QuillenSuslin (click here) is an Involutive package dedicated to the Quillen-Suslin theorem:

  1. D. Quillen, Projective modules over polynomial rings, Invent. Math., 36 (1976), 167-171,

  2. A. Suslin, The projective modules are free over polynomial rings, Dklady-Soviet Math., 229 (1976), 1063-1066,

  3. T. Y. Lam, Serre's Problem on Projective Modules, Monograph in Mathematics, Springer Verlag, 2006,

and its applications in multidimensional systems theory:

  1. computation of flat outputs and injective parametrizations,
  2. Lin-Bose's generalizations of Serre's conjecture,
  3. computation of (weakly) coprime factorizations of rational matrices,
  4. reduction and decomposition problems using the OreMorphisms package,
  5. Serre's reductions using the forthcoming Serre package, ...

The QuillenSuslin package can be used to compute:

  1. bases of finitely generated free modules over a commutative polynomial ring with coefficients in a computable field or in certain principal ideal domains,
  2. injective parametrizations,
  3. solutions of Lin-Bose's generalizations of Serre's conjecture,
  4. (weakly) coprime factorizations of rational matrices, ...

For more details, see:

  1. A. Fabiańska, A. Quadrat, Applications of the Quillen-Suslin theorem to multidimensional systems theory, Gröbner Bases in Control Theory and Signal Processing, H. Park, G. Regensburger (Eds.), Radon Series on Computation and Applied Mathematics 3, de Gruyter publisher, 23-106.

The QuillenSuslin package was developed by A. Fabiańska during her PhD thesis (Aachen University) in collaboration with W. Plesken and A. Quadrat.

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