Université de Versailles-St Quentin, Laboratoire de Mathématiques, 45 avenue des États-Unis 78035 Versailles cedex, France
e-mail: divizio[at]math.cnrs.fr          Office: bâtiment Fermat, office 3305

#### 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