Section: Software and Platforms

OreMorphisms

Participants : Alban Quadrat [correspondent] , Thomas Cluzeau [ENSIL, Univ. Limoges] .

The OreMorphisms package [95] of OreModules [91] is dedicated to the implementation of homological algebraic tools such as the computations of homomorphisms between two finitely presented modules over certain noncommutative polynomial algebras (Ore algebras), of kernel, coimage, image and cokernel of homomorphisms, Galois transformations of linear multidimensional systems and idempotents of endomorphism rings. Using the packages Stafford and Quillen-Suslin , the factorization, reduction and decomposition problems can be constructively studied for different classes of linear multidimensional systems. Many linear systems studied in engineering sciences, mathematical physics and control theory have been factorized, reduced and decomposed by means of the OreMorphisms package. The binary of the package is freely available at http://www-sop.inria.fr/members/Alban.Quadrat/OreMorphisms/index.html .

A Mathematica version of the OreMorphims package is in development. It is being developed by Maris Tõnso (Institute of Cybernetics, University of Tallinn), Thomas Cluzeau (ENSIL, University of Limoges) and Alban Quadrat within the PHC Parrot project CASCAC. The Mathematica version of the OreMorphims package is based on the implementation of Gröbner bases over Ore algebras available in the Mathematica HolonomicFunctions package developed by Christoph Koutschan.