2017/07/15 by Zhipeng Lu, Lu, Zhipeng
Computer Science · Mathematics · #05E40 #14Q25 #Advanced Differential Equations and Dynamical Systems #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:05E40 #msc:14Q25
paper · pdf · doi:10.48550/arxiv.1707.04754
openalex publication_date 2017/07/15 · arxiv created 2021/03/16 · arxiv updated 2021/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study varieties defined by parameterizing polynomials of derivatives through a computational algebro-geometric approach, especially relying on Combinatorial Nullstellensatz and Noether normalization. We establish that these polynomials form regular sequences easily. This allows us to calculate the dimension of thus defined varieties and consequently give a proof to the Casas-Alvero conjecture.