#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: |
---------------------------+------------------------------------------------
Description changed by nthiery:
Old 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
New description:
Patch taken from Sage-Combinat:
http://combinat.sagemath.org/patches/file/tip/root_systems-4326-nt.patch
Depends on: #6136 #6253 #6250 #5891
-------------
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:6>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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