MuPAD-Combinat was an open-source algebraic combinatorics package for the computer algebra system MuPAD. It has now been reincarnated into Sage-Combinat, with the same mission statement: to provide an extensible toolbox for computer exploration in algebraic combinatorics, and foster code sharing between researchers in this area. The development started in spring 2001, and the package currently contains functions to deal with most usual combinatorial classes (partitions, tableaux, decomposable classes, ...). It also supplies the user with tools for constructing new combinatorial classes and combinatorial (Hopf) algebras. As an application, it provides some well-known combinatorial Hopf algebras like the algebra of symmetric functions and many generalizations. There is also some support for combinatorial Lie algebras, operads, (affine) Weyl groups, crystals, Schubert polynomials, ... The development was carried over by a community of researchers around the world, in close collaboration but independently of the MuPAD/Sciface team. In June 2008, after months of discussions and experiments, an enthusiastic consensus emerged in the community to join the now viable fully open source mathematical software Sage. We were particularly glad to have taken this decision when we learned in September 2008 that MuPAD/Sciface was bought out by Mathworks (i.e. Matlab). The development of MuPAD-Combinat itself is essentially stalled. Still, the code will remain publicly available (as always under GPL), and hopefully remain compatible with MuPAD for some time. Users should feel free to ask us for minor bug fixes. This migration is a massive investment: seven years of hard work to migrate over! Luckily, a lot of experience was gained since 2000, and a lot of the design is now pretty clear. The migration is going smoothly thanks to the efforts of many (see the road map). And it is readily paying back!

This software is also referenced in ORMS.

References in zbMATH (referenced in 24 articles , 1 standard article )

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  1. Duchamp, Gérard H.E.; Hivert, Florent; Novelli, Jean-Christophe; Thibon, Jean-Yves: Noncommutative symmetric functions. VII: Free quasi-symmetric functions revisited (2011)
  2. Bandlow, Jason; Schilling, Anne; Thiéry, Nicolas M.: On the uniqueness of promotion operators on tensor products of type $A$ crystals (2010)
  3. Bergeron, N.; Descouens, F.; Zabrocki, M.: A filtration of $(q,t)$-Catalan numbers (2010)
  4. Hivert, Florent; Novelli, Jean-Christophe; Thibon, Jean-Yves: Inversion of some series of free quasi-symmetric functions (2010)
  5. Lam, Thomas; Schilling, Anne; Shimozono, Mark: Schubert polynomials for the affine Grassmannian of the symplectic group (2010)
  6. Novelli, J.-C.; Thibon, J.-Y.; Williams, L.K.: Combinatorial Hopf algebras, noncommutative Hall-Littlewood functions, and permutation tableaux (2010)
  7. Novelli, Jean-Christophe; Saliola, Franco; Thibon, Jean-Yves: Representation theory of the higher-order peak algebras (2010)
  8. Novelli, Jean-Christophe; Thibon, Jean-Yves: Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions (2010)
  9. Bergeron, Nantel; Descouens, François; Zabrocki, Mike: A non-commutative generalization of $k$-Schur functions (2009)
  10. Fourier, Ghislain; Okado, Masato; Schilling, Anne: Kirillov-Reshetikhin crystals for nonexceptional types (2009)
  11. Hivert, Florent; Schilling, Anne; Thiéry, Nicolas M.: Hecke group algebras as quotients of affine Hecke algebras at level 0. (2009)
  12. Hivert, Florent; Thiéry, Nicolas M.: The Hecke group algebra of a Coxeter group and its representation theory. (2009)
  13. Novelli, Jean-Christophe; Thibon, Jean-Yves: A one-parameter family of dendriform identities. (2009)
  14. Nzeutchap, Janvier: Young-Fibonacci insertion, tableauhedron and Kostka numbers (2009)
  15. Descouens, Francois: Ribbon tableaux, ribbon rigged configurations and Hall-Littlewood functions at roots of unity (2008)
  16. Descouens, François; Morita, Hideaki: Factorization formulas for Macdonald polynomials (2008)
  17. Novelli, Jean-Christophe; Thibon, Jean-Yves: Noncommutative symmetric functions and Lagrange inversion (2008)
  18. Schilling, Anne: Combinatorial structure of Kirillov-Reshetikhin crystals of type $D_n^(1)$, $B_n^(1)$, $A^(2)_2n-1$ (2008)
  19. Thiery, Nicolas M.: Implementing algebraic combinatorics some feedback from the development of MuPAD-Combinat (abstract only) (2008)
  20. Novelli, Jean-Christophe; Thibon, Jean-Yves: Hopf algebras and dendriform structures arising from parking functions. (2007)

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