A Two-Dimensional Improvement for Farr-Gao Algorithm

Farr-Gao algorithm is a state-of-the-art algorithm for reduced Gr?bner 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 Gr?bner 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.

Farr-Cao algorithm is a state-of-the-art algorithm for reduced Crobner 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 GrSbner bases associated with tower subsets of given point sets. Experimental results show that the preprocessed Farr-Cao algorithm is more efficient than the classical one.