## Section: Software

### QuillenSuslin

Participants : Alban Quadrat [correspondent] , Anna Fabiańska [Univ. Aachen] .

The Quillen-Suslin package [110] contains an implementation of the famous Quillen-Suslin theorem [130] , [133] . In particular, this implementation allows us to compute bases of free modules over a commutative polynomial ring with coefficients in a field (mainly $\mathbb{Q}$) and in a principal ideal domain (mainly $\mathbb{Z}$). The development of the Quillen-Suslin package was motivated by different constructive applications of the Quillen-Suslin theorem in multidimensional systems theory [110] (e.g., the Lin-Bose conjectures, the computation of (weakly) left/right/doubly coprime factorizations of rational transfer matrices, the computation of injective parametrizations of flat linear multidimensional systems with constant coefficients, the reduction and decomposition problems, Serre's reduction problem). To our knowledge, the Quillen-Suslin package is the only implementation of the Quillen-Suslin theorem nowadays available. The binary of the package is freely available at http://wwwb.math.rwth-aachen.de/QuillenSuslin .