Bill Allombert

Bill Allombert

Logo IMB Logo CNRS
Ingénieur de recherche en calcul scientifique (Research scientific computing engineer)
Bâtiment A33 (IMB), Bureau 383
Téléphone : +33 5 40 00 26 17

About Me

I have completed a PhD in Mathematics at the University of Bordeaux I in the Laboratoire A2X. My field of research is Algorithmic Number Theory. I am now a scientific computing engineer (CNRS) at the Institut de Mathématiques de Bordeaux (UMR 5251). Formerly I was a scientific computing engineer at the Université Montpellier 2 at the I3M and LIRMM.

I work in the Pole MCD of the Cellule Informatique de l'IMB on development of mathematical software related to number theory.

I am a member of the ERI project OpenDreamKit and ANR project FLAIR and CIAO.

I was awarded the 2020 Crystal Medal by the French CNRS for my work on PARI/GP, thanks to the support of the number theory community, and the Richard Dimick Jenks Memorial Prize 2021 Award for the PARI/GP computer algebra system.

Software Projects

PARI/GP computer algebra system Logo PARI
Main developer
GP2C compiler
Author and maintainer
Debian project Logo Debian
Official Debian developer
GAP computer algebra system
GAP developer, member of the GAP council and Debian packager.


  • Théorie de Galois effective pour les corps de nombres et les corps finis. Développement du système PARI. PhD Thesis, Université Bordeaux I, 2001.
  • An Efficient Algorithm for the Computation of Galois Automorphisms Math. Comp., 73, 245, 2001, 359-375.
  • Explicit Computation of Isomorphisms Between Finite Fields , Finite Fields, 8, 2002, 332-342.
  • (with Karim Belabas) Practical Aurifeuillian factorization, J. Théor. Nombres Bordeaux 20, 2008, no. 3, 543-553
  • A new interpretor for PARI/GP, J. Théor. Nombres Bordeaux 20, 2008, no. 3, 531-541
  • (with Yuri Bilu and Amalia Pizarro-Madariaga) CM-Points on Straight Lines , in: C. Pomerance, M. Rassias (eds.), Analytic Number Theory In Honor of Helmut Maier’s 60th Birthday, 1-18, Springer, 2015.
  • (with Jean-Paul Allouche et Michel Mendès-France) Euler's divergent series and an elementary model in Statistical Physics Ars Mathematica Contemporanea 12, 2017, no. 1, 67-76
  • (with Nicolas Brisebarre and Alain Lasjaunias) On a two-valued sequence and related continued fractions in power series fields The Ramanujan Journal, 2017
  • (with Gaetan Chenevier) Unimodular hunting II
  • Talks

  • Ateliers PARI/GP 2023
  • Ateliers PARI/GP 2022b
  • summer school COGENT 2022
  • CHARM 2022 (online)
  • Ateliers PARI/GP 2022
  • Ateliers PARI/GP 2021b online
  • PARI Day 2021
  • Ateliers PARI/GP 2020
  • Ateliers PARI/GP 2019b
  • Cohomology of Arithmetic Groups Lattice and Number Theory (CIRM 28/03/2019)
  • Ateliers PARI/GP 2019
  • On the computation of automorphisms of a nilpotent Galois extension of number fields Bordeaux 18/12/2018
  • ZETAS 2018 école d'été
  • EJC théorie des nombres 2018
  • Ateliers PARI/GP 2018b
  • Ateliers PARI/GP 2018
  • Ateliers PARI/GP 2017c
  • Ateliers PARI/GP 2017b
  • Ateliers PARI/GP 2017
  • Ateliers PARI/GP 2016
  • Les aspect combinatoires des fonctions L d'Artin Bordeaux 15/12/2015
  • Tutorial: elliptic curves over finite fields in PARI/GP ECC 2015, Bordeaux 24/09/2015
  • Ateliers PARI/GP 2015
  • Symbolic integration in prime characteristic Bordeaux 02/12/2014
  • Faster computation of Heegner points on elliptic curves over Q of rank 1 ICTP 11/09/2014
  • Ateliers PARI/GP 2014
  • Minimums de formes quadratiques binaires et nombres de Markoff Bordeaux 10/12/2013
  • Ateliers PARI/GP 2013
  • Comptage de points sur les courbes elliptiques en petite caractéristique Besançon 06/12/2012, Bordeaux 20/11/2012, IHP 12/11/2012
  • Ateliers PARI/GP 2012
  • Calcul de points rationnels sur une courbe elliptique de rang analytique 1 Bordeaux 02/03/2011
  • Calcul du groupe des classes et du groupe des unités de corps de nombres de grand degré Limoges 10/01/2011, Lyon 13 Avril 2010
  • Calcul de groupes de ramifications globaux Bordeaux 06/12/2010
  • Expérimentations avec le calcul du groupe des classes de corps de nombres de grand degré Besançon 21/01/2010, Montpellier 28/09/2009, Besançon 10/06/2009
  • Utilisation de PARI/GP pour la théorie algébrique des nombres Besançon 22/01/2010
  • Groupes algébriques et logarithmes discrets Montpellier 09/04/2009