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

- 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:

- M. S. Boudellioua, A. Quadrat,
*Serre's reduction of linear functional systems*, Mathematics in Computer Science, 4 (2010), 289-312. - 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. -
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.