Differential Equations and Algebraic Relations

We consider a linear differential equationLy = 0 of ordernwith coefficients inC(z) whose differential Galois groupGis supposed to be reductive and unimodular. We give an algorithm for the construction of a system of generators of the ideal of algebraic relations, with coefficients inC(z), among the entries of a fundamental matrix of solutions ofLy = 0, starting from the data of aC-algebra basis of theGinvariant polynomials with coefficients inCinnvector variables.