Factorization of linear differential operators in exponential extensions

Abstract

We present here an algorithm for an efficient computation of factorizations of linear differential operators with power series coefficients in an exponential extension of a base field. This algorithm is based on the results presented by Mark van Hoeij on factorization of linear differential operators with coefficients in C((x)). On the positive slopes of the Newton polygon associated to the linear differential operator, if the factors of the Newton polynomial are coprime, the algorithm does not require the use of differential algebra but only Bezout's theorem.