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This is the definitive version of these Web pages and of the ACE 3.0 sources (February 1999).

Voyez l'annonce du livre de Sébastien Veigneau Approches impérative et fonctionnelle de l'algorithmique, Applications en C et Caml-Light, qui inclut de nombreux exercices corrigés.

Have a look on the Sébastien Veigneau's book Approches impérative et fonctionnelle de l'algorithmique, Applications en C et Caml-Light, which includes many exercices with solutions.

ACE is a MAPLE library devoted to Algebraic Combinatorics computations. It is available for Maple V release 1, 2, 3, 4 and since 1999, for Maple V release 5. This is a joint effort of a number of people from the University of Marne-la-Vallée. The development has been supervised by Alain Lascoux and Jean-Yves Thibon.

When using the ACE system, thank you for including references to ACE in your articles.

The project started in April 1994, at the University of Marne-la-Vallée, with the development of three MAPLE packages, dealing respectively with the symmetric group, Schubert polynomials and noncommutative symmetric functions. These packages were available in July 1994. We made up our minds to develop a more general project about algebraic combinatorics on October 1994. The aim was to build an ``easy to use'' Algebraic Combinatorics Environment. We have chosen MAPLE because this system is widely used by combinatorists and it has a convenient user's interface. We had in mind to develop an efficient toolbox of functions for research in algebraic combinatorics. The interface had to be very flexible for first experimentations, whereas it may be more interesting to use some specific programs for large scale computations: for instance, we refer the reader to the SYMMETRICA system that is well suited for such computations.

We also refer the reader to the new system µ-EC developped by Vincent Prosper (University of Marne-la-Vallée) which includes the SYMMETRICA system (to compute with symmetric functions) and can be seen as an environment of computation in combinatorics for the computer algebra system MuPAD. The µ-EC system includes many functions available in ACE.

The story started in 1994. ACE 1.0 was divided into various packages dealing with specific objects such as noncommutative symmetric functions, Schubert polynomials, tableaux or Hecke algebra, each package having the ability to use some functions defined in the other packages. The first version of ACE was available for any Ms-Dos or Unix system, for MAPLE V Release 1, 2 and 3.

The second version ACE 2.0 was available since June 1996 for any Ms-Dos, Unix and Macintosh system. It provided new packages and new functions in the already existing packages. Several people have been involved in the project in order to develop new programs as for instance to work with the hyperoctahedral group and with several algebras associated to the hyperoctahedral groups B(n), together with their realizations as algebras of operators on the ring of polynomials. Moreover, a package has been developed to work with the representation theory of classical Lie groups (symplectic and orthogonal groups), whereas a new package was devoted to computations in the polynomial ring Z[x1, ..., xn] regarded as a free module of rank n! over the ring Sym[x1, ..., xn] of symmetric polynomials, and another one was devoted to calculations in the Fock space representations of the quantum affine algebras Uq(sl^(n)).

The third version of ACE, that is ACE 3.0, has been released at the beginning of 1998. Many changes have been made in order to get a coherent system devoted to computations in algebraic combinatorics. Many function names have been changed, many functions have disappeared, either becoming internal functions or being included as options of other more general ones. Function names have been strictly normalized.

ACE 3.0 has thus less functions but more functionalities. In particular, several packages have been included such as two packages to handle partitions and compositions of integers, one package to work in the free algebra, one package dealing with symmetric functions on different alphabets.

The ACE system, version 3.0, is now available for Maple V Release 1, 2, 3, 4 and 5 for any Ms-Dos, Unix and Macintosh system.

I hope this system will be useful for further developments in computer science in relation with algebraic combinatorics. I would like to thank you for your interest in ACE, quant à moi, je vais désormais voler vers d'autres horizons...

Sébastien Veigneau,
Université de Marne-la-Vallée,
February 15, 1999.

Find out more about ACE 3.0 at
Copyright © 1994, 1995, 1996, 1997, 1998 Sébastien Veigneau, Institut Gaspard Monge, Université de Marne-la-Vallée
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