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 enumerative combinatorics 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% #15633, #15634
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, #11563, #14107
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
      • #10554: Better support for casual usage of symmetric functions
      • Replace Symmetrica by lrcalc whenever possible
      • #10930 (prototype): specializations for symmetric functions (Martin Rubey, ???)
      • #9558: Make is_symmetric method for polynomials or where else useful
    • Multisymmetric Functions (Paul Bryan, Emmanuel Briand)
    • #11979 (prototype): Divided power algebras (Bruce)
    • #6629 (prototype) Implement Schubert polynomials (Viviane Pons, AdrienBoussicault?, Nicolas Borie)
    • #6889 (prototype): Invariant rings of permutation group (Nicolas Borie)
    • Implement more generic algorithms:
      • Antipode defined recursively
      • Product and coproduct defined by duality
      • Group like elements from primitive idempotents
    • #14901 (prototype): Lie algebras, Kac-Moody algebras, quantum groups (Travis Scrimshaw)
    • Planar algebras
    • Operads (#15633, #15634, basic support, partially depends on #10662) (FlorentHivert?, FredericChapoton?)
  • Monoids, algebras, and their representation theory:
    • Finite dimensional algebras:
      • Decomposition of the center, construction of minimal idempotents (as in MuPAD-Combinat)
      • Quiver, Cartan matrix, radical filtration (as in MuPAD-Combinat)
    • Finite monoids and semigroups
      • #12914 (prototype): Representation theory of finite semigroups (Franco, Tom, Anne, Florent, Nicolas)
      • #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: Add rings for the center of the symmetric group algebras Mathieu Guay-Paquet, Valentin Feray
    • Quivers and path algebras:
    • Experiment with KBMAG / PLURAL / Letterplace (see #4539) to easily implement algebras like affine nilCoxeter algebra, affine nilTemperley Lieb algebra, affine local plactic algebra).
  • Root systems, Coxeter groups, Hecke algebras:
    • #8906 (needs finalization): Optional package for gap3
    • Integrate/interface PyCox?
    • Root systems:
      • Constructing a root/coroot lattice realization from a pair of matrices Christian Stump
    • Coxeter groups, reflection groups:
      • #11187 (prototype): Implementation of finite reflection groups
      • #11109 (prototype): Stable grothendieck polynomials in type A affine (Nicolas Thiéry)
    • Automatic finite Coxeter/(affine)Weyl type recognition, using graph isomorphism with predefined cartan types (complex reflection group is harder)
    • Representations of Coxeter groups and Hecke algebras (through pyCox, ...) Geck, Franco,
      • 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
    • Further improve root systems, Coxeter groups and the like, getting features, inspiration, code, doc, tests, developers from Chevie (...)
  • Crystals:
    • Implement more models of Crystals?
  • Cluster algebras (Christian Stump, Gregg Musiker, Hugh Thomas):
    • #10819: Implementation of the cluster complex
    • #11010: Implementation of the SubwordComplex as defined by Knutson and Miller

The complete implementation of the core features are merged in Sage-5.9 . A further road map can be found at

  • Modules and vector spaces:
    • #10673: Roadmap for (Combinatorial)FreeModule?
    • Tensor products over an algebra, and application to representation theory
    • #9280 graded algebras
    • Graded morphisms of modules (inverse, adjoint, ...)
  • Categories & coercion: See also the Categories Road Map
    • #10668, #10667: Cleanup support for morphisms Nicolas Thiéry, Simon King
    • (prototype) Implement multiparameter morphisms This could be extracted and finalized without much work Nicolas
    • #8900 (prototype): Implement multiparameter overloaded functions, with explicit registration Nicolas Thiery
  • Analytic combinatorics:
    • #10669: MacMahon? partition analysis, aka Omega operator (Jason Bandlow, Greg Musiker)
    • #10519 (needs review): Computation of asymptotics for multivariate rational fractions
    • #11515: guessing formulas for sequences (Martin Rubey?)
    • automatic summation (Burcin Erocal)
  • Posets:
    • Support for lazy/infinite posets
  • Dynamics (Vincent Delecroix)
    • Rauzy fractals, ...
    • Flat surfaces, origamis
    • Interval exchange transforms
  • Words and languages (Vincent Delecroix, Thierry Monteil, ...):
    • Languages
    • Categorification
  • Automorphic Forms, Combinatorial Representation Theory, and Multiple Dirichlet Series ICERM
  • Tutorials
    • Merge in Sage as many of our tutorials
      • Notebook and help (is this a tutorial or a primer?)
      • Programming in Sage and Python
      • 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!


  • 2014-2015:
    • Modules & vector spaces:
      • #11111: More support for finite dimensional free modules and algebras
      • #8678: module morphisms (tensor products, inverses, ...)
    • Categories & coercion:
      • #10963: More functorial constructions (Nicolas Thiéry)
    • Quivers and path algebras:
      • #12630: Representations of quivers and quiver algebras (Jim Stark)
    • Refactoring:
    • Posets:
    • Trees:
  • 2013:
    • Symmetric functions and generalizations:
    • #11929: Implement quasi-symmetric functions (JasonBandlow?, Franco Saliola, Chris Berg, Mike Zabrocki)
    • #8899: Implement Non Commutative Symmetric Functions (JasonBandlow?, Franco Saliola, Chris Berg, LenniTevlin?, MikeZabrocki?)
    • #15150: Implement NCSym (Travis Scrimshaw, Mike Zabrocki, Franco Saliola)
    • Monoids, algebras, and their representation theory:
      • #6654: new features in group algebra category Valentin Feray
      • Free monoids, free groups (#12339), free algebras (see #7797)
      • #7797: Full interface to letterplace from singular
    • Root systems, Coxeter groups, and Hecke algebras:
      • Root systems:
        • #12882: Allows a generalized Cartan matrix as input for Dynkin diagrams Christian Stump
        • Constructing a root/coroot lattice realization from a pair of matrices Christian Stump
        • #12838: Root poset should treat type A1 properly Christian Stump
      • Coxeter groups, reflection groups:
        • Computation of reflection degrees from positive roots (easy)
        • #8359: permutation representation of a Coxeter group, using GAP3
        • #12912: Interface to Coxeter 3 from Fokko Ducloux (MikeHansen?)
        • #12774: various enhancements for Coxeter and Weyl groups
      • #8327: implement the universal cyclotomic field, using the Zumbroich basis (Christian Stump)
      • #14261: Implement the many realizations of the Hecke algebra (Brant Jones, Andrew Mathas)
    • Crystals:
      • #11305: Bijection between Rigged Configurations and Crystal Paths (Travis Scrimshaw)
      • #12251: Implementation of Littelmann path model for crystals (Anne Schilling, Mark Shimozono, Reda Chhaibi)
      • #13872: All affine type bijections between rigged configurations and tensor products of KR tableaux (Travis Scrimshaw)
      • #14130: Implementation of generalized Young wall model for affine type A crystals (Lucas Roesler, Ben Salisbury, Travis Scrimshaw)
      • #14192: Implementation of marginally large Young tableaux model for crystals of type A, B, C, D, and G (Ben Salisbury, Travis Scrimshaw)
      • #14413: Implementation of elementary crystals (Ben Salisbury)
      • #14759: Implementation of modified Nakajima monomial model for crystals (Arthur Lubovsky, Ben Salisbury)
    • Cluster algebras (Christian Stump, Gregg Musiker, Hugh Thomas):
      • #13425: Implementation of mutation type checking
      • #13424: Implementation of mutation classes
      • #13369: Implementation of the class ClusterSeed (reviewed by Salvatore Stella)
      • #10538: Implementation of the class ClusterQuiver (reviewed by Dylan Rupel)
      • #10527: Implementation of the class QuiverMutationType
      • #12587: Simplicial complexes lack hash function
      • #11523: Implementation of Cohen-Macaulay test for simplicial complexes
    • Categories and coercion:
      • #7420: Use breath-first-search or Dijkstra in coercion, as discussed (Nicolas Thiery)
      • #11935: Make parent/element classes independent of base rings (SimonKing?, NicolasThiery?)
    • Analytic combinatorics:
      • #11641 (prototype): guesser of combinatorial statistics, (Chris Berg, Franco Saliola, Christian Stump)
      • #10358 (needs_finalization): The sloane_find command is now completely broken (Thierry Monteil)
    • Posets:
      • #12848: Bug in order_ideal_complement_generators: 'down' (Franco, Anne)
      • #13240 poset polynomials
    • Enumerative combinatorics:
      • #11407: Add normalization to clonable lists (Florent Hivert)
      • #8703: Improve Trees (Florent Hivert)
      • #10193: graded/... enumerated sets
      • #6538: Reimplement from scratch IntegerListsLex?, fixing its 8-year old bugs
      • #6812: Enumerate integer vectors modulo to the action of a Permutation Group (Nicolas Borie)
      • #12250: Combinatorics of k-tableaux and the like (Anne Schilling, Mike Zabrocki)
      • #14141: Implementation of Knutson-Tao puzzles (Franco Saliola, Anne Schilling, Allen Knutson, Avi Dalal)
    • #11688 graded modules
    • Trees:
      • #15121 (a quick way to create trees)
  • 2011:
    • #8702: Fast datastructure for (combinatorial) objects with prototype (clone) design pattern (Florent Hivert)
    • #11290: Implementation of non-commutative k-Schur functions in the nilCoxeter algebra (Anne Schilling, Chris Berg)
    • Documentation: #11251, #11282
    • Debugging, profiling: #11287
    • Installation: #11296
    • Posets: #10065, #11293
    • Combinatorics: #11300, #11301, #11314
      • #11742, #11700: Cores (Anne Schilling)
      • #10155: Cyclic sieving phenomenon (Christian Stump)
    • Certainly many more!
    • Crystals:
      • #11546: Energy function for Crystals (Anne Schilling)
      • #11183: Stembridge rules (Tom Denton)
      • #10485: Thematic tutorial (Anne Schilling)
      • #10446: Schutzenberger involution, promotion, etc (Anne Schilling)
      • #8442: Lie tutorial (Dan Bump)
  • 2008: Switching to Sage!
    • October: 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: 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 final stable release of MuPAD-Combinat dropped.
  • Port of decomposable objects (from MuPAD-combinat) / species (from aldor-combinat) by Mike Hansen, funded by Google Summer of Code
  • June 24th, FPSAC (Valparaiso, Chile):
  • Official announcement of the migration
  • Goal: elementary combinatorics users can start directly with Sage
  • June 19th: Visit of Florent to Davis. Final decision to migrate!
  • February: 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: presentation of MuPAD-Combinat at the AMS meeting in San-Diego; meeting and discussions with the Sage team
  • 2007: Early contacts with Sage
    • June: design discussions between Nicolas and Mike at the Axiom Workshop 2007
  • February: First contact with Mike Hansen who wanted to port some features of MuPAD-Combinat, which we very much encouraged. In the following month, Mike translated 30k lines of code, which accounts for most of the basic combinatorics (tableaux, permutations, ...), and symmetric functions.
  • 2006-2008: Aldor-Combinat
    • Species (Martin Rubey, Ralf Hemmecke)
  • 2000-2008: 100k lines of code in MuPAD-Combinat, 20 contributers, 25+ papers
    • Symmetric functions (François Descouens, NicolasThiery?, ...)
    • NCSF, QSym, Hopf algebras, Kac algebras (Florent Hivert, NicolasThiery?)
    • Operads (Frédéric Chapoton)
    • Quivers and path algebras (Patrick Le Meur)
    • Crystals (Anne Schilling, ...)
    • Root systems, Weyl groups (NicolasThiery?, ...)
    • Representation theory of algebras (Florent Hivert, ...)
    • Enumerative combinatorics (tableaux, compositions, integer vectors, trees, ...)
    • Decomposable classes/species (NicolasThiery?, FlorentHivert?, Sébastien Cellier, Paul Zimmermann...)
    • Coercion system (NicolasThiery?)
    • Categories for algebraic combinatorics (NicolasThiery?)
    • Graph & Graphviz (Teresa Gomez Diaz)
  • December 2000: Birth of MuPAD-Combinat
Last modified 4 years ago Last modified on Aug 13, 2018, 7:12:12 AM

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