#16841: Define parabolic subgroup of a Coxeter group
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Reporter: amri | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: combinatorics | Resolution:
Keywords: coxeter-group | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nthiery):
I just attached proof-of-concept code I had written back in 2010 at
the joint Sage-Combinat/Chevie days.
Further work needed:
- Update the existing `subgroups` methods (for permutation groups,
matrix groups, ...) so that it accepts
- Implement a class for subsets of an existing set, implemented by
wrapping elements of the ambient set, as is done in my class
ReflectionSubgroup.
- Implement a generic default `subgroup` method using the above class,
and passing by default the category Groups().Subobjects().
- Implement two categories, one for reflection subgroups, and one for
parabolic subgroups (the later being generated by a subset of the
simple reflections). CoxeterGroups.SubObjects (or later on
ReflectionGroups.Subobjects) is probably a good candidate for the
latter. A name is needed for the former.
- Plug everything together :-)
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Ticket URL: <http://trac.sagemath.org/ticket/16841#comment:2>
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