Computing Groebner bases of ideal interpolation

Abstract

We present algorithms for computing the reduced Gröbner basis of the vanishing ideal of a finite set of points in a frame of ideal interpolation. Ideal interpolation is defined by a linear projector whose kernel is a polynomial ideal. In this paper, we translate interpolation condition functionals into formal power series via Taylor expansion, then the reduced Gröbner basis is read from formal power series by Gaussian elimination. Our algorithm has a polynomial time complexity. It compares favorably with MMM algorithm in single point ideal interpolation and some several points ideal interpolation.