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, to appear in Journal of Symbolic Computation, 2011.

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