A Two-Dimensional Improvement for Farr-Gao Algorithm
This is an incremental improvement for researchers working on computational algebraic geometry, specifically those using the Farr-Gao algorithm.
The paper presents a preprocessing strategy to improve the Farr-Gao algorithm for computing reduced Gröbner bases of vanishing ideals of finite points, achieving greater efficiency than the classical algorithm.
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.