A bivariate preprocessing paradigm for the Buchberger-Möller algorithm

Authors:
Xiaoying Wang;Shugong Zhang;Tian Dong
Affiliations:
School of Mathemathics, Key Lab. of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun 130012, PR China;School of Mathemathics, Key Lab. of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun 130012, PR China;School of Mathemathics, Key Lab. of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun 130012, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

For the last almost three decades, since the famous Buchberger-Moller (BM) algorithm emerged, there has been wide interest in vanishing ideals of points and associated interpolation polynomials. Our paradigm is based on the theory of bivariate polynomial interpolation on cartesian point sets that gives us a related degree reducing interpolation monomial and Newton bases directly. Since the bases are involved in the computation process as well as contained in the final output of the BM algorithm, our paradigm obviously simplifies the computation and accelerates the BM process. The experiments show that the paradigm is best suited for the computation over finite prime fields that have many applications.