[GAP Forum] Speedup of GAP program

[Kasper Andersen]

Hi,

In connection with a joint project with Bob Oliver and Joana Ventura I 
have been carrying out a number of computations for the 2-groups of order 
at most 2^8 in Magma. To check them and to learn GAP at the same time, I 
have tried to port my programs to GAP.

Unfortunately GAP seems to be significantly slower (a factor of acround 
2.7) than Magma. Before I go any further I wonder if there is a way to 
speed up GAP. As a test I have been running the following GAP program:

iscritical := function(S,P)
   return 1;
end;

criticalsubgroups := function(S)
   local kappa,SmodZ,L;
   if IsAbelian(S) then
     return [];
   else
     # Only check subgroups containg Z(S)
     kappa:=NaturalHomomorphismByNormalSubgroup(S,Center(S));
     SmodZ:=FactorGroup(S,Center(S));
     L:=SubgroupsSolvableGroup(SmodZ);
     L:=List(L,x->PreImage(kappa,x));
     return Filtered(L,P->(iscritical(S,P) <> -1));
   fi;
end;

n:=2^7;

for i in [1..NumberSmallGroups(n)] do
   S:=SmallGroup(n,i);
   L:=criticalsubgroups(S);
   Print(n," ",i,"\n");
od;

Some comments are in order: To simplify the timings I have left out the 
code for the function iscritical, so the above program simply computes the 
conjugacy classes of subgroups P containing Z(S) for all 2-groups S of 
order 2^7. Moreover my original function does not return true/false but 
rather -1 (=false), 0 (=undecided) and 1 (=true). For simplicity I have 
left this in.

Unfortunaly even this simple program runs a factor of 2.7 slower than the 
corresponding Magma program. Are there any ways to speed this up?

Another question: One of the conditions for criticality is that P is 
centric in S, i.e. that C_S(P) is contained in P. Does anyone know any 
better algorithm for computing all such subgroups than testing all 
subgroups containing Z(S) one by one?

best wishes,

Kasper Andersen