MULTIYEAR PROGRAM
RESEARCH SCHOOL - ÉCOLE DE RECHERCHE
Francophone Computer Algebra Days
Journées nationales de calcul formel
4 – 8 March 2024
Scientific Committee
Comité scientifique
Magali Bardet (Université de Rouen)
Alin Bostan (INRIA Saclay)
Nicolas Brisebarre (CNRS – ÉNS Lyon)
Laurent Busé (INRIA Sophia Antipolis)
Xavier Caruso (CNRS – Université de Bordeaux)
Eleonora Guerrini (Université de Montpellier)
Vincel Hoang Ngoc Minh (Université Sorbonne Paris Nord)
Mioara Joldes (CNRS – Université de Toulouse)
Pierre-Vincent Koseleff (Sorbonne Université)
Guillaume Moroz (INRIA Nancy)
Clément Pernet (Université Grenoble Alpes)
Adrien Poteaux (Université de Lille 1)
Mohab Safey El Din (Sorbonne Université)
Pierre-Jean Spaenlehauer (INRIA Nancy Grand-Est)
Tristan Vaccon (Université de Limoges)
Organizing Committee
Comité d’organisation
Jérémy Berthomieu (Sorbonne Université)
Florent Bréhard (CNRS – Université de Lille)
Aude Maignan (Université de Grenoble Alpes)
Fatemeh Mohammadi (KU Leuven)
François Ollivier (CNRS – École Polytechnique)
contact: orga-jncf2024@groupes.renater.fr
Computer Algebra refers to the study and design of algorithms for manipulating mathematical expressions and objects. It is naturally at the interface between Mathematics, Computer Science, and various application fields. It covers a wide range of subjects, such as effective linear algebra, algorithmic number theory, integration and summations in closed-form expression, differential and polynomial system solving, or special functions. The French Computer Algebra community takes part in the organization of the main international conferences (ISSAC, FoCM, MEGA, . . . ). On top of scientific excellence in their theoretical works, members of this community also develop for widely used software such as Maple, SageMath and Magma, and software libraries such as mpfr, pari, fgb, rs, linbox, etc. The vitality of this community is also recognized by prestigious national prizes (e.g. CNRS medal). This success is notably due to the Journées Nationales de Calcul Formel (JNCF), which is a remarkable opportunity for researchers to discuss recent and ongoing work with their peers. Expected outcomes include:
- A better integration of young researchers. The JNCF are an ideal opportunity for young researchers to present their results for the first time and also to get an overview of the various advances in Computer Algebra. This is especially important in the Computer Algebra community, where researchers need to build skills in both Computer Science and Mathematics.
- New collaborations and interactions. The JNCF have traditionally been an opportunity to create successful collaborations between researchers from different parts of France. The JNCF has also opened to an international community, while remaining primarily French-speaking. The previous editions already included courses and contributed talks by colleagues from other European and Mediterranean countries.
Le calcul formel désigne la conception et l’analyse d’algorithmes pour la manipulation d’expressions et d’objets mathématiques. C’est une discipline à l’interface des mathématiques, de l’informatique et de différents domaines d’application. Il recouvre de nombreux sujets, de la théorie algorithmique des nombres à la résolution de systèmes polynomiaux ou différentiels en passant par les fonctions spéciales ou l’algèbre linéaire effective. La communauté française de calcul formel participe à l’organisation des principales conférences internationales (ISSAC, FoCM, MEGA, . . . ). Reconnus internationalement pour leurs contributions théoriques, les membres de la communauté participent également au développement de logiciels largement utilisés comme Maple, SageMath, Magma, ainsi que de bibliothèques comme mpfr, pari, fgb, rs, linbox, etc. Sa vitalité doit beaucoup aux Journées nationales de calcul formel (JNCF), qui représentent une opportunité remarquable pour les chercheurs d’échanger avec leurs pairs autour de travaux récents ou en cours. Les résultats que nous attendons sont en particulier :
- Faciliter l’intégration des jeunes chercheurs. Les journées représentent une opportunité idéale pour les jeunes chercheurs de présenter leurs résultats pour la première fois et de se faire une idée d’ensemble des avancées dans le domaine. Cela revêt une importance particulière dans la communauté du calcul formel, où il est nécessaire d’acquérir de l’expérience à la fois en informatique et en mathématiques.
- De nouvelles collaborations et interactions. Les JNCF ont traditionnellement été l’occasion de démarrer des collaborations fructueuses entre chercheurs de différents pôles en France. Elles sont depuis quelques années ouvertes à une communauté internationale, tout en maintenant un caractère majoritairement francophone. Lors des dernières éditions, des cours et exposés étaient assurés par des collègues d’autres pays européens ou méditerranéens.
LECTURES
Magali Bardet (Université de Rouen) Algebraic Cryptanalysis in codebased and multivariate cryptography
Lucia Di Vizio (Université de Versailles-St Quentin) Functional equations and combinatorics
Starting from a presentation of the many recent applications of Galois theory of functional equations to enumerative combinatorics, we will introduce the Galois theory of (different kinds) of difference equations. We will focus on the point of view of the applications, hence with little emphasis on the technicalities of the domain, but I’m willing to do an hour of « exercises » (i.e. to go a little deeper into the proofs), if a part of the audience is interested.
Christoph Koutschan (RICAM) Creative Telescoping for D-Finite Functions.
D-finite functions play a prominent role in computer algebra because they are well suited for representation in a symbolic software system, and because they include many functions of interest, such as special functions, orthogonal polynomials, generating functions from combinatorics, etc. Whenever one wishes to study the integral or the sum of a D-finite function, the method of creative telescoping may be applied. This method has been systematically introduced by Zeilberger in the 1990s, and since then has found applications in various different domains. In this lecture, we explain the underlying theory, review some of the history and talk about some recent developments in this area.
Vincent Neiger (Sorbonne Université) Designing and exploiting fast algorithms for polynomial matrices
Matrices whose coefficients are univariate polynomials over a field are a basic mathematical object which arises at the core of fundamental algorithms in computer algebra: sparse or structured linear system solving, rational approximation or interpolation, division with remainder for bivariate polynomials, etc. After presenting this context, we will give an overview of recent progress on efficient computations with such matrices. Next, we will show how these results have been exploited to improve complexity bounds for a selection of problems which, interestingly, do not necessarily involve polynomial matrices a priori: computing the characteristic polynomial of a scalar matrix; performing modular composition of univariate polynomials; changing the monomial order for multivariate Gröbner bases.
CONTRIBUTED TALKS
Matteo Abbondati (Université de Montpellier) Decoding Simultaneous Rational Evaluation Codes
François Boulier (Université de Lille) Software demo: DifferentialAlgebra
Maxime Bridoux (INRIA Rennes-Bretagne Atlantique) On Bounding The Degree Of Irreducible Darboux Polynomials
Hadrien Brochet (INRIA Saclay – Ile-de-France) A New Creative Telescoping Algorithm For Multiple Integrals
Louis Gaillard (ENS Lyon) Solving parameter-dependent semi-algebraic systems with Hermite matrices
Alexis Galan (Université Grenoble Alpes) Optimal Communication Unbalanced Private Set Union
Jürgen Gerhard (Maplesoft) Software demo: What’s New in Maple 2024
Sriram Gopalakrishnan (Sorbonne Université) Gröbner bases of maximal minors and critical point computations
Alexandre Guillemot (INRIA Saclay – Ile-de-France) Validated Numerics for Algebraic Path Tracking
Tom Hubrecht (ENS – PSL) Towards a correctly rounded power function in double precision
Lucas Legrand (Université de Limoges) Gröbner bases over polytopal affinoid algebras
Tobias Metzlaff (University of Kaiserslautern-Landau) Symplectic singularities and diagonal invariants
Rafael Mohr (Sorbonne Université) Computing Generic Fibers of Polynomial Ideals with FGLM
Hadrien Notarantonio (INRIA Saclay – Ile-de-France) Software demo: [ddesolver] A Maple package for Discrete Differential Equations
Epiphane Nouetowa (Université de Rennes) Iterative decoding of skew cyclic codes
Lucas Ottow (Université de Montpellier) Fast Computations on Shared Polynomials in MPC
Pierre Pébereau (Sorbonne Université) Cryptanalysis of multivariate signatures: Singular points of UOV and VOX
Eric Pichon-Pharabod (INRIA Saclay – Ile-de-France) Topology and periods of elliptic surfaces
Rémi Prébet (Catholic University of Leuven) Faster algorithms for connectivity queries in unbounded real algebraic sets
Louis Roussel (Université de Lille) Parameter Estimation with Integral Elimination
Georgy Scholten (Sorbonne Université) Global Optimization of Analytic Functions
Damien Vidal (Université Picardie Jules Vernes) Analyzing the Crossbred Algorithm for the MQ Problem
SPONSORS
