#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 tscrim):
I think it is best to have them be consistent, which we can easily do by
making `CoxeterGroup.reflections` return a family indexed by the
reflections whose values are the roots.
With that being said, in many ways I feel that it is more natural for the
family to be indexed by the roots and the values be reflections. It means
we can just do `for x in W.reflections()` as I don't think of roots as
''being'' reflection (instead of corresponding to).
I would return a family with the keys being roots and values being
reflections. Since iteration over a family is iteration over the values,
this will be consistent with complex reflection groups returning a tuple
(taking advantage of ducktyping). At least, I don't think of reflections
having a natural total ordering, so you should only be iterating over all
them.
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Ticket URL: <http://trac.sagemath.org/ticket/20027#comment:4>
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