Abstract
Gao, Volny and Wang (2010) gave a simple criterion for signature-based algorithms to compute Gröbner bases. It gives a unified frame work for computing Gröbner 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 Gröbner 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.
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This research was 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, and Fundamental Research Funds for the Central Universities of Central South University under Grant No. 2013zzts008.
This paper was recommended for publication by Editor HU Lei.
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Zheng, L., Liu, J., Liu, W. et al. A new signature-based algorithms for computing Gröbner bases. J Syst Sci Complex 28, 210–221 (2015). https://doi.org/10.1007/s11424-015-2260-z
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DOI: https://doi.org/10.1007/s11424-015-2260-z