A New Signature-Based Algorithms for Computing Gr?bner Bases

作     者：ZHENG Licui LIU Jinwang LIU Weijun LI Dongmei 

作者机构：School of Mathematics and StatisticsCentral South University Department of Mathematics and Computing SciencesHunan University of Science and Technology 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2015年第28卷第1期

页      面：210-221页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.11471108,11426101 Hunan Provincial Natural Science Foundation of China under Grant Nos.14JJ6027,2015JJ2051 Fundamental Research Funds for the Central Universities of Central South University under Grant No.2013zzts008 

主　　题：Factor Grobner basic signature-based. 

摘      要：Gao, Volny and Wang （2010） gave a simple criterion for signature-based algorithms to compute GrSbner bases. It gives a unified frame work for computing GrSbner bases for both ideals and syzygies, the latter is very important in free resolutions in homological algebra. Sun and Wang （2011） later generalized the GVW criterion to a more general situation （to include the F5 Algorithm）. Signature-based algorithms have become increasingly popular for computing GrSbner bases. The current paper introduces a concept of factor pairs that can be used to detect more useless J-pairs than the generalized GVW criterion, thus improving signature-based algorithms.