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Computing Groebner bases of ideal interpolation - MaRDI portal

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Computing Groebner bases of ideal interpolation

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Publication:6504786

arXiv2111.07340MaRDI QIDQ6504786

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Abstract: We present algorithms for computing the reduced Gr"{o}bner 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 Gr"{o}bner 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.












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