# Computing Characteristic Polynomials of p-Curvatures in Average Polynomial Time

2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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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Conference papers
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https://hal.archives-ouvertes.fr/hal-03270585
Contributor : Raphaël Pagès Connect in order to contact the contributor
Submitted on : Thursday, July 1, 2021 - 11:53:13 AM
Last modification on : Saturday, December 4, 2021 - 3:44:02 AM

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### Citation

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. ⟨10.1145/3452143.3465524⟩. ⟨hal-03270585v2⟩

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