## Section: New Results

### Small certificates of inconsistency of quadratic fewnomial systems

Participant : Pierre-Jean Spaenlehauer [contact] .

In collaboration with Jean-Charles Faugère (EPI PolSys) and Jules Svartz (Min. de Éducation Nationale), we studied the problem of certifying the inconsistency of sparse quadratic polynomial systems. Finding certificates of inconsistency is a classical problem in computational commutative algebra, and these certificates are in general of size exponential in the input size. We identify families of quadratic fewnomial systems for which there exist certificates of size linear in the size of the input and we propose algorithms to compute them in polynomial time.