What I did : a) I went over typos of "suggested addition" p2 l-3 changed [$\calA$ is a Lie algebra morphism from $(\ncs{\C}{X},[,])$ to the Lie algebra generated by the polysystem $\{A_i\}_{i=0,n}$~:]--> [$\calA$ is a morphism of algebras from $(\ncs{\C}{X},[,])$ to the algebra generated by the polysystem $\{A_i\}_{i=0,n}$~:] p3 l8 [is to construct the fundamental system of solutions]--> [is to construct a fundamental system of solutions] l11 [in order to obtain the {\it universal} Picard-Vessiot extension]--> [in order to obtain this {\it universal} Picard-Vessiot extension] l-8 [with an element $d\in \frak{Der}(\A)$]--> [with a distinguished derivation $d\in \frak{Der}(\A)$ ] [we shall see in the applications.]--> [we shall see some in the applications.] p6 th 3.2 l5 [which do not contain]-->[which does not contain] p8 Conclusion l3 [but can be taken into account at the computational level as]--> [but can be taken into account at the very computational level because] [large rings allows to express] --> [large rings allows to express uniquely] Bibliography [{\sc Duchamp G., Reutenauer C.}]-->[G. Duchamp G., C. Reutenauer]