I have to do some computations in a braid group B_n
and I would like to know if someone had implemented
the Duhornoy algorithm in Gap which is very efficient
or if it is useless because Chevie does it better ?
I am the implementor of Braid groups in Chevie. I think that compared
to Dehornoy's algorithm (which alas, as far as I know, applies only to
braid groups of type A), the algorithm in Chevie is fairly efficient on
braids with few strands; but if you want to work in the braid group of
An where n exceeds about 10, Dehornoy's algorithm would be more efficient.
Anyway, I think that Dehornoy is considering implementing his algorithm
in GAP. You should contact him. If you or him write an implementation,
I might incorporate it then in Chevie -- I think it should not be too
difficult to write an implementation; the reason I did not do it is that
I am interested in all braid groups, not especially in those of type A.