Section: New Results

Gröbner bases for sparse algebraic systems

Participant : Pierre-Jean Spaenlehauer [contact] .

In collaboration with Jean-Charles Faugère and Jules Svartz (PolSys project-team), new Gröbner bases algorithms have been proposed in [20] to solve efficiently sparse systems of multivariate polynomial equations. Moreover, new complexity bounds have also been proved; they extend in a unified way previous bounds known for solving multi-homogeneous systems with Gröbner bases. For such systems, a proof-of-concept prototype implementation of these algorithms achieves large speed-ups compared to state-of-the-art optimized Gröbner bases algorithms.