Section: New Results

Computing Small Certificates of Inconsistency of Quadratic Fewnomial Systems

Participant : Pierre-Jean Spaenlehauer [contact] .

This is a joint work with Jean-Charles Faugère (Inria, EPI Polsys) and Jules Svartz (Inria EPI Polsys/Ministère Éducation Nationale). Most of the results have been obtained in 2015. This work was finalized and published in 2016 [10].

We study how Gröbner bases algorithms can be adapted to compute certificates that quadratic fewnomial systems (i.e., systems in which only a small subset of monomials occur in the equations) do not have any solution. The main results are algorithms and complexity bounds which take into account the sparsity of the monomial support of the system, under some mild genericity assumptions on the coefficients of the systems.