2020/10/27 by Sergey Yurkevich, Yurkevich, Sergey
Computer Science · Mathematics · #13-02 #14-01 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #History and Overview (math.HO) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2010.14386
openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are many viewpoints on algebraic power series, ranging from the\nabstract ring-theoretic notion of Henselization to the very explicit\nperspective as diagonals of certain rational functions. To be more explicit on\nthe latter, Denef and Lipshitz proved in 1987 that any algebraic power series\nin n variables can be written as a diagonal of a rational power series in one\nvariable more. Their proof uses a lot of involved theory and machinery which\nremains hidden to the reader in the original article. In the present work we\nshall take a glimpse on these tools by motivating while defining them and\nreproving most of their interesting parts. Moreover, in the last section we\nprovide a new significant improvement on the Artin-Mazur lemma, proving the\nexistence of a 2-dimensional code of algebraic power series.\n