2020/12/10 by Xiang‐dong Hou, Hou, Xiang-dong, Christopher Sze +1
Computer Science · Mathematics · #11C20 #11T06 #12F10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2012.05944
openalex publication_date 2020/12/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Let F be a field and let F(X1,…,Xn) be the field of rational functions in n variables X1,…,Xn over F. Let T=X1+⋯+Xn∈ F(X1,…,Xn) and let m be a positive integer such that char F\nmid m. Is it possible to express each Xi as a rational function in X1m…,Xnm and T over F? It is not difficult to prove that this can be done but it is another matter to show how this is done. We answer the above question affirmatively with a nonconstructive proof and a constructive proof.