The Vanishing Ideal of a Finite Set of Points with Multiplicity Structures

DOI10.1007/978-3-662-43799-5_21zbMath1352.68298arXiv1301.4630OpenAlexW1553791880MaRDI QIDQ2799566

Yuxue Ren, Xiaopeng Zheng, Na Lei

Publication date: 12 April 2016

Published in: Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4630

zbMATH Keywords

reduced Gröbner basisvanishing idealintersection of idealspoints with multiplicity structures

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Cites Work

• A fast algorithm for the multivariate Birkhoff interpolation problem
• Decoding of Reed Solomon codes beyond the error-correction bound
• Computing ideals of points
• From algebraic sets to monomial linear bases by means of combinatorial algorithms
• Gröbner bases of ideals defined by functionals with an application to ideals of projective points
• The lex game and some applications
• The vanishing ideal of a finite set of closed points in affine space
• Algebraic soft-decision decoding of reed-solomon codes
• Improved decoding of Reed-Solomon and algebraic-geometry codes
• Numerical Polynomial Algebra

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