We design a fast algorithm that computes, for a given linear differential operator with coefficients in Z[ ], all the characteristic polynomials of its -curvatures, for all primes < , in asymptotically quasi-linear bit complexity in . We discuss implementations and applications of our algorithm. We shall see in particular that the good performances of our algorithm are quickly visible. CCS CONCEPTS• Computing methodologies → Algebraic algorithms.

We present an algorithm for factoring linear differential operators with coefficients in a finite separable extension of F p ( x ). Our methods rely on specific tools arising in positive characteristic: p -curvature, structure of simple central algebras and p -Riccati equations.