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 ...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.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11471108,11426101Hunan Provincial Natural Science Foundation of China under Grant Nos.14JJ6027,2015JJ2051Fundamental Research Funds for the Central Universities of Central South University under Grant No.2013zzts008
文摘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.
