Slides of this talk (PDF)
The first purpose of this talk is to recall briefly constructive results
on Serre's reduction of determined/overdetermined/underdetermined
linear functional systems obtained recently by M. S. Boudellioua (Sultan
Qaboos University, Oman) and A. Quadrat(INRIA Sophia Antipolis,
France). Serre's reduction aims at finding an equivalent presentation of
a linear functional system which contains fewer equations and unknowns.
We shall explain why this problem can be reduced to the case where the
equivalent system contains only one equation. Then, we will discuss our
implementation of these results in an OreModules package called Serre.
Finally, we will concentrate on the zero-dimensional case (D-finite or
holonomic linear functional systems) where we can go further in this
analysis and explain the links between these results and the Jacobson
normal form of a matrix with entries in a principal ideal domain (e.g.,
ODEs with rational coefficients). The different results will be
illustrated with explicit examples coming from control theory and
engineering sciences. This is a work in progress in collaboration with
A. Quadrat (INRIA Sophia Antipolis, France) |