with Moulay A. Barkatou, Thomas Cluzeau, Jacques-Arthur Weil. Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation (ISSAC), 63–70. 
Abstract:
We consider a linear differential system [A] : y' = A y, where A has coefficients in the differential field 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, of probabilistic nature, to compute the Lie algebra
g of G. The algorithm is implemented in Maple.
HAL: hal-01676487