MAX: a MAPLE package for the (max,+) algebra

MAX is a MAPLE package implementing

• the basic scalar-matrix operations, including star, karp-algorithm.
• the rational operations in the so called MinMax[[gamma,delta]] algebra
• symbolic computations of periodic throughputs of timed event graphs.

The package is documented in the chapters VIII,IX of my thesis.

The package has been reasonably and widely tested (even by students at \'Ecole des Mines). It suffers two important defaults: (1) the syntax is rather painful due to bad historical choices. (2) the rational MinMax[[gamma,delta]] part could be made faster by using different rational representations.

Avaibility MAX works on Maple V.0--V.2 and (with inelegant syntax changes) on Maple V.3. (Porting it to Maple V.4 is a non-immediate thing, rather than spending time in this, my intention is rather to invest time in developing faster C code). The package is available as is on email demand to me: Stephane.Gaubert@inria.fr.

but there are some better NEW softwares

• Max-Plus toolbox of SCILAB The numerical part of the toolbox is now superseded by the free max-plus toolbox of scilab, a fast implementation (in Fortran and C) of max-plus linear algebra algorithms, including the fast Howard's multichain policy iteration algorithm to compute the eigenvalues of max-plus linear maps
• ERS Alain Jean-Marie developed a collection of C programs for the analysis of Discrete Event Systems, including some max-plus algorithms and a TCL/TK interface. His program, called ERS, is available from his page
• C++ MinMax[[gamma,delta]] library Laurent Hardouin and his team at Angers implemented the algebra of max-plus rational series (in fact, the so-called minmax[[gamma,delta]] subalgebra) in C++. His "lminmaxgd" library is available from his page