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A new signature-based algorithms for computing Grobner bases

Abstract: 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.