Abstract
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 algorithm.
As an application to Algebraic Geometry, we show how to compute in polynomial time a minimal basis of an ideal of projective points.
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Marinari, M.G., Möller, H.M. & Mora, T. Gröbner bases of ideals defined by functionals with an application to ideals of projective points. AAECC 4, 103–145 (1993). https://doi.org/10.1007/BF01386834
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DOI: https://doi.org/10.1007/BF01386834