#20402: Make subword complexes compatible with real reflection groups
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Reporter: stumpc5 | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.2
Component: combinatorics | Resolution:
Keywords: reflection group, | Merged in:
coxeter group, subword complex, | Reviewers:
days80 | Work issues:
Authors: Christian Stump | Commit:
Report Upstream: N/A | 295d784db0ae24bed97ed7b4d3777df9dbd652c2
Branch: u/stumpc5/20402 | Stopgaps:
Dependencies: #11187 |
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Comment (by tscrim):
Replying to [comment:35 nthiery]:
> Oh, I had not noticed that `CoxeterMatrixGroup` were acting on plain
vectors with '*'. As you mention this is very ambiguous. For a Weyl group
this is even worst: is the vector interpreted as in the span of the
(co)roots? of the (co)weights? in the ambient space?
For `CoxeterMatrixGroup`, it is given as a (faithful) representation, so
the basis of a vector space is (implicitly) given, which is the roots. For
the Weyl group, it is also given as a representation, so again, we have a
basis which we define the action on. So I see no ambiguity, and in fact, I
think the Weyl groups are very explicit about this.
> For now, I'd rather keep the notations as explicit as possible (in
particular, it's easier to document a method `.action` than an overloaded
operator). And leave us room in the future to overload '*', either by
default, or upon explicit request from the user.
I agree, that it is easier to document `action()` than an overloaded
operator, but I think it is only marginally easier. The first thing I
would (and do) look at is the class-level documentation for what I can do
with a particular object. So if we have examples in there that describe
the action of `*`, I think that makes it easily accessible what we are
doing, in addition to the naturality of the action. Or am I forgetting
something (again, in the [finite] Coxeter group setting)?
--
Ticket URL: <http://trac.sagemath.org/ticket/20402#comment:40>
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