Computing Characteristic Polynomials of p-Curvatures in Average Polynomial Time

06/28/2021

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by   Raphaël Pagès, et al.

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