I tried to do some computations with the existing Iwahori-Hecke
algebra module inside sage earlier this year. I needed to work over
the rational function field C(x), for an indeterminate x. In the end I
gave up and went back to using some gap3 code that I have, which
builds on chevie, because it was unbelievably slow. As polynomials
(and rational functions?) are supposed to be fast in sage I put the
slowness down to the implementation of permutations inside sage, but I
didn't do any profiling so perhaps this is unfair.

In any case, I agree that it would be nice to have a faster and more
accessible implementation of permutations inside sage.

Andrew

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