A new conception for computing gröbner basis and its applications

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.

22 pages

References in corpus (2)

• F5C: a variant of Faugere's F5 algorithm with reduced Groebner bases
• A New Proof for the Correctness of F5 (F5-Like) Algorithm

Cited by in corpus (6)

• A survey on signature-based Gröbner basis computations
• The Termination of Algorithms for Computing Gröbner Bases
• Solving Detachability Problem for the Polynomial Ring by Signature-based Groebner Basis Algorithms
• A Generalized Criterion for Signature-based Algorithms to Compute Gröbner Bases
• An analysis of inhomogeneous signature-based Gröbner basis computations
• Signature-Based Gröbner Basis Algorithms --- Extended MMM Algorithm for computing Gröbner bases