A bivariate preprocessing paradigm for the Buchberger-Möller algorithm

DOI10.1016/j.cam.2010.04.035zbMath1203.13031arXiv1001.1186OpenAlexW2052074478MaRDI QIDQ989141

Shugong Zhang, Xiaoying Wang, Tian Dong

Publication date: 27 August 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1186

zbMATH Keywords

Buchberger-Möller algorithmbivariate Lagrange interpolationCartesian setdegree reducing interpolation space

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Numerical interpolation (65D05)

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Uses Software

• Maple

Cites Work

• Interpolation from spaces spanned by monomials
• Multivariate Birkhoff interpolation
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Computing ideals of points
• From algebraic sets to monomial linear bases by means of combinatorial algorithms
• A computational algebra approach to the reverse engineering of gene regulatory networks
• Gröbner bases of ideals defined by functionals with an application to ideals of projective points
• The lex game and some applications
• Polynomial Interpolation in Several Variables: Lattices, Differences, and Ideals
• Gröbner Bases, Coding, and Cryptography: a Guide to the State-of-Art
• Lagrange interpolation on subgrids of tensor product grids
• Using Algebraic Geometry
• Computing Gröbner bases of ideals of few points in high dimensions
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