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On sait, par la méthode du vecteur cyclique, réduire un système différentiel linéaire à coefficients séries formelles à une équation différentielle scalaire. Ce procédé permet le calcul explicite de l’invariant de Katz. Cependant du point de vue pratique on constate que la méthode est d’un maniement lourd et couteux (cf.A. Hilali, Thèse de 3ème cycle IMAG, Grenoble 1982). Dans cet article, on construit un algorithme simple permettant le calcul de cet invariant sans l’utilisation du vecteur cyclique....
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