [3 0 0 0 0], [1 7 0 5 0] ]
kash> while FindQuotientOfShapeEnumNext(s) do
> i := 1;
> od;
kash> Print("Total: ", s.no, "\n");
> Total: 360

</pre>

<p>


<hr>

<p>
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