# Changes between Version 4 and Version 5 of Ticket #4326

Ignore:
Timestamp:
06/11/09 05:54:59 (10 years ago)
Comment:

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Unmodified
• Property Authors changed from to nthiery with help from schilling, bump, Nicolas Borie, Qiang Wang, Steve Pon
• Property Summary changed from Root systems improvements to [with patch, needs review] Root systems improvements
• Property Reviewers changed from to bump
 v4 Current patch: http://combinat.sagemath.org/patches/file/tip/root_systems-4326-nt.patch Patch from Sage-Combinat: http://combinat.sagemath.org/patches/file/tip/root_systems-4326-nt.patch Doc: - Use $F_4$ instead of F4 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: - 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 - associated coroot in the root and weight space - 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. - affine ambient space Categorification of RootLatticeRealization / ... New category CoxeterGroupModules Support for non crystalographic root systems