Optimized Gröbner basis algorithms for maximal determinantal ideals and critical point computations

Sriram Gopalakrishnan, Vincent Neiger, Mohab Safey El Din

Given polynomials $g$ and $f_1,\dots ,f_p$, all in $\mathbb{k}[x_1,\dots ,x_n]$ for some field $\mathbb{k}$, we consider the problem of computing the critical points of the restriction of $g$…