Integro-differential algebra.

The team is specialist in formal manipulations of
nonlinear
PDE (partial differential equations).
We developed algorithms in C
(
BLAD) which are useful for solving
parameter estimation problems (see this
poster
for more information).

Recently, we have developed new algorithms to replace differential equations by integral equations [BLLRR16], which are usually more suited numerically. An ongoing challenge is to develop an elimination theory for integro-differential equations. Students already have contributed in that area, and are welcome to join us on this thematic. For more details, you can have a look at [BLRUV17] and [BKLPPRU14]

High performance computing (HPC).

We are currently using HPC for improving Numerical and Symbolic Computations
in the following directions:

- numerical integration of systems of integro-differential equations [BCCLLPQV18]
- fast polynomial evaluation over modular integers (collaboration with Prof. Mike Monogan, Vancouver, Canada)

Fast algorithms for singularities of plane algebraic curves.

One thematic of the team involves the elaboration of fast algorithm to study the local
behaviour of singularities of plane algebraic curves. This involves theoretical
improvment on the complexity of Puiseux series computation
[PR15]
and practical consideration (a C implementation of a modular-numeric strategy is currently done).
An HPC implementation is strongly considered.

- Master Internship - Validated Numerical Software For Algebraic Curves With Singularities (Sujet) (unaffected)

- Louis Roussel (GIS5 Polytech'Nantes 2022) who worked on computing Integral Equations using Machine Learning
- Ambroise Fleury (L3 2018 - Accélération SIMD d'évaluations de polynômes) who achieved a 10x speedup on polynomial evalution
- Joseph Lallemand (ENS Cachan - 2014) who contributed to [BLLRR16]