#11010: Implementation of the SubwordComplex as defined by Knutson and Miller
-------------------------------------+-------------------------------------
Reporter: stumpc5 | Owner: tbd
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.0
Component: combinatorics | Resolution:
Keywords: subword complex, | Merged in:
simplicial complex | Reviewers: Frédéric Chapoton
Authors: Christian Stump | Work issues:
Report Upstream: N/A | Commit:
Branch: u/chapoton/11010 | 1b10c95a312057dee7d920ff4d06ea713ef5338b
Dependencies: | Stopgaps:
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Changes (by stumpc5):
* status: positive_review => needs_work
Comment:
I am rather confused now:
* First Sage start
{{{
sage: W = CoxeterGroup(['B',4])
sage: W.coxeter_matrix().coxeter_type()
Coxeter type of ['B', 4]
sage: W = CoxeterGroup(['C',4])
sage: W.coxeter_matrix().coxeter_type()
Coxeter type of ['B', 4]
}}}
* Second Sage start
{{{
sage: W = CoxeterGroup(['C',4])
sage: W.coxeter_matrix().coxeter_type()
Coxeter type of ['C', 4]
sage: W = CoxeterGroup(['B',4])
sage: W.coxeter_matrix().coxeter_type()
Coxeter type of ['C', 4]
}}}
In particular, the root systems {{{W.roots()}}} are not correct in both
second cases.
Also, the plotting now assumes that the first index is the type B/C
special one. This is, it is expected that
{{{
sage: s0 = W.simple_reflection(W.index-set()[0])
sage: s1 = W.simple_reflection(W.index-set()[1])
sage: (s0*s1).order()
4
}}}
I doubt that this is correct in the current implementation of {{{Coxeter
groups}}} where the last index is expected to be special. If so, I will
add some magic to figure out the proper labelling...
--
Ticket URL: <http://trac.sagemath.org/ticket/11010#comment:71>
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