Computing Ideals of Points

We address the problem of computing ideals of polynomials which vanish at a finite set of points. In particular we develop a modular Buchberger–Möller algorithm, best suited for the computation over Q, and study its complexity; then we describe a variant for the computation of ideals of projective points, which uses a direct approach and a new stopping criterion. The described algorithms are implemented in CoCoA, and we report some experimental timings.