Bill Allombert

Bill Allombert

Logo IMB Logo CNRS
Ingénieur d'étude en calcul scientifique (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.

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, Alnuth contributor 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
  • Talks

  • 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