#4326: [with patch, needs review] Root systems improvements
---------------------------+------------------------------------------------
Reporter: nthiery | Owner: nthiery
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-combinat
Component: combinatorics | Keywords: root systems
Reviewer: bump | Author: nthiery with help from schilling,
bump, Nicolas Borie, Qiang Wang, Steve Pon
Merged: |
---------------------------+------------------------------------------------
Changes (by newvalueoldvalue):
* keywords: => root systems
* reviewer: => bump
* author: => nthiery with help from schilling, bump, Nicolas Borie,
Qiang Wang, Steve Pon
Old description:
> Current patch:
> http://combinat.sagemath.org/patches/file/tip/root_systems-4326-nt.patch
>
> Doc:
> - Use $F_4$ instead of F4
>
> DynkinDiagram:
> - allow for slicing notation for column/row extraction: c[i,:]
>
> AmbientSpace:
> - fundamental coweights by appropriate scaling of the fundamental
> weights
> - embedding coweight lattice
>
> WeightLatticeRealization
> - scalar product with coweight lattice in finite dimension
>
> Generic:
> - (signed) reduced word for a chamber/alcove
> - fix rank(): for the affine cases it currently returns the same
> as n.
>
> Classical case:
> - reverse map to coroot space and coroot lattice by scalar product with
> the fundamental weights
> - => associated coroot
> - s_\alpha on the (co)root and (co)weight lattice for any root \alpha
>
> Affine case:
> - analogues whenever well defined
> - reduced words for translations elements.
New description:
Patch from Sage-Combinat:
http://combinat.sagemath.org/patches/file/tip/root_systems-4326-nt.patch
Documention:
- quickref + links in sage.combinat.root_system
- Long introduction in CartanTypes
- ...
Cartan Types:
- Object oriented clean up: each cartan type has its own class (in
.type_....py) which contains all its specific data (dynkin diagram,
ascii art, ...). All the dispatch logic is now concentrated in the
CartanType factory.
- fixed the definition of rank for affine types (Anne Schilling)
- systematic implementation of the classical type underlying an affine
type (Anne Schilling)
- New methods: is_untwisted_affine, special_node, a, acheck,
translation_factors, symmetrizer, row_annihilator col_annihilator
(partly Nicolas Borie)
- Relabelled Cartan types (with composition, classical, special_node,
dual)
- Use A~... B~* BC~ convention for affine types;
Kac' convention implemented by renaming them (see CartanType?)
- F3 is nonexistent so use F4 in one test (Dan Bump)
- ascii art for reducible (Dan Bump), relabelled, and dual Cartan types
Root systems:
- Preliminary plots (Nicolas Borie)
- New methods for affine root systems (mostly Nicolas Borie):
null_(co)root, level
- RootSystem(["A",3,1]) returns None rather than the ambient space
for type A_3 (which was wrong!)
- positive and negative roots for all (finite) root lattice realizations
Coxeter groups:
- New categories: (Finite) CoxeterGroups, (Finite, Affine) WeylGroups
standardized methods: first_descent, has_descent, descents,
reduced_word, length, from_reduced_word, with systematic associated
test (test_has_descent, ...) simple_reflections,
simple_projections, coset_representatives, binary_factorisations, ...
(many of them were extracted and generalized from WeylGroup)
- lower and upper cover for Bruhat order (Steve Pon)
- affine stanley symmetric functions for types A, A affine
- Documentation (with help from Qiang Wang, Nicolas Borie)
The following are not yet addressed, and will be bumped to a subsequent
patch:
DynkinDiagram:
- allow for slicing notation for column/row extraction: c[i,:]
AmbientSpace:
- fundamental coweights by appropriate scaling of the fundamental weights
- embedding coweight lattice
WeightLatticeRealization
- scalar product with coweight lattice in finite dimension
Classical case:
- reverse map to coroot space and coroot lattice by scalar product with
the fundamental weights
- associated coroot in the root and weight space
- s_\alpha on the (co)root and (co)weight lattice for any root \alpha
Affine case:
- affine ambient space
Categorification of RootLatticeRealization / ...
New category CoxeterGroupModules
Support for non crystalographic root systems
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4326#comment:5>
Sage <http://sagemath.org/>
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