2005/05/14 by Guoting Chen, Yujie Ma, Chen, Guoting +1
Computer Science · Engineering · Mathematics · #34M15 #68W30 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Numerical methods for differential equations #Polynomial and algebraic computation #Primary 34A09 #Secondary 14Q05 #math.CA #math.CV #msc:14Q05 #msc:34A09 #msc:34M15 #msc:68W30
paper · pdf · doi:10.48550/arxiv.math/0505299
arxiv created 2005/05/14 · openalex publication_date 2005/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
First order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero. Combining with Fuchs' conditions for algebraic differential equations without movable critical point, an algorithm is given for the computation of rational general solutions of these equations if they exist under the assumption that a rational parametrization is provided. It is based on an algorithmic reduction of first order algebraic differential equations with algebraic genus zero and without movable critical point to classical Riccati equations.