Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System
Résumé
We consider a linear differential system [A] : y' = A y with coefficients in C(x). The differential Galois group G of [A] is a linear algebraic group which measures the algebraic relations among solutions. Although there exist general algorithms to compute G, none of them is either practical or implemented. This paper proposes an algorithm to compute the Lie algebra g of G when [A] is absolutely irreducible. The algorithm is implemented in Maple.