Optimizing Magma Code

PowerGroup

If the user is working with enumerated sets of pc-groups that are all subgroups of a common over-group \(G\), then the following optimization is strongly recommended. Define the set to have the universe PowerGroup(G). For any subgroup \(H\) of \(G\), we can find a canonical form for the generators of \(H\). This allows us to have a very good hashing function for the subgroups.

Example: Power Group Two (ex-952208)

The following example illustrates the optimization.

> G := ExtraSpecialGroup( GrpPC, 3, 3 );
> P := PowerGroup(G);
> time s1 := {  P | sub< G | Random(G), Random(G) > : x in { 1..500}  };
Time: 1.140
> time s2 := { Parent(G) | sub< G | Random(G), Random(G) > : x in { 1..500}  };
Time: 9.769

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