MuPAD-Combinat is an open-source algebraic combinatorics package for
the computer algebra system 2.0.0 and higher. Its main purpose is to
provide an extensible toolbox for computer exploration, and foster
code sharing between researchers in this area.
http://mupad-combinat.sf.net/
MuPAD-Combinat version 1.2.0 (stable) has just been released:
https://sourceforge.net/project/showfiles.php?group_id=20513
New combinatorial libraries:
- combinat::necklaces
- combinat::lyndonWords
So far, they allow to count and generate necklaces and Lyndon words
with prescribed content (say all the Lyndon words one can build out
of [1,1,1,2,2,2,3]). This uses a Constant Amortized Time algorithm
from Joe Sawada (2003).
- combinat::ribbons and skewTableaux (stable)
- combinat::ribbonsTableaux
- combinat::graphs: Interface with Brendan McKay's Nauty library for
generating and manipulating graphs up to an isomorphism
- combinat::lrcalc: Interface with Anders Buch's
Littlewood-Richardson Calculator C library.
Used for faster symmetric function computations
- combinat::chooseNK, multisetNK, splitNK (experimental)
Improvements in combinat::generator:
- support for copying generators
- multiset, powerset, space efficient cartesian product
Improvements in combinat::decomposableObjects:
- Standalone generator in the labelled and unlabelled cases
- New constructors:
Lyndon(B), BoxedProd(B, C) (rewritten as MultX(DivX(B), C)
- Restrictions on length and size of the components for generating
unlabelled sets, multisets, cycles, ...
- Functional Domain constructor for count, unrank, random, generator
- Tighter type checking, and improved error messages
Improvements by Xavier Molinero on the complexity of existing things
like unrank and random for combinat::chooseNK, and extensions to
multiset, permutations(n,k), ...
New algebraic features:
- Improved support for Hopf algebras
- Dom::TensorProductOfFreeModules
- Cat::ModuleWithSeveralBases, Cat::AlgebraWithSeveralBases, ...
Generic support for free modules with several basis, with
conversions between them and so on (experimental)
- Automatic computation of the representation theory of
a finite dimensional algebra (experimental)
- experimental::FreeOperad, Cat::Operad, Cat::OperadWithBasis:
basic support for operads (experimental)
- Many new and improved examples of combinatorial algebras
Improvements to MAPITL:
- MuPAD objects as standard C++ objects (experimental)
- Seamless embedding of static C++ objects in MuPAD cells (experimental)
Misc improvements:
- IPC should be functional again on most platforms
- Improved html documentation (less broken links, nicer output)
Building is now possible on most platforms (requires latex + tex4ht)