Serre's reduction of linear systems of partial differential equations with holonomic adjoints

Thomas Cluzeau (1) , Alban Quadrat (2, 3)

1 DMI
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 L2S - Laboratoire des signaux et systèmes

Given a linear functional system (e.g., ordinary/partial di erential system, di erential time-delay system, di erence system), Serre's reduction aims at nding an equivalent linear functional system which contains fewer equations and fewer unknowns. The purpose of this paper is to study Serre's reduction of underdetermined linear systems of partial di erential equations with either polynomial, formal power series or analytic coe cients and with holonomic adjoints in the sense of algebraic analysis. We prove that these linear partial di erential systems can be de ned by means of a single linear partial di erential equation. In the case of polynomial coe cients, we give an algorithm to compute the corresponding equation.

Domains: Computer Science [cs]; Symbolic Computation [cs.SC]

Thomas Cluzeau, Alban Quadrat. Serre's reduction of linear systems of partial differential equations with holonomic adjoints. 2010. ⟨hal-00760057⟩