Section: Partnerships and Cooperations

National Initiatives

• De rerum natura. This project, set up by the team, was accepted this year and will be funded until 2023. It gathers over 20 experts from four fields: computer algebra; the Galois theories of linear functional equations; number theory; combinatorics and probability. Our goal is to obtain classification algorithms for number theory and combinatorics, particularly so for deciding irrationality and transcendence.

Alin Bostan together with Marc Mezzaroba (CNRS, Sorbonne Université) and Tanguy Rivoal (CNRS, Université Grenoble-Alpes) have done a “research in pairs” on the Fast Computation of Values of D-Finite Functions, from December 2 to 6, 2019, at CIRM (Luminy, France). The aim of the joint project was to investigate the implications of arithmetic properties of linear differential equations on the computational complexity of their numerical solutions. They focussed on E- and G-functions, which are power series solutions of differential equations that additionally satisfy strong arithmetic conditions and play a major role in Diophantine approximation. The main goal for this research session was to understand several remarks, given without proof by Chudnovsky and Chudnovsky in the late 1980s, and stating that number-theoretic properties could lead to slightly better complexity bounds for E- and G-functions than in the general case.