Details:
Title  Serre’s reduction of linear partial differential systems with holonomic adjoints  Author(s)  Thomas Cluzeau, Alban Quadrat  Type  Article in Journal  Abstract  Given a linear functional system (e.g., an ordinary/partial differential system, a differential timedelay 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.  Keywords  Serre’s reduction, Underdetermined linear systems of partial differential equations, Holonomic D modules, Constructive module theory, Mathematical system theory  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111002343 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  10  Pages  1192  1213  Year  2012  Note  Symbolic Computation and its Applications  Edition  0  Translation 
No  Refereed 
No 
