2010/09/13 by Camilo Sanabria, Sanabria, Camilo
Computer Science · Mathematics · #34M15 #39A45 #Advanced Differential Equations and Dynamical Systems #Algebra over a field #Algebraic equation #Algebraic number #Applied mathematics #Commutative Algebra (math.AC) #Computer science #Differential (mechanical device) #Differential algebraic equation #Differential algebraic geometry #Differential equation #Extension (predicate logic) #FOS: Mathematics #Mathematical analysis #Mathematical economics #Mathematics #Nonlinear system #Numerical methods for differential equations #Ordinary differential equation #Physics #Polynomial and algebraic computation #Pure mathematics #Thermodynamics #math.AC #msc:34M15 #msc:39A45
paper · pdf · doi:10.48550/arxiv.1009.2538
published in arXiv (Cornell University) (Cornell University)
arxiv created 2010/09/13 · openalex publication_date 2010/09/13 · arxiv updated 2010/09/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its Galois Group G has finite determinant group and is reductive. In this context, the ideal of algebraic relations satisfied by a full system of solutions is generated by the G-invariants it contains. This result extends a theorem of E. Compoint.