The Serre package handles Serre's reduction of linear functional systems, i.e., finds a presentation of finitely presented left module over an Ore algebra (available in the Maple Ore_algebra package) with fewer generators and relations, i.e., find a representation of the corresponding linear functional system containing fewer unknowns and equations.

Serre's reduction was first developed in

  1. J.-P. Serre, Sur les modules projectifs, Séminaire Dubreil-Pisot, vol. 2, 1960/1961, in Oeuvres, Collected Papers, Vol. II 1960-1971, Springer, 1986, 23-34,

for full row rank matrix with entries in a commutative polynomial ring with coefficients in a field, to study complete intersection in algebraic geometry. Serre's reduction can be extended to a larger class of rings and, in particular, to the Ore algebras available in the Maple Ore_algebra package.

Serre's reduction has recently been proved to be a useful technique for simplifying linear (functional/control) systems. It is thus a useful tool for algebraically preconditioning a linear (functional/control) system, and it can be used before the study of its structural properties or applying numerical methods.

For more details, see:

  1. M. S. Boudellioua, A. Quadrat, Serre's reduction of linear functional systems, Mathematics in Computer Science, 4 (2010), 289-312.
  2. T. Cluzeau, A. Quadrat, Serre's reduction of linear systems of partial differential equations with holonomic adjoints, Journal of Symbolic Computation, 47 (2012), 1192-1213.
  3. T. Cluzeau, A. Quadrat, Further results on the decomposition and Serre's reduction of linear functional systems, Proceedings of the 5th Symposium on System Structure and Control, Grenoble (France), (04-06/02/13).

This forthcoming package, built upon the OreModules package, is developed by T. Cluzeau and A. Quadrat.

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