We address the problem of computing ideals of polynomials which vanish at a
finite set of points. In particular we develop a modular Buchberger-Moller
algorithm, best suited for the computation over Q, and study its complexit
y; then we describe a variant for the computation of ideals of projective p
oints, which uses a direct approach and a new stopping criterion. The descr
ibed algorithms are implemented in CoCoA, and we report some experimental t
imings. (C) 2000 Academic Press.