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A two-dimensional improvement for Farr-Gao algorithm

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Abstract

Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gröbner bases of vanishing ideals of finite points, which has been implemented in Maple as a build-in command. This paper presents a two-dimensional improvement for it that employs a preprocessing strategy for computing reduced Gröbner bases associated with tower subsets of given point sets. Experimental results show that the preprocessed Farr-Gao algorithm is more efficient than the classical one.

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Authors and Affiliations

  1. School of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), Jilin University, Changchun, 130012, China

    Tian Dong

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  1. Tian Dong
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Correspondence to Tian Dong.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11101185 and 11171133.

This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.

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Dong, T. A two-dimensional improvement for Farr-Gao algorithm. J Syst Sci Complex 29, 1382–1399 (2016). https://doi.org/10.1007/s11424-016-4113-9

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  • DOI: https://doi.org/10.1007/s11424-016-4113-9

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