Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System

DOI10.1145/2930889.2930932zbMath1364.12003OpenAlexW2478362166MaRDI QIDQ2985809

Thomas Cluzeau, Lucia Di Vizio, Jacques-Arthur Weil, Moulay A. Barkatou

Publication date: 10 May 2017

Published in: Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/2930889.2930932

zbMATH Keywords

algorithmscomputer algebraLie algebrasdifferential Galois theorylinear differential systemsreduced formseigenringsGrothendieck-Katz \(p\)-curvature conjecture

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Differential algebra (12H05) Lie algebras of linear algebraic groups (17B45) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Related Items (11)

Degree bound for toric envelope of a linear algebraic group ⋮ Hiroshi Umemura and French mathematics ⋮ Intrinsic Approach to Galois Theory of 𝑞-Difference Equations ⋮ Darboux transformations for orthogonal differential systems and differential Galois theory ⋮ Effective algebraic independence of values of \(E\)-functions ⋮ Reduced forms of linear differential systems and the intrinsic Galois-Lie algebra of Katz ⋮ On the computation of the Galois group of linear difference equations ⋮ Galois groups of linear difference-differential equations ⋮ Linear differential systems with small coefficients: various types of solvability and their verification ⋮ Differential Galois Theory and Integration ⋮ Computing the Lie algebra of the differential Galois group: the reducible case

Uses Software

• Isolde
• Maple

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