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

Gao,Volny and Wang(2010) gave a simple criterion for signature-based algorithms to compute Grobner bases.It gives a unified frame work for computing Grobner 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 Grobner 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.