#11187: Implementation of finite reflection groups
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Reporter: stumpc5 | Owner: tbd
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: reflection group, | Merged in:
days49, days 64.5 | Reviewers:
Authors: Christian Stump | Work issues:
Report Upstream: N/A | Commit:
Branch: | 43f505667c936dc07ed42a653383e844f2555cab
u/stumpc5/11187-new | Stopgaps:
Dependencies: #18620 |
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Comment (by stumpc5):
Replying to [comment:104 kdilks]:
> for {{{W = ReflectionGroup(23)}}}, there are two elements where my
computer returns a different
> reduced word than expected
This computation is currently done purely in my code, and it's not related
to `chevie`. The iterator comes from `_iterator_tracking_words` so let's
see what happens there.
Related here, and indeed also to your question on `long_element`, observe
that currently
{{{
sage: W = ReflectionGroup(23); W
Irreducible complex reflection group of rank 3 and type H3
sage: W.category()
Join of Category of finite permutation groups and Category of irreducible
finite coxeter groups
sage: W = ReflectionGroup(['H',3]); W
Irreducible real reflection group of rank 3 and type H3
sage: W.category()
Join of Category of finite permutation groups and Category of irreducible
finite coxeter groups
}}}
Since the iter algorithm for coxeter groups is slightly smarter (it takes
into account that the weak order is graded), the two iter functions are
different.
But:
* both iter functions are supposed to return the same iteration through
the group
* both iter functions should always return the elements in the very same
order (in contrary to what we see on my vs on your machine)
I found a bug (having a {{{set}}} rather than a {{{list}}} in one spot),
so let's see if this is fixed with my next push in a few minutes after all
tests pass here.
> Unrelated, but I also can't get the long_element() method to work.
The reason is, that you constructed the real group as a complex group, so
the long element for {{{ReflectionGroup(['H',3])}}} works while it
currently doesn't work for {{{ReflectionGroup(23)}}}. I do have to fix
that and be more careful constructing the right class instance.
--
Ticket URL: <http://trac.sagemath.org/ticket/11187#comment:105>
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