Hi,
I am used to do a lot of calculation with distances of permutations.
According to me,
NrMovedPoints(a/b)
is very efficient to compute d(a,b).
More difficult is to find the element b of G which is "closest" to a. I
would do it rather straightforward.
G:=PGL(2,53); Size(G);
closest:=function(G,a)
local md,x,b;
md:=NrMovedPoints(G); b:="";
for x in G do
if NrMovedPoints(x/a)<md then
md:=NrMovedPoints(x/a);
b:=x;
fi;
od;
return b;
end;
a:=Random(SymmetricGroup(NrMovedPoints(G)));
b:=closest(G,a);
time;
You can check the result by
NrMovedPoints(a/b);
Collected(List(G,u->NrMovedPoints(a/u)));
I hope this helps.
Bye,
Gabor
On 01/17/2013 08:52 AM, A L wrote:
Hello,
For a project, I need to compute the minimal Hamming distance between a
fixed permutation and a (large) permutation group. What is the "correct"
way to do this in GAP? I am looking for the most efficient method, both for
the Hamming distance computation between individual elements, as well as
ways to avoid brute-force comparison with each element in the group
(perhaps utilizing information about the group's structure).
Any help or pointers/references would be appreciated. I am new to GAP and
have tried my best to wade through the extensive documentation.
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