%0 Journal Article
%T Serre's reduction of linear partial differential systems with holonomic adjoints
%+ DMI (XLIM-DMI)
%+ Dynamical Interconnected Systems in COmplex Environments (DISCO)
%+ Laboratoire des signaux et systèmes (L2S)
%A Cluzeau, Thomas
%A Quadrat, Alban
%< avec comité de lecture
%@ 0747-7171
%J Journal of Symbolic Computation
%I Elsevier
%V 47
%N 10
%P 1192-1213
%8 2012
%D 2012
%R 10.1016/j.jsc.2011.12.041
%K Serre's reduction
%K Underdetermined linear systems of partial differential equations
%K Holonomic D-modules
%K Constructive module theory
%K Mathematical system theoryJournal articles
%X Given a linear functional system (e.g., an ordinary/partial differential system, a differential time-delay system, a difference 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 either polynomial, formal power series or locally convergent power series coefficients, and with holonomic adjoints in the sense of algebraic analysis. We prove that these linear partial differential systems can be defined by means of only one linear partial differential equation. In the case of polynomial coefficients, we give an algorithm to compute the corresponding equation.
%G English
%L hal-00765942
%U https://hal.science/hal-00765942
%~ UNILIM
%~ EC-PARIS
%~ CNRS
%~ INRIA
%~ UNIV-PSUD
%~ INRIA-SACLAY
%~ SUP_LSS
%~ XLIM
%~ XLIM-DMI
%~ INRIA_TEST
%~ SUP_SYSTEMES
%~ TESTALAIN1
%~ INRIA2
%~ UNIV-PARIS-SACLAY
%~ UNIV-PSUD-SACLAY
%~ DISCO-L2S