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