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Conference Papers Year : 2021

Computing Characteristic Polynomials of p-Curvatures in Average Polynomial Time

Abstract

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.
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Dates and versions

hal-03270585 , version 1 (28-06-2021)
hal-03270585 , version 2 (01-07-2021)

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Raphaël Pagès. Computing Characteristic Polynomials of p-Curvatures in Average Polynomial Time. ISSAC 2021 - International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint-Petersbourg / Virtual, Russia. pp.329-336, ⟨10.1145/3452143.3465524⟩. ⟨hal-03270585v2⟩
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