A Two-Dimensional Improvement for Farr-Gao Algorithm

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${}^{\circledR }$ as a build-in command. In this paper, we present 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.

arXiv comment19 pages, 4 figures, submitted to J. Syst. Sci . Complex