An Improvement for GVW

• 作者: ZHENG Licui LI Dongmei LIU Jinwang
• 来源期刊: 系统科学与复杂性学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 427-436
• 页数: 10页
• 语种: 英文
• DOI: 10.1007/s11424-021-9051-5

摘要

Gao,et al.(2015) gave a simple algorithm to compute Gr(o)bner bases named GVW.It can be used to compute Gr(o)bner bases for both ideals and syzygies at the same time,and the latter plays an important role in free resolutions in homological algebra.In GVW algorithms the authors need to compute all the J-pairs firstly and then use GVW criterion (which refers the criterions used in GVW) to determine which one is useless or which one the authors should do top-reduction.In this paper,based on the study of relations between J-pairs,the authors propose the concept of factor.This concept allows the authors to filter the useless J-pairs in a rather convenient way.Moreover,by using this concept,the authors may easily determine which two pairs' J-pair need not to be computed.Besides,the Gr(o)bner basis which the authors obtained is relatively simpler than the one in GVW.