Changes between Version 5 and Version 6 of Ticket #15703


Ignore:
Timestamp:
04/08/14 06:09:35 (7 years ago)
Author:
nthiery
Comment:

Legend:

Unmodified
Added
Removed
Modified
  • Ticket #15703

    • Property Keywords groups days57 added
  • Ticket #15703 – Description

    v5 v6  
    11This is a follow up to: #9290.
    22
    3 Refactor CoxeterMatrixGroup and WeylGroup to make the later a subclass of the former, and lift as many features as possible from WeylGroup to CoxeterMatrixGroup. This includes:
    4 - Building the matrices from a root lattice realization
    5 - Implementing the following methods:
    6   {{{
     3- Create a class CoxeterDiagram (similar to DynkinDiagram)
     4  Edge labels: m_{i,j}, possibly with number <-1 for oo
     5
     6  Starter: just use a plain digraph.
     7
     8- Implement the method dynkin_diagram() which builds the cartan matrix
     9  for the geometric representation
     10
     11  Starter: just make this a function
     12
     13- Feed this to RootSystem, and check that the root space and weight
     14  space are built properly. Rename the weyl_group method to
     15  reflection_group, with an alias from weyl_group.
     16
     17- Long run: stuff specific to the crystallographic case, starting with
     18  this weyl_group method, should go in
     19  RootLatticeRealizations.Crystallographic. That's for a follow up
     20  ticket on using axioms for root systems; but let's not depend on
     21  #10963 right now.
     22
     23- Refactor CoxeterMatrixGroup and WeylGroup to make the later a
     24  subclass of the former, and lift as many features as possible from
     25  WeylGroup to CoxeterMatrixGroup.
     26
     27Tests:
     28{{{
     29  sage: C = CoxeterDiagram(...)           # good name? or CartanDatum(coxeter_matrix=...) [1] ? or?
     30  sage: L = RootSystem(C).root_space()
     31  sage: W = L.reflection_group()
    732  sage: W = CoxeterGroup(['H',3])
    833  sage: W.domain()
    9   }}}
    10 
    11 As a prerequisite, implement root spaces and weight spaces for non-crystallographic Coxeter groups.
     34}}}
    1235
    1336Sage Days 57 in Cernay will be a good occasion to work on this.
     37
     38Follow ups: #16087
     39
     40[1]: Generally speaking, it's planned to rename CartanType to CartanDatum.