A new conception for computing gröbner basis and its applications

2010/12/24 by Lei Huang, Huang, Lei · 1 citation
Computer Science · Engineering · #33F10 #68W30 #Advanced Numerical Analysis Techniques #Commutative Algebra (math.AC) #Cryptography and Residue Arithmetic #F.2.1 #FOS: Computer and information sciences #FOS: Mathematics #I.1.2 #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.1012.5425

openalex publication_date 2010/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a conception for computing gröbner basis. We convert some of gröbner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm's finite termination problem can be described by equivalent conditions, so all the above algorithms can be determined when they terminate finitely. At last, a new criterion is presented. It is an improvement for the Rewritten and Signature Criterion.

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• Signature-Based Gröbner Basis Algorithms --- Extended MMM Algorithm for computing Gröbner bases

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