#9290: Implement Coxeter groups in their geometric representation
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Reporter: nthiery | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-wishlist
Component: combinatorics | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by nthiery:
Old description:
New description:
The root system / coxeter group code is designed from the ground up to
allow for this extension.
Steps:
- Double check {{{CartanType(["H",3]).coxeter_diagram()}}} and friends
- Given a coxeter diagram, construct the dynkin diagram {{{g}}}
corresponding to the geometric representation; most of the time,
this will involve roots of unity, and require e.g. a cyclotomic
field (see also #8327)
- Make sure that {{{L = RootSystem(g).root_space()}}} accepts such a
diagram
- Make sure that {{{WeylGroup(L)}}} accepts such a root space
- Fix all the interfaces to properly reflect the generalization
(e.g. WeylGroup above should really be CoxeterGroup).
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9290#comment:2>
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