id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
4326 Root systems improvements nthiery nthiery "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
- highest_coroot returning self.coroot_lattice().highest_root()
Affine case:
- affine ambient space
- Fix:
{{{
sage: R = RootSystem([""A"",2,1]).weight_lattice()
sage: R.rho_classical()
...
TypeError: unsupported operand parent(s) for '*': 'Rational Field' and 'Weight lattice of the Root system of type ['A', 2, 1]'
}}}
Categorification of RootLatticeRealization / ...
New category CoxeterGroupModules
Support for non crystalographic root systems" enhancement closed major sage-4.3 combinatorics fixed root systems sage-combinat sage-4.3.alpha0 Nicolas M. Thiéry, Anne Schilling, Daniel Bump, Nicolas Borie, Qiang Wang, Steve Pon Daniel Bump, Mike Hansen N/A