Serre’s reduction of linear partial differential systems based on holonomy

Given a linear functional system (e.g., an ordinary/partial differential system), Serre’s reduction aims at finding 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 differential equations with analytic coefficients whose formal adjoints are holonomic in the sense of algebraic analysis. In particular, we prove that every analytic linear system of ordinary differential equations with at least one input is equivalent to a sole analytic ordinary differential equation. I. ALGEBRAIC ANALYSIS APPROACH TO LINEAR