Serre鈥檚 reduction of linear partial differential systems with holonomic adjoints

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• 作者：Thomas Cluzeau^a ; ^{cluzeau@ensil.unilim.fr} ; Alban Quadrat^b ; ¹ ; ^{alban.quadrat@inria.fr}
• 关键词：Serre&rsquo ; s reduction ; Underdetermined linear systems of partial differential equations ; Holonomic D-modules ; Constructive module theory ; Mathematical system theory
• 刊名：Journal of Symbolic Computation
• 出版年：2012
• 期刊代码：140_07477171
• 类别：cp
• 出版时间：October, 2012
• 卷：47
• 期：10
• 页码：1192-1213
• 文件大小：386 K

摘要

Given a linear functional system (e.g., an ordinary/partial differential system, a differential time-delay system, a difference system), Serre鈥檚 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鈥檚 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.