GROBNER BASES OF IDEALS DEFINED BY FUNCTIONALS WITH AN APPLICATION TO IDEALS OF PROJECTIVE POINTS

In this paper we study 0-dimensional polynomial ideals defined by a dual basis, i.e. as the set of polynomials which are in the kernel of a set of linear morphisms from the polynomial ring to the base field. For such ideals, we give polynomial complexity algorithms to compute a Grobner basis, generalizing the Buchberger-Moller algorithm for computing a basis of an ideal vanishing at a set of points and the FGLM basis conversion algorithm. As an application to Algebraic Geometry, we show how to compute in polynomial time a minimal basis of an ideal of projective points.