First presenter Co-presenter(s)
Name :  Thomas Cluzeau * Name:   
E-mail: E-mail:  
Affiliation: École Nationale Supérieure d'Ingénieurs de Limoges Name:   
Department: Département Mathématiques Informatique  E-mail:    
City: Limoges Name:   
State/Province:   E-mail:    
Country: France Name:   
10-01  E-mail:    
Session: 10- Algebraic and Algorithmic Aspects of Differential and Integral Operators Schedule:
Thursday, 11:00
Related website:  
Title of
Serre's Reduction of Linear Functional Systems: Theory, Implementation and Applications
Slides of this talk (PDF)

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)