2005/03/15 by Katsutoshi Amano, Amano, Katsutoshi
Computer Science · Mathematics · Physics and Astronomy · #13B05 #39A05 #Advanced Differential Equations and Dynamical Systems #Commutative Algebra (math.AC) #FOS: Mathematics #General Mathematics (math.GM) #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AC #math.GM #msc:13B05 #msc:39A05
paper · pdf · doi:10.48550/arxiv.math/0503291
80 pages; [v4 -> v5] Added some explanation before Contents, several minor changes
openalex publication_date 2005/03/15 · arxiv created 2006/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a compilation of three separated studies. The main part (Part 3) deals with a unified Picard-Vessiot theory including Picard-Vessiot theories of differential and difference equations. Changes: [v1 -> v2] Corrected descriptions on "ZXi-linearly independece" in Part 2 (p11, p13, p16) [v2 -> v3] The proof of Proposition 3.5.7 (iii) in v2 is not completed. (Only the proof of Proposition 3.5.8 (ii) is influenced and a revised proof is given.) [v3 -> v4] Lemma 3.5.10 in the previous version is false (see Remark 3.5.10 in the presented version). The proof of Prop. 3.5.9 (ii) and the proof of Lemma 3.9.9 are influenced and revised proofs are given. There are several minor changes too. [v4 -> v5] Added some explanation before Contents, several minor changes. This shall be the final replacement.