#8414: lattice -> space in weyl_groups.py
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Reporter: bump | Owner: bump
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.3.4
Component: combinatorics | Keywords:
Author: Daniel Bump | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by nthiery):
* status: needs_review => needs_work
Comment:
Hi Dan!
Sorry for the late reply; I am just back from vacations.
Depending on how the Weyl group is constructed, W.lattice() can actually
be a lattice:
{{{
sage: WeylGroup(RootSystem(["A",3]).root_lattice())
Weyl Group of type ['A', 3] (as a matrix group acting on the root lattice)
sage: WeylGroup(RootSystem(["A",3]).root_lattice()).lattice()
Root lattice of the Root system of type ['A', 3]
}}}
In fact, the name was meant as short hand for "which realization of the
root lattice the group is naturally acting upon".
That being said, I agree that this name is not good. In particular, we
probably will want to generalize this soon to handle Coxeter groups
implemented as permutation groups (e.g. acting on the roots) instead of
matrix groups. So the semantic of this method should probably be to return
which ever natural space (or set) the group is naturally acting on. Its
name should reflect that.
Any good suggestions?
- natural_action_space?
- root_system_realization?
- ...?
As for the reflections: this sounds like a useful feature, thanks! May I
suggest an alternative implementation, namely to:
- make reflections to be a family (still with the roots as keys) instead
of a dictionary
- Add an "inverse" feature to finite families (at least those without
duplicates) returning the family with the keys and values exchanged.
Then, you would do W.reflections().inverse_family() instead of
W.reflections(keys=reflections). This would solve the problem at hand, be
of general usefulness, and not clutter the Weyl group interface.
Thanks in advance!
Best,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8414#comment:4>
Sage <http://www.sagemath.org>
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