Hey, Thanks Kannappan for your work on this! By the way: would you mind > using the occasion to move this method to the CoxeterGroups category? > Of course, calling "W.longest_element()" for an infinite coxeter group > W is not a wise thing to do; but we recently had the need for > computing longest elements for finite parabolic subgroups and > ``W.longest_element(I)`` would have been useful. Ideally there would > be a warning or error if called without argument or on an infinite > parabolic subgroup, but that might be tricky to detect. > > I'd throw a type error if the group W was infinite since this does not exist. Also I would think it would be (relatively) easy to check if subgroup the group is finite since there are only 3 infinitely families and would be easy to detect when it does not fall into these types (basically if the Coxeter matrix has something off the sub/super diagonals or is type D), the rest are exceptional and could just be a big case check by equality. Of course this would only be after it has been broken up into connected components. Perhaps I'm over simplifying things...
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