#6588: Categories for root systems
--------------------------------------------------------+-------------------
Reporter: nthiery | Owner:
mhansen
Type: enhancement | Status:
needs_review
Priority: major | Milestone:
sage-5.0
Component: combinatorics | Keywords: root
systems, categories
Work_issues: | Upstream: N/A
Reviewer: Anne Schilling, Mark Shimozono, PatchBot | Author:
Nicolas M. Thiéry
Merged: | Dependencies:
#10817
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Description changed by nthiery:
Old description:
> See the top of the patch for a complete description of the changes.
>
> Review ongoing on the Sage-Combinat queue.
New description:
New Features:
- Extended weight lattice/space for affine types
- coxeter_matrix and coxeter_diagram (for crystallographic types)
- Embeddings of the root lattice/space in root lattice realizations
- Embeddings of the weight lattice/space in weight lattice realizations
- Partial conversion from the root space to the root lattice
- Iterator for any Coxeter group, and weak order ideals thereof
- Facade option for weak_poset's and bruhat_poset's of finite coxeter
groups
- weak_poset's of finite coxeter groups are lattices; added link
weak_lattice -> weak_poset
(courtesy of Christian Stump)
- Enumerated set for grassmannian elements, and is_grasmmannian test
- Added method register_as_conversion to morphisms
Refactoring:
- RootLatticeRealization and WeightLatticeRealization are now categories
- Use abstract_methods where appropriate
- Cleanup of an_element
- to_coroot_lattice_morphism: renamed to to_coroot_lattice_space, and
moved from RootLatticeRealization to RootSpace (it does not make
sense for, e.g., the weight lattice).
- Moved the implementation of associated_coroot in
root_lattice_realization to root_space where it belongs
Tests and bug fixes:
- 100% doctests on sage.combinat.root_system, except for weyl_group and
weyl_characters
- 100% doctests on CoxeterGroups
- Add minimal documentation to AffineWeylGroups
- Added systematic tests for associated_coroot
- Fixed further missing features revealed by this test:
- reducible Cartan types were not seen as finite/simply
laced/crystallographic as appropriate
- symmetrizer needed to be generalized to reducible cartan types
(including D2)
- the relabelling for reducible cartan types was broken for affine types
- More tests for scalar products
- Added systematic consistency check between the simple_root and
simple_roots methods
- same thing for fundamental_weight and fundamental_weights
- Fixed a SL vs GL glitch when obtaining simple roots for reducible cartan
types revealed by the above
- Fixed imports (extraneous ones, and a missing one reported by M.
Shimozono and others)
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6588#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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