A parametric version of the Hilbert Nullstellensatz
Rida Ait El Manssour, Nikhil Balaji, Klara Nosan, Mahsa Shirmohammadi, James Worrell · Society for Industrial and Applied Mathematics eBooks · 2025
Hilbert’s Nullstellensatz is a fundamental result in algebraic geometry that gives a necessary and sufficient condition for a finite collection of multivariate polynomials to have a common zero in an algebraically closed field. Associated with this result, there is the computational problem HN of determining whether a system of polynomials with coefficients in the field of rational numbers has a common zero over the field of algebraic numbers.