Pierre Lairez

Chargé de recherche

Inria Saclay Île-de-France

Équipe Specfun

email
INRIA Saclay Île-de-France, Bât. Alan Turing
1 rue Honoré d'Estienne d'Orves
Campus de l'École polytechnique
91120 Palaiseau
France
location
48.7146, 2.2056
map
phone
(0033) 01 77 57 80 36
office
1155
gpg public key

## Recent and forthcoming activities

• 10 jul 2017
conference

Invited speaker at FoCM 2017 in Barcelona.

• 12 jun 2017
conference

Invited speaker at MEGA 2017 in Nice.

• 24 mar 2017
seminar

Sommes binomiales multiples, séminaire probabilités et théorie ergodique de la fédération Poisson, Tours.

• 31 jan 2017
seminar

Étude de la stabilité numérique de la résolution des équations différentielles p-adiques, séminaire d'algèbre et géométrie, université de Versailles St-Quentin.

• 25 oct 2016
seminar

Étude de la stabilité numérique de la résolution des équations différentielles p-adiques, séminaire calcul et preuves, Inria Saclay.

• 1 oct 2016
news

I move back to Inria as a permanent researcher.

• 21 jul 2016
award

Distinguished paper award at ISSAC 2016 for “On p-adic differential equations with separation of variables”, with T. Vaccon.

• 25 mar 2016
seminar

Une solution déterministe au 17e problème de Smale, séminaire de l'IRMAR, Université de Rennes.

## Latest work

### Precision concerns in p-adic algorithms

2016

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.