2014/10/01 by Yao Sun, Sun, Yao, Dingkang Wang +5
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC
paper · pdf · doi:10.48550/arxiv.1410.0105
arxiv created 2014/10/01 · openalex publication_date 2014/10/01 · arxiv updated 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The GVW algorithm, presented by Gao et al., is a signature-based algorithm for computing Gröbner bases. In this paper, a variant of GVW is presented. This new algorithm is called a monomial-oriented GVW algorithm or mo-GVW algorithm for short. The mo-GVW algorithm presents a new frame of GVW and regards \em labeled monomials instead of \em labeled polynomials as basic elements of the algorithm. Being different from the original GVW algorithm, for each labeled monomial, the mo-GVW makes efforts to find the smallest signature that can generate this monomial. The mo-GVW algorithm also avoids generating J-pairs, and uses efficient methods of searching reducers and checking criteria. Thus, the mo-GVW algorithm has a better performance during practical implementations.