Abstract
Gao, et al. (2015) gave a simple algorithm to compute Gröbner bases named GVW. It can be used to compute Gröbner bases for both ideals and syzygies at the same time, and the latter plays an important role in free resolutions in homological algebra. In GVW algorithms the authors need to compute all the J-pairs firstly and then use GVW criterion (which refers the criterions used in GVW) to determine which one is useless or which one the authors should do top-reduction. In this paper, based on the study of relations between J-pairs, the authors propose the concept of factor. This concept allows the authors to filter the useless J-pairs in a rather convenient way. Moreover, by using this concept, the authors may easily determine which two pairs’ J-pair need not to be computed. Besides, the Gröbner basis which the authors obtained is relatively simpler than the one in GVW.
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This research was supported by the National Natural Science Foundation of China under Grant No. 11871207, the General Project of Hunan Provincial Education Department under Grant No. 17C0635, and the Natural Science Foundation of Hunan Provincial under Grant No. 2017JJ3084.
This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.
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Zheng, L., Li, D. & Liu, J. An Improvement for GVW. J Syst Sci Complex 35, 427–436 (2022). https://doi.org/10.1007/s11424-021-9051-5
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DOI: https://doi.org/10.1007/s11424-021-9051-5