SAGBI and Gröbner Bases Detection

In this talk, we will introduce the detection algorithm for SAGBI bases in polynomial rings, which is analogous to the Gröbner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We will explore the software package SagbiGbDetection, and demonstrate its functionality with concrete examples. This package enables users to identify term orders for which a given set of input polynomials forms either a Gröbner basis for the ideal they generate or a SAGBI basis for the subalgebra.