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 Gröbner basis, generalizing the Buchberger-Möller algorithm for computing a basis of an ideal vanishing at a set of points and the FGLM basis conversion algorith
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