#20027: Different behavior for reflections for matrix Coxeter group and Weyl
groups
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: defect | Status: new
Priority: major | Milestone: sage-7.1
Component: combinatorics | Resolution:
Keywords: coxeter groups, | Merged in:
reflections | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 25958261175f453493c4da055cccfe5a1880ecb2
public/combinat/fix_reflections_coxeter_groups-20027| Stopgaps:
Dependencies: |
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Changes (by {'newvalue': u'Travis Scrimshaw', 'oldvalue': ''}):
* commit: => 25958261175f453493c4da055cccfe5a1880ecb2
* branch: => public/combinat/fix_reflections_coxeter_groups-20027
* author: => Travis Scrimshaw
Comment:
Okay, here is where I am at. I flipped the key/value order on
`WeylGroup.reflections()`. I made `CoxeterGroup.reflections()` return a
family. Additionally, I did some cleanup on the `@cached_method` returning
mutable objects. This included removing the caching of `positive_roots` as
it did not appear to be called anywhere except in `roots()`, which is
cached, so I don't see a reason to cache it (moreover, getting the keys
from a `Family` should be fast).
So now my questions are these:
- Do we want to issue a warning for the change in behavior for
`WeylGroup.reflections()`? If so, how should we?
- Do we want to lift one or both of these implementations to the category
(and on this ticket)?
- Do we want to implement an iterator over all reflections for infinite
groups? This could be done by a `RecursivelyEnumeratedSet` which goes by
conjugating by simple reflections corresponding to the non-descents of a
given reflection.
@stumpc5 I agree that convex orders are natural and important, but we
would still need a natural/canonical reduced expression for the long
element. Although I guess we could use the reduced expression that gives
the BZL strings (I only know this for type A,,n,, though...), but this
still feels somewhat artificial to me.
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=90b278a1f7b2ecd08c2a95d7d57a36cbbdfbeb3c
90b278a]||{{{Reversing the family for reflections.}}}||
||[http://git.sagemath.org/sage.git/commit/?id=8c9b809c83f6da647f4cbee69de0ce31ae5f864d
8c9b809]||{{{Making CoxeterGroup.reflections return a Family and some
touchups.}}}||
||[http://git.sagemath.org/sage.git/commit/?id=25958261175f453493c4da055cccfe5a1880ecb2
2595826]||{{{Removing caching of CoxeterGroup.positive_roots().}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/20027#comment:8>
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