Non-negativity and rational sums of squares over zero-dimensional varieties

Appears in collection : 2023 - T3 - WS2 - Geometry of polynomial system solving, optimization and topology

In this work in progress with Lorenzo Baldi and Bernard Mourrain, we extend previous results on univariate rational sums of squares, obtained with Bernard and Agnes Szanto, to the case of a non-negative rational polynomial on a basic zero-dimensional semi-algebraic set defined by rational polynomials.