Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients

Understand

Assessing non-negativity of multivariate polynomials over the reals, through the computation of {\em certificates of non-negativity}, is a topical issue in polynomial optimization.

• This is usually tackled through the computation of {\em sums-of-squares decompositions} which rely on efficient numerical solvers for semi-definite programming.
• This method faces two difficulties.
• The first one is that the certificates obtained this way are {\em approximate} and then non-exact.