Changes between Version 58 and Version 59 of SageCombinatRoadMap


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Timestamp:
05/06/12 10:42:04 (3 years ago)
Author:
nthiery
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  • SageCombinatRoadMap

    v58 v59  
    4545* Hopf algebras, Symmetric functions, and generalizations 
    4646 * Symmetric Functions 
     47   * #11563: Make lrcalc a standard package 
    4748   * #12525: SFAHomogeneous does not work with RealField 
    4849   * Refactor SymmetricFunctions using «multiple realizations» and deprecate SFASchur and friends 
     
    6364 * #6889: Invariant rings of permutation group 
    6465 
    65    * #10305 (prototype): Add rings for the center of the symmetric group algebras 
    66      Mathieu Guay-Paquet, Valentin Feray 
    67  
    68 * Root systems 
    69  
     66* Representation theory: 
     67  * Finite dimensional algebras: 
     68    * Decomposition of the center, construction of central idempotents (as in MuPAD-Combinat) 
     69    * Quiver, Cartan matrix, radical filtration (as in MuPAD-Combinat) 
     70    * Depends on: #11111 
     71  * Finite monoids 
     72    * #12914 (prototype): Representation theory of finite semigroups 
     73    * #8360 (finalize) interface to Jean-Éric Pin's Semigroupe package 
     74    * #12915: Interfaces to the GAP packages KBMag (and to Monoids, Citrus, ...) 
     75  * Group algebras: 
     76    * #10305 (prototype): Add rings for the center of the symmetric group algebras 
     77      Mathieu Guay-Paquet, Valentin Feray 
     78    * #6654: new features in group algebra category 
     79      Valentin Feray 
     80  * Path algebras: 
     81    * #9889 (prototype): A new module implementing Monomial Algebras 
     82 
     83  * Experiment with KBMAG / PLURAL (see #4539) to implement various 
     84    algebras like affine nilCoxeter algebra, affine nilTemperley Lieb 
     85    algebra, affine local plactic algebra), see also patch 
     86    nilTemperley-as.patch in the sage-combinat queue) (AnneSchilling) 
     87    This could possibly make use of KBMAG. 
     88 
     89* Root systems: 
    7090  * #8906 (needs finalization): Optional package for gap3 
    71   * Constructing a root/coroot lattice realization from a pair of matrices 
    72     Work in progress by Christian Stump 
     91  * Integrate/interface PyCox 
     92  * Root systems: 
     93    * Constructing a root/coroot lattice realization from a pair of matrices 
     94      Work in progress by Christian Stump 
     95    * Allows a generalized Cartan matrix as input for Dynkin diagrams 
     96  * Coxeter groups, reflection groups: 
     97    * Computation of reflection degrees from positive roots (easy) 
     98    * #8359 (needs finalization): permutation representation of a Coxeter group, using GAP3 
     99    * Implement general Coxeter groups given by a Coxeter diagram 
     100    * #12912: Interface to Coxeter 3 from Fokko Ducloux (MikeHansen) 
     101    * #12774: (needs review): various enhancements for Coxeter and Weyl groups 
     102    * #11187 (prototype): Implementation of finite reflection groups 
     103 
    73104  * Automatic finite Coxeter/(affine)Weyl type recognition, using graph 
    74105    isomorphism with predefined cartan types (complex reflection group is harder) 
    75106      (Volunteers?) 
    76   * Computation of reflection degrees from positive roots (easy) 
    77   * #8359 (needs finalization): permutation representation of a Coxeter group, using GAP3 
    78107  * #8327 (needs review): implement the universal cyclotomic field, using the Zumbroich basis 
    79108    Christian Stump 
    80   * Implement general Coxeter groups given by a Coxeter diagram 
    81   * #12912: Interface to Coxeter 3 from Fokko Ducloux (MikeHansen) 
    82  
    83   * Port over the character tables (depends on 1 to be most useful) 
    84   * Representations/character tables of the Hecke algebras 
    85   * #12774: (needs review): various enhancements for Coxeter and Weyl groups 
    86   * Port Specht (AndrewMathas) 
    87   * Implement data structures for character tables / use it systematically in Sage (Volunteers? Nicolas has some design notes about this): 
    88     * of groups in Sage / GAP 
    89     * of semi-simple algebras (in Sage / GAP) 
    90     * of a coset 
    91     * See #7555: fix Cayley tables, add operation tables 
    92  
    93  * Further improve root systems, Coxeter groups and the like, 
    94    getting features, inspiration, code, doc, tests, developers from Chevie (...) 
    95  * Implement the many representations of the Hecke algebra (AndrewMathas, ...) 
    96  * Implement more models of Crystals (alcove and littlemann path, ...): #8984, ... 
    97  
    98 * Modules and vector spaces 
    99   * Tensor products of morphism 
     109  * Representations of Coxeter groups and Hecke algebras 
     110    * Port over the character tables 
     111    * Representations/character tables of the Hecke algebras 
     112    * Port Specht (AndrewMathas) 
     113    * Implement data structures for character tables / use it systematically in Sage (Volunteers? Nicolas has some design notes about this): 
     114      * of groups in Sage / GAP 
     115      * of semi-simple algebras (in Sage / GAP) 
     116      * of a coset 
     117      * See also #7555: fix Cayley tables, add operation tables 
     118  * Implement the many realizations of the Hecke algebra (AndrewMathas, ...) 
     119 
     120  * Further improve root systems, Coxeter groups and the like, 
     121    getting features, inspiration, code, doc, tests, developers from Chevie (...) 
     122 
     123 
     124* Crystals: 
     125  * Implement more models of Crystals? 
     126  * #11305: Bijection between Rigged Configurations and Crystal Paths 
     127  * #12251: Implementation of Littelmann path model for crystals 
     128 
     129* Cluster algebras (Christian Stump, ...): 
     130  * #10819: Implementation of the cluster complex 
     131  * #10538: Implementation of the classes ClusterSeed and Quiver 
     132  * #11010: Implementation of the SubwordComplex as defined by Knutson and Miller 
     133  * #12587: Simplicial complexes lack hash function 
     134  * #11523: Implementation of Cohen-Macaulay test for simplicial complexes 
     135 
     136* Modules and vector spaces: 
    100137  * Generalized tensor product 
    101138  * #10673: Roadmap for (Combinatorial)FreeModule 
    102139  * #11111 (needs finalization): More support for finite dimensional free modules and algebras 
    103  
    104 * Categories 
     140    Depends on #8678 
     141  * #8678: module morphisms (tensor products, inverses, ...) 
     142 
     143* Categories & coercion: 
    105144 
    106145 * #10963: More functorial constructions (NicolasThiéry) 
    107  
     146 * #10668, #10667: Cleanup support for morphisms 
     147 * (prototype) Implement multiparameter morphisms 
     148   This could be extracted and finalized without much work 
     149 * #8900 (prototype): Implement multiparameter overloaded functions, with explicit registration 
     150   Depends on #7420; #383 is not enough 
     151   NicolasThiery 
     152 * #7420 (prototype): Use breath-first-search or Dijkstra in Coercion, as discussed in  (volunteers?) 
     153   NicolasThiery 
    108154 
    109155* Combinatorics 
     
    121167   * #5268: Further cleanup of Enumerated sets 
    122168   * #11407: Add normalization to clonable lists 
     169   * Use ClonableIntArray and friends for all combinatorial object: permutations, partitions, compositions... 
     170   * Fix everything from: http://wiki.sagemath.org/combinat/Weirdness 
    123171   * #10534 (needs review): Optimizations for the generation of subwords, subsets, and set partitions 
    124172     VincentDelecroix 
     
    131179     * #11529 (needs review): Rooted_trees 
    132180 
    133  
    134181== Former road maps and history == 
    135182 
    136183* Todo for/at Sage Days 20.5 (May 2010): 
    137     * Finalize the basic Cython data-sctructure for combinatorial objects (in progress #8702, FlorenHivert) 
    138     * Finalize the cleanup of combinatorial object: permutations, partitions, compositions... 
    139     * #8876: Generalize #7914 (Florent) 
    140       - Support for a (partial) inverse function on terms 
    141         (when the indices of the domain do not coincide with those of the codomain) 
    142       - Non invertible triangular morphism: 
    143         - phi.preimage(y): returns the preimage x of y or None if it does not exists (or raise an exception?) 
    144          - phi.reduce(y): returns (x, r) such that y = phi(x) + r, and r contains no leading term of phi(domain) 
    145           (that would be euclidean division if phi was x -> x * p where p is some polynomial) 
    146           Better name for that method? 
    147     * (6) Use breath-first-search or Dijkstra in Coercion, as discussed in #7420 (volunteers?) 
    148     * (7) Allow for user defined overloaded operators, with signature declarations (#383 is a progress, but not enough) (NicolasThiéry, depends on (6)) 
    149     * #7980: Extract basic support for the "concrete representation of 
    150       an abstract algebra" relation out of the ncsf patch (JasonBandlow) 
    151     * (7), #7980 are building blocks for further progress in qsym/ncsf/polynomials with several basis (#6889) 
    152     * (9) is a building block for the representation theory of monoids 
    153     * (10) is the main building block for the representation theory of finite dimensional algebra 
    154184    * Design and implement framework for computing with representations / modules / character rings 
    155     * Finalize interface to Jean-Éric Pin's Semigroupe package (#8360), and 
    156       extend further the semigroup/monoid/group algebra code (#6654, ...) 
    157     * Explore / expose the functionalities of KBMAG for computing with (semi)groups defined by presentations 
    158     * Discussion about implementation of various algebras (affine nilCoxeter algebra, affine nilTemperley Lieb algebra, affine local plactic algebra), see also patch nilTemperley-as.patch in the sage-combinat queue) (AnneSchilling) This could possibly make use of KBMAG. 
    159     * Categorification of the crystal code (AnneSchilling) #8911 
     185 
    160186    * Words improvements:  
    161187        * #8595, #8618, #8574, #8673 and #8674 (misc defect fixes),  
     
    174200 
    175201* 2012: 
     202  * Optimizations: 
     203    * #11115: Rewrite cached_method in Cython 
    176204  * Symmetric functions and generalizations: 
    177     * #10333: Interface for lrcalc 
    178   * Categories: #9469, #8119, #12527 
     205    * #10333: An interface to Anders Buch's Littlewood-Richardson Calculator ``lrcalc`` 
     206  * Categories: #9469, #8119, #12527, #12877, #11943 
    179207  * Coercion: #11250, #11257 
    180208  * Enumerated sets: #11118 
     
    189217 
    190218* 2011: 
    191   * #8702: Datastructure for objects with prototype (clone) design pattern. 
     219  * #8702: Fast datastructure for (combinatorial) objects with prototype (clone) design pattern. 
     220  * #11290: Implementation of non-commutative k-Schur functions in the nilCoxeter algebra 
     221  * Documentation: #11251, #11282 
     222  * Debugging, profiling: #11287 
     223  * Installation: #11296 
     224  * Posets: #10065, #11293 
     225  * Combinatorics: #11300, #11301, #11314 
    192226 
    193227* 2010: 
    194   * #6655: Cleanups and new features about corners and cells in partition and tableau 
    195228  * Root systems, crystals, ... 
    196229    * #8984: Implementation of the Lenart--Postnikov alcove path crystal 
    197230    * #8380: Interface with GAP3 
    198   * Categories: 
     231    * #8911: Categorification of Crystals 
     232  * Categories, parents, elements: 
    199233    * #8001: Stronger category tests 
    200234    * #7921: Categories for extension types via __getattr___ 
     235    * #8044: Categories for finite/permutation/symmetric groups 
     236    * #9138, #9056, #8917, #8913, #8579 
     237    * #8120: UniqueRepresentation and hash value 
     238    * #8028: Improvements to element_wrapper 
    201239  * Symmetric functions: 
    202240    * #8259: Conversion from symmetric polynomials to basis of monomial symmetric functions 
    203   * #7004: Refactor the graph layout code, and add interface with graphviz for acyclic layout 
    204241  * Modules and vector spaces: 
    205242    * #8876: Triangular morphisms with domain and codomain having different index sets 
     
    208245    * #9651: Addition on CombinatorialFreeModule directly on dictionaries (closed: fixed) 
    209246    * #9648: ModulesWithBasis allows module_morphism's to a wider class of ... (closed: fixed) 
     247 
     248  * Graphs: 
     249    * #7004: Refactor the graph layout code, and add interface with graphviz for acyclic layout 
     250  * Enumerated sets: 
     251    * #8519: NN, NonNegativeIntegers, PositiveIntegers, IntegerRange, ... 
     252    * #6655: Cleanups and new features about corners and cells in partition and tableau 
    210253 
    211254* 2009: