Pierre Lairez
Chargé de recherche
Inria Saclay Île-de-France
Équipe Specfun
Invited speaker at FoCM 2017 in Barcelona.
Invited speaker at MEGA 2017 in Nice.
I move back to Inria as permanent researcher.
Distinguished paper award at ISSAC 2016 for “On p-adic differential equations with separation of variables”, with T. Vaccon.
Une solution déterministe au 17e problème de Smale, séminaire de l'IRMAR, Université de Rennes.
Une solution déterministe au 17e problème de Smale, séminaire de l'équipe CASYS, Laboratoire J. Kuntzmann.
“On p-adic differential equations with separation of variables”, with T. Vaccon.
Automatisation du calcul avec les sommes binomiales, seminar “Computations and Proofs” at Specfun, Inria Saclay.
2016
w/ T. Vaccon
P-adic numbers often appears in computer algebra when one want to solve a problem over a finite field $\mathbb F_p$ using an algorithm that performs divisions by $p$: we consider the data over the finite field as the approximation of some exact $p$-adic numbers, proceed to the computation over the field of $p$-adic numbers and then we obtain the result back in $\mathbb F_p$ by reducing modulo $p$. Naturally, we cannot compute with $p$-adic numbers with infinite precision, for the same reason as for real numbers. So we have to deal with approximations, and this raises questions about the numerical stability of algorithms when they are run with $p$-adic numbers.
In “On p-adic differential equations with separation of variables”, we study the problem of computing a power series solution to an ordinary differential equation. We show that the usual Newton method achieve the optimal loss of precision, this allows for a significant speedup.