Ticket #9290 (new enhancement)
Implement Coxeter groups in their geometric representation
|Reported by:||nthiery||Owned by:||sage-combinat|
Description (last modified by nthiery) (diff)
The root system / coxeter group code is designed from the ground up to allow for this extension.
- 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
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