A characterization of reduced forms of linear differential systems

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• 作者：Ainhoa Aparicio-Monforte^a ; ^{aparicio@risc.uni-linz.ac.at} ; Elie Compoint^b ; ^{Elie.Compoint@math.univ-lille1.fr} ; Jacques-Arthur Weil^c ; ^{Jacques-Arthur.Weil@unilim.fr}
• 关键词：34M03 ; 34M15 ; 34M25 ; 34Mxx ; 20Gxx ; 17B45 ; 17B80 ; 34A05 ; 34A26 ; 34A99
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：217
• 期：8
• 页码：1504-1516
• 全文大小：305 K

文摘

A differential system , with is said to be in reduced form if where is the Lie algebra of the differential Galois group of .

In this article, we give a constructive criterion for a system to be in reduced form. When is reductive and unimodular, the system is in reduced form if and only if all of its invariants (rational solutions of appropriate symmetric powers) have constant coefficients (instead of rational functions). When is non-reductive, we give a similar characterization via the semi-invariants of . In the reductive case, we propose a decision procedure for putting the system into reduced form which, in turn, gives a constructive proof of the classical Kolchin-Kovacic reduction theorem.