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words, syllables, letters and their inverse for fpgroup and pc group elems in all variations

Open fingolfin opened this issue 4 months ago • 8 comments

Just talked with @fieker: we have syllables(g::Union{FPGroupElem, SubFPGroupElem}) and letters(g::FPGroupElem)

  1. [ ] both of these should be available for FPGroupElem and SubFPGroupElem
  2. [ ] but ideally also both for PcGroupElem and SubPcGroupElem (as a subcase of the old issue #952)
  3. [ ] I just noticed there is also a nice WeylGroup type with a word method (cc @lgoettgens) -- it would make sense to have syllables and letters for those, too
  4. [ ] conversely, there is a word method for WeylGroup which looks similar to letters (except it returns a Vector{UInt8} -- of course if the generators are involutions one doesn't need inverses. Anyway: perhaps there should also be a word method for fp and pc (sub) group elems (to be decided what it should return
  5. [ ] in all these case, we also want a "reverse" function that takes the output of one of these function, plus a parent (sub)group, and re-constructs a group element.
  6. [ ] ... and the docstrings for these functions should always also mention their "inverse" (and ideally include an example showing a roundtrip)

@ThomasBreuer perhaps you can have a look?

fingolfin avatar Sep 26 '24 11:09 fingolfin