> Frederic,
> 
> I pushed a patch (coxeter_ms.patch) to the sage-combinat server.
> 
> Now you should get
> 
> sage: W=WeylGroup(['A',2])
> sage: w=W.from_reduced_word([1,2,1])
> sage: w.inversions()
> [alpha[1], alpha[1] + alpha[2], alpha[2]]
> 
> which is much nicer.
> 
> --Mark

Jean Michel wrote:

> The  list  of  inversions,  in  my  view,  should  preferably  be a list
> of
> reflections (which does not need the existence of roots and makes sense
> for
> abstract Coxeter groups).

It seems to me that inversions could have a switch such
that it returns either the positive root or the corresponding
reflection. (The second could be valid in an arbitrary Coxeter
group.)

In other words, something like this:

sage: w.inversions()
[alpha[1], alpha[1] + alpha[2], alpha[2]]

sage: w.inversions(reflections=True)
[s1,s1*s2*s1,s2]

Dan

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