We cannot use it for hashing as I found the following:

sage: G4 = ReflectionGroup(4)
sage: elt = G4[22]
sage: elt
(1,12)(2,24)(3,19)(4,22)(5,17)(6,20)(7,23)(8,9)(10,21)(11,13)(14,18)(15,16)
sage: y = (elt * G4.gen(1)) * G4.gen(1) * G4.gen(1)
sage: elt == y
True
sage: hash(elt) == hash(y)
False
sage: elt._reduced_word
[0, 0, 1, 0, 0, 1]
sage: y._reduced_word
[1, 0, 0, 1, 0, 0]

Either we figure out how to make this consistent or we need to change the hashing.

CC: @stumpc5

Component: group theory

Keywords: gap3, complex reflection group

Author: Travis Scrimshaw, Christian Stump

Branch/Commit: u/tscrim/hash_reflection_groups-34912 @ 14d6f61

Reviewer: Christian Stump, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/34912