is an Involutive
package dedicated to the Quillen-Suslin theorem:
and its applications in multidimensional systems theory:
- D. Quillen,
Projective modules over polynomial rings, Invent. Math., 36 (1976), 167-171,
- A. Suslin,
The projective modules are free over polynomial rings,
Dklady-Soviet Math., 229 (1976), 1063-1066,
- T. Y. Lam,
Serre's Problem on Projective Modules, Monograph in Mathematics,
Springer Verlag, 2006,
computation of flat outputs and injective parametrizations,
Lin-Bose's generalizations of Serre's
computation of (weakly) coprime factorizations of rational
reduction and decomposition problems using the OreMorphisms package,
Serre's reductions using the forthcoming Serre package, ...
The QuillenSuslin package can be used to compute:
- bases of finitely generated free modules over a commutative
polynomial ring with coefficients in a computable field or in
certain principal ideal domains,
- injective parametrizations,
- solutions of Lin-Bose's generalizations of Serre's conjecture,
- (weakly) coprime factorizations of rational matrices, ...
For more details, see:
- 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.
An OreModules version of the QuillenSuslin package is in development.
The OreModules package was developed by A. Fabiańska
during her PhD thesis
(Aachen University) in collaboration with A. Quadrat.
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