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- Pierre Lairez
- Math. Comput.
- 2014

A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on… (More)

- Alin Bostan, Pierre Lairez, Bruno Salvy
- J. Symb. Comput.
- 2015

Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial… (More)

- Pierre Lairez
- Foundations of Computational Mathematics
- 2017

We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the… (More)

- Alin Bostan, Pierre Lairez, Bruno Salvy
- ISSAC
- 2013

Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork… (More)

- Felipe Cucker, Peter Burgisser, Pierre Lairez
- J. ACM
- 2017

We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets that works in weak exponential time. That is, of a set of… (More)

- Pierre Lairez, Marc Mezzarobba, Mohab Safey El Din
- ISSAC
- 2019

Let S\subset \bR^n be a compact basic semi-algebraic set defined as the real solution set of multivariate polynomial inequalities with rational coefficients. We design an algorithm which takes as… (More)

- Alin Bostan, Frédéric Chyzak, Pierre Lairez, Bruno Salvy
- ISSAC
- 2018

Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another… (More)

- Pierre Lairez, Tristan Vaccon
- ISSAC
- 2016

Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate… (More)

We consider the 3×3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables. This answers a… (More)

- Pierre Lairez
- ArXiv
- 2017

How many operations do we need on the average to compute an approximate root of a random Gaussian polynomial system? Beyond Smale's 17th problem that asked whether a polynomial bound is possible, we… (More)