2024/08/26 by Thomas Kahle, Kahle, Thomas, Julian Vill +1 · 1 citation
Computer Science · Mathematics · #13P25 #14M25 #62R01 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #Primary: 13F65 #Rings, Modules, and Algebras #Secondary: 13P10
paper · pdf · doi:10.48550/arxiv.2408.14323
openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an effective algorithm that decides if a prime ideal in a polynomial ring over the complex numbers can be transformed into a toric ideal by a linear automorphism of the ambient space. If this is the case, the algorithm computes such a transformation explicitly. The algorithm can compute that all Gaussian graphical models on five vertices that are not initially toric cannot be made toric by any linear coordinate change. The same holds for all Gaussian conditional independence ideals of undirected graphs on six vertices.