#20027: Different behavior for reflections for matrix Coxeter group and Weyl 
groups
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       Reporter:  tscrim                       |        Owner:  sage-
           Type:  defect                       |  combinat
       Priority:  major                        |       Status:  new
      Component:  combinatorics                |    Milestone:  sage-7.1
       Keywords:  coxeter groups, reflections  |   Resolution:
        Authors:                               |    Merged in:
Report Upstream:  N/A                          |    Reviewers:
         Branch:                               |  Work issues:
   Dependencies:                               |       Commit:
                                               |     Stopgaps:
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Comment (by stumpc5):

 > At least, I don't think of reflections having a natural total ordering

 See Dyer "Hecke algebras and shellings of Bruhat intervals" for the
 importance of reflection orderings ;-). I usually want them to come at
 least in some "convex order" as in that paper...

 Anyway, I am fine with giving freedom to the keys, and only force that
 iteration does iters through the actual reflections.

--
Ticket URL: <http://trac.sagemath.org/ticket/20027#comment:7>
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