2021/06/18 by Satoshi Koike, Koike, Satoshi, Laurenţiu Păunescu +1
Computer Science · Mathematics · #14P10 #32S15 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2106.09918
openalex publication_date 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let d be a positive integer. We show a finiteness theorem for semialgebraic RL triviality of a Nash family of Nash functions defined on a Nash manifold, generalising Benedetti-Shiota's finiteness theorem for semialgebraic RL equivalence classes appearing in the space of real polynomial functions of degree not exceeding d. We also prove Fukuda's claim, Theorem 1.3, and its semialgebraic version Theorem 1.4, on the finiteness of the local R types appearing in the space of real polynomial functions of real polynomial function germs of degree not exceeding d.