The Number of Gröbner Bases in Finite Fields (Research)

DOI10.1007/978-3-030-42687-3_9zbMath1440.13116arXiv1907.01080OpenAlexW3043789427MaRDI QIDQ5118668

Anyu Zhang, Brandilyn Stigler

Publication date: 26 August 2020

Published in: Advances in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.01080

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Polynomials over finite fields (11T06) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

Uses Software

• M4GB

Cites Work

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• Estimating the number of tetrahedra determined by volume, circumradius and four face areas using Groebner basis
• Estimating the volumes of the cones in a Gröbner fan
• Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM
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• A computational algebra approach to the reverse engineering of gene regulatory networks
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Quantifier Elimination over Finite Fields Using Gröbner Bases
• Small Gröbner fans of ideals of points
• Computing Gröbner fans
• M4GB
• Computing Gröbner bases of ideals of few points in high dimensions
• A Lower Bound for the Volume of Strictly Convex Bodies with many Boundary Lattice Points
• Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
• Cutting corners