#
Journées Nationales de Calcul Formel 2024

CIRM, Luminy, 4 - 8 mars 2024

## Cours

Quatre cours de trois heures sont prévus. Le reste du temps sera consacré à des exposés d'une vingtaine de minutes portant sur des travaux de recherche récents.

### Algebraic Cryptanalysis in codebased and multivariate cryptography.

par Magali Bardet (Université de Rouen, LITIS, Rouen)

### Functional equations end combinatorics.

par Lucia Di Vizio (CNRS, LMV, Versailles)

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.### Creative Telescoping for D-Finite Functions.

par Christoph Koutschan (Österreichische Akademie der Wissenschaften, RICAM, Linz, Austria)

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.### Designing and exploiting fast algorithms for polynomial matrices.

par Vincent Neiger (Sorbonne Université, Paris)

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.