A new proof for the correctness of the F5 algorithm

DOI10.1007/s11425-012-4480-1zbMath1286.13026OpenAlexW2259972220MaRDI QIDQ365812

Yao Sun, Ding-Kang Wang

Publication date: 9 September 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-012-4480-1

zbMATH Keywords

Gröbner basiscorrectness of F5F5F5-reductionF5B

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Polynomials over commutative rings (13B25)

Related Items (7)

Solving multivariate polynomial matrix Diophantine equations with Gröbner basis method ⋮ An improvement for GVW ⋮ Resultant elimination via implicit equation interpolation ⋮ Axioms for a theory of signature bases ⋮ A survey on signature-based algorithms for computing Gröbner bases ⋮ An improvement over the GVW algorithm for inhomogeneous polynomial systems ⋮ A new signature-based algorithms for computing Gröbner bases

Uses Software

• F5C

Cites Work

• The F5 algorithm in Buchberger's style
• Extended \(F_5\) criteria
• F5C: A variant of Faugère's F5 algorithm with reduced Gröbner bases
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Generalization of the F5 algorithm for calculating Gröbner bases for polynomial ideals
• A new incremental algorithm for computing Groebner bases
• A new framework for computing Gröbner bases
• A signature-based algorithm for computing Gröbner bases in solvable polynomial algebras
• Signature-based algorithms to compute Gröbner bases
• A generalized criterion for signature related Gröbner basis algorithms
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