Version 68 (modified by nthiery, 6 years ago) (diff)


Roadmap and status report for Sage-Combinat

This page is an attempt at drawing a road map for Sage-Combinat, starting with the migration from MuPAD-Combinat.

Please feel free to edit this page to add more items, or add your names for topics you contributed to or would be interested in contributing to (this helps knowing who does what and who to contact for further collaborations).


All Sage-Combinat tickets

Progress of the migration from MuPAD to Sage

Topic Progress Comments
Basic combinatorial classes 75% 2007-08 by Mike
Decomposable objects / Species 75% #10662
Trees 30%
Posets 100%
Words 100%
Symmetric functions 90%
k-Schur & the like 90%
Root systems / ... 90%
Crystals 90%
Category framework 100%
Hopf algebra framework 80%
Free modules & such 80%
Algebra (desosseur, ...) 50%
Operads 15%
Linbox interface 100% (compares to 10% in MuPAD)
GAP interface 80% (compares to 1% in MuPAD)
Interface for fast Gröbner basis 100% (compares to 0% in MuPAD)
Nauty 100% (compares to 50% in MuPAD
Symmetrica 60%
lrcalc 95% #10333
GLIP 50% #6812
graphviz / dot2tex 80% #7004, #10518
Database access 100%
MachineIntegerListsLex? 0% Will be easy via cython
Basic abstract data structures 100% (fast stacks, AVL, dancing links) compares to just the basic ones in MuPAD + no real way to implement some with serious speed ourselves

Road map

  • Hopf algebras, Symmetric functions, and generalizations
    • Symmetric Functions
      • #11563: Make lrcalc a standard package
      • #12525: SFAHomogeneous does not work with RealField?
      • Refactor SymmetricFunctions? using «multiple realizations» and deprecate SFASchur and friends See also: #7980
      • #10930 (prototype): specializations for symmetric functions Martin Rubey, ???
      • #10554: Better support for casual usage of symmetric functions
      • #9558: Make is_symmetric method for polynomials or where else useful
      • #9194: Expose and extend the thematic tutorial on symmetric functions
    • #11929 (prototype): Implement quasi-symmetric functions JasonBandlow?, Valentin Feray, ???
    • #8899 (prototype): Implement Non Commutative Symmetric Functions JasonBandlow?, AdrienBoussicault?, LenniTevlin?, JeanYvesThibon?, MikeZabrocki?
    • #11979 (prototype): Divided power algebras Bruce
    • Implement Schubert polynomials (Viviane Pons, AdrienBoussicault?, Nicolas Borie)
    • #6889 (prototype): Invariant rings of permutation group
    • Implement more generic algorithms:
      • Antipode defined recursively
      • Product and coproduct defined by duality
      • Group like elements from primitive idempotents
    • Kac algebras
    • Quantum groups
    • Planar algebras
  • Monoids, algebras, and their representation theory:
    • Finite dimensional algebras:
      • Decomposition of the center, construction of central idempotents (as in MuPAD-Combinat)
      • Quiver, Cartan matrix, radical filtration (as in MuPAD-Combinat)
      • Depends on: #11111
    • Finite monoids and semigroups
      • #12914 (prototype): Representation theory of finite semigroups
      • #8360 (needs finalization) interface to Jean-Éric Pin's Semigroupe package
      • #12915: Interfaces to the GAP packages KBMag (and to Monoids, Citrus, ...)
    • Calculus on modules (direct sums, tensor products, induction, restriction, quotients, radical, ...) (in progress for semigroups)
    • Tower of algebras: representations, Grothendieck rings, ...
    • Group algebras:
      • #10305 (prototype): Add rings for the center of the symmetric group algebras Mathieu Guay-Paquet, Valentin Feray
      • #6654 (prototype): new features in group algebra category Valentin Feray
    • Path algebras:
      • #9889 (prototype): A new module implementing Monomial Algebras
      • #12630 (needs review): Representations of quivers and quiver algebras
    • Experiment with KBMAG / PLURAL / Letterplace (see #4539) to easily implement algebras like affine nilCoxeter algebra, affine nilTemperley Lieb algebra, affine local plactic algebra).
    • Free monoids, free groups (#12339), free algebras (see #7797)
    • #7797 (needs review): Full interface to letterplace from singular
  • Root systems, Coxeter groups, Hecke algebras:
    • #8906 (needs finalization): Optional package for gap3
    • Integrate/interface PyCox?
    • Root systems:
      • #12882 (prototype): Allows a generalized Cartan matrix as input for Dynkin diagrams Work in progress by Christian Stump
      • Constructing a root/coroot lattice realization from a pair of matrices
      • #12838 (needs finalization): Root poset should treat type A1 properly
    • Coxeter groups, reflection groups:
      • Computation of reflection degrees from positive roots (easy)
      • #8359 (needs finalization): permutation representation of a Coxeter group, using GAP3
      • Implement general Coxeter groups given by a Coxeter diagram
      • #12912: Interface to Coxeter 3 from Fokko Ducloux (MikeHansen?)
      • #12774: (needs review): various enhancements for Coxeter and Weyl groups
      • #11187 (prototype): Implementation of finite reflection groups
      • #11109: Stable grothendieck polynomials for affine Weyl group elements in type A
    • Automatic finite Coxeter/(affine)Weyl type recognition, using graph isomorphism with predefined cartan types (complex reflection group is harder)
    • #8327 (needs review): implement the universal cyclotomic field, using the Zumbroich basis Christian Stump
    • Representations of Coxeter groups and Hecke algebras
      • Port over the character tables
      • Representations/character tables of the Hecke algebras
      • Port Specht (AndrewMathas?)
      • Implement data structures for character tables / use it systematically in Sage (Volunteers? Nicolas has some design notes about this):
        • of groups in Sage / GAP
        • of semi-simple algebras (in Sage / GAP)
        • of a coset
        • See also #7555: fix Cayley tables, add operation tables
    • Implement the many realizations of the Hecke algebra (AndrewMathas?, ...)
    • Further improve root systems, Coxeter groups and the like, getting features, inspiration, code, doc, tests, developers from Chevie (...)
  • Crystals:
    • Implement more models of Crystals?
    • #11305 (prototype): Bijection between Rigged Configurations and Crystal Paths
    • #12251 (needs review): Implementation of Littelmann path model for crystals
  • Cluster algebras (Christian Stump, ...):
    • #10819: Implementation of the cluster complex
    • #10538: Implementation of the classes ClusterSeed? and Quiver
    • #11010: Implementation of the SubwordComplex? as defined by Knutson and Miller
    • #12587: Simplicial complexes lack hash function
    • #11523: Implementation of Cohen-Macaulay test for simplicial complexes
  • Modules and vector spaces:
    • #10673: Roadmap for (Combinatorial)FreeModule?
    • #11111 (needs finalization): More support for finite dimensional free modules and algebras Depends on #8678 and #10963
    • #8678 (needs finalization): module morphisms (tensor products, inverses, ...)
    • Tensor products over an algebra, and application to representation theory
    • #9280: graded modules
    • Graded morphisms of modules (inverse, adjoint, ...)
  • Combinatorics
    • #10662: Improve combinatorial species / decomposable classes
    • Basic support for operads (partially depends on #10662) FlorentHivert?, FredericChapoton?
    • Generating series, analytic combinatorics, ...:
      • #10669: MacMahon? partition analysis, aka Omega operator
      • #10519 (needs review): Computation of asymptotics for multivariate rational fractions
    • Posets:
      • #12848: Bug in order_ideal_complement_generators: 'down'
      • Support for lazy/infinite posets
      • #12916: Dedekind-MacNeil? completion of finite posets
    • Enumerated sets:
  • Tutorials
    • Merge in Sage as many of our tutorials
      • Notebook and help (is this a tutorial or a primer?)
      • Calculus and Linear algebra
      • Combinatorics (to be taken from «Calcul Mathématique Avec Sage» NicolasThiery? and Hugh Thomas
  • Sage-Combinat workflow:
    • Write down the properties we want our workflow to have, and improve it!


  • 2011:
    • #8702: Fast datastructure for (combinatorial) objects with prototype (clone) design pattern.
    • #11290: Implementation of non-commutative k-Schur functions in the nilCoxeter algebra
    • Documentation: #11251, #11282
    • Debugging, profiling: #11287
    • Installation: #11296
    • Posets: #10065, #11293
    • Combinatorics: #11300, #11301, #11314
    • Certainly many more!
  • July 2009: FPSAC'09 (RISC, Linz, Austria)
    • Goal: Most features ported
    • Goal: Most of the research done with Sage-Combinat
    • Goal: All new users can start directly with Sage
  • October 08: Sage Days 10 (Nancy, France)
    • Get the core MuPAD-Combinat developers started with Sage
    • Design, prioritization, planning
    • Design of the categories and (Hopf) algebra framework using the new coercion system
  • September 08: announcement that Sciface is purchased by Mathworks (Matlab).
    • MuPAD does not qualify anymore as a "reasonably priced high quality computer algebra system".
    • Sciface cancels its formerly liberal licence policy for MuPAD-Combinat developers.
    • Plan for a last stable release of MuPAD-Combinat dropped.
  • Summer 2008: port of decomposable objects (from MuPAD-combinat) / species (from aldor-combinat) by Mike Hansen, funded by Google
  • June 24th 2008, FPSAC (Valparaiso, Chile):
    • Official announcement of the migration
    • Goal: elementary combinatorics users can start directly with Sage
  • June 19th 2008: Visit of Florent to Davis. Final decision to migrate!
  • February 2008: Sage Days 7 (Los Angeles)
    • Technical experimentation with Sage to see how fit it is for our purposes.
    • Partial port of the crystals library (#2742, AnneSchilling? and NicolasThiéry?)
    • Implementation of Xin's Omega algorithm by Jason and Greg #10669
  • January 2008: presentation of MuPAD-Combinat at the AMS meeting in San-Diego; meeting and discussions with the Sage team
  • June 2007: design discussions between Nicolas and Mike at the Axiom Workshop 2007
  • February 2007: First contact with Mike Hansen who wanted to port some features of MuPAD-Combinat, which we very much encouraged. Since then Mike translated 30k lines of code, which accounts for most of the basic combinatorics (tableaux, permutations, ...), and symmetric functions.

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