Computing the Lie algebra of the differential Galois group: The reducible case. (September 2022)

• Record Type: Journal Article
• Authors: Dreyfus, Thomas; Weil, Jacques-Arthur
• Is Part Of: Journal of symbolic computation. Volume 112(2022)
• Page Start: 122
• Page End: 163
• Publication Date: 2022-09
• Subjects: primary 34A05 68W30 34M03 34M15 34M25 17B45; Ordinary differential equations -- Differential Galois theory -- Computer algebra -- Lie algebras; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.01.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we explain how to compute the Lie algebra of the differential Galois group of a reducible linear differential system. We achieve this by showing how to transform a block-triangular linear differential system into a Kolchin-Kovacic reduced form. We combine this with other reduction results to propose a general algorithm for computing a reduced form of a general linear differential system. In particular, this provides directly the Lie algebra of the differential Galois group without an a priori computation of this Galois group.