Changes between Version 4 and Version 5 of Ticket #4326


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

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  • Ticket #4326

    • 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 Keywords root systems added
    • Property Reviewers changed from to bump
  • Ticket #4326 – Description

    v4 v5  
    1 Current patch: http://combinat.sagemath.org/patches/file/tip/root_systems-4326-nt.patch
     1Patch from Sage-Combinat: http://combinat.sagemath.org/patches/file/tip/root_systems-4326-nt.patch
    22
    3 Doc:
    4  - Use $F_4$ instead of F4
     3Documention:
     4 - quickref + links in sage.combinat.root_system
     5 - Long introduction in CartanTypes
     6 - ...
     7
     8Cartan Types:
     9 - Object oriented clean up: each cartan type has its own class (in
     10   .type_....py) which contains all its specific data (dynkin diagram,
     11   ascii art, ...). All the dispatch logic is now concentrated in the
     12   CartanType factory.
     13 - fixed the definition of rank for affine types (Anne Schilling)
     14 - systematic implementation of the classical type underlying an affine type (Anne Schilling)
     15 - New methods: is_untwisted_affine, special_node, a, acheck,
     16   translation_factors, symmetrizer, row_annihilator col_annihilator (partly Nicolas Borie)
     17 - Relabelled Cartan types (with composition, classical, special_node, dual)
     18 - Use A~... B~* BC~ convention for affine types;
     19   Kac' convention implemented by renaming them (see CartanType?)
     20 - F3 is nonexistent so use F4 in one test (Dan Bump)
     21 - ascii art for reducible (Dan Bump), relabelled, and dual Cartan types
     22
     23Root systems:
     24 - Preliminary plots (Nicolas Borie)
     25 - New methods for affine root systems (mostly Nicolas Borie):
     26   null_(co)root, level
     27 - RootSystem(["A",3,1]) returns None rather than the ambient space
     28   for type A_3 (which was wrong!)
     29 - positive and negative roots for all (finite) root lattice realizations
     30
     31Coxeter groups:
     32 - New categories: (Finite) CoxeterGroups, (Finite, Affine) WeylGroups
     33   standardized methods: first_descent, has_descent, descents,
     34   reduced_word, length, from_reduced_word, with systematic associated
     35   test (test_has_descent, ...) simple_reflections,
     36   simple_projections, coset_representatives, binary_factorisations, ...
     37   (many of them were extracted and generalized from WeylGroup)
     38 - lower and upper cover for Bruhat order (Steve Pon)
     39 - affine stanley symmetric functions for types A, A affine
     40 - Documentation (with help from Qiang Wang, Nicolas Borie)
     41
     42The following are not yet addressed, and will be bumped to a subsequent patch:
    543
    644DynkinDiagram:
     
    1452 - scalar product with coweight lattice in finite dimension
    1553
    16 Generic:
    17  - (signed) reduced word for a chamber/alcove
    18  - fix rank(): for the affine cases it currently returns the same
    19    as n.
    20 
    2154Classical case:
    2255 - reverse map to coroot space and coroot lattice by scalar product with the fundamental weights
    23  - => associated coroot
     56 - associated coroot in the root and weight space
    2457 - s_\alpha on the (co)root and (co)weight lattice for any root \alpha
    2558
    2659Affine case:
    27  - analogues whenever well defined
    28  - reduced words for translations elements.
     60 - affine ambient space
     61
     62Categorification of RootLatticeRealization / ...
     63New category CoxeterGroupModules
     64Support for non crystalographic root systems