- We submitted an application for the European Academic Software Award 2004

We just passed stage 1. Next deadline is March 10 for stage 2.

This page has been used to prepare the content of the submission form for stage 1; we will shortly use it for the submission form for stage 2. Comments welcome!

Florent Hivert, Nicolas M. Thiéry, et al.

(or should we include Teresa, JC, François, ...?)

MuPAD-Combinat is an open-source algebraic combinatorics package for the computer algebra system MuPAD 2.0.0 and higher. The main purpose of this package is to provide an extensible toolbox for computer exploration.

Research in algebraic combinatorics relies heavily on computer exploration. This requires the development and the use of efficient, versatile, and extendible computer algebra tools. Once developed, those tools ought to be made freely available, for further research in algebraic combinatorics and in many related fields (polynomial systems, statistical mechanics, ...), as well as for teaching.

To this end, we want to foster the sharing of code in our community, by setting up a common open-source development platform which would act as a repository.

The development started in spring 2001, and the package currently contains functions to deal with usual combinatorial classes (partitions, tableaux, decomposable classes, ...), Schubert polynomials, characters of the symmetric group, and weighted automata. It supplies the user with tools for constructing new combinatorial classes and combinatorial algebras and, as an application, provides some well-known combinatorial algebras like the algebra of symmetric functions and various generalizations.

MuPAD-Combinat has already played a significant role in various research projects that lead to 10 publications altogether.

Now that the architecture of the core of the project is setup, we are actively advertising it, in order to attract new users and developers.

The developers, as well as most of the current and target users are participants of the ACE (Algebraic Combinatorics in Europe) research

- training network of the European Community

MuPAD-Combinat represents about 65000 lines of MuPAD and C++ code together with 450 pages of doc, written by 3 main developers and altogether about 20 contributers.

The development is done in close colaboration with the MuPAD team in Germany, and the core of the package is integrated in the official library of MuPAD since version 2.5.0.

The statistics on sourceforge indicates 400 downloads, and 6000 page views http://sourceforge.net/project/stats/?group_id=20513, but it's difficult to obtain a serious usage estimatation from those figures. Also, since our code is included in the standard distribution of MuPAD we may have users that don't even know about our project.

We are preparing a list of publications where MuPAD-Combinat has been used during the research process.

We know personally of half a dozen intensive users (most of them taking part in the development), and a dozen occasional users, distributed over several universities, in France, Tunisia and Germany. We expect to have new users in Spain and USA soon. Most of them are researchers, and use it for computer exploration. Usage for teaching has just started recently.

We have used this package to study the combinatorial properties of the Hopf algebra of Loday and Ronco, which is obtained by defining a suitable product on binary trees. Here is a sample product computation:

o * o = o + o + o + o + o + o / \ / \ / \ / \ / \ / \ / \ / \ /\ \ /\ \ /\ /\ /\ \ /\ /\ /\ \ / \ /\ \ \ /\ \ / \ /\/ /\ \ /\

This algebra appears in various contexts, in particular in renormalization problems in theoretical physics and in the theory of operads in algebraic topology.

Thanks to computer exploration, we have been able to discover that this algebra is very close to the well known algebra of symmetric functions. This allowed us to construct by analogy several basis of this algebra. Surprisingly all these constructions are based on the combinatorics of the algorithm of binary search trees, which every computer science undergraduate knows of. This established a beautiful bridge between many different domains of science.

Our software is already used in several countries. English being widespread in our community, the language is not too much of a restriction.

No reason not to be portable across Europe or more.

64Mo to be comfortable?

100 Megs for both MuPAD and MuPAD-Combinat

MuPAD >= 2.0.0. Freely available for education and research.

CDROM, Downloadable files, Paper

The project is distributed in the form of a package for MuPAD. We also provide a live demonstration cdrom. Finally, we have submitted an article describing the project to the Séminaire Lotharingien de

- Combinatoire

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