Note on the construction of Picard-Vessiot rings for linear differential equations
Ruyong Feng
TL;DR
This paper presents a method for constructing Picard-Vessiot rings associated with linear differential equations, which are fundamental in understanding their solution structures and symmetries.
Contribution
It introduces a novel approach to explicitly construct Picard-Vessiot rings for linear differential equations.
Findings
Provides a systematic construction method
Simplifies the process of finding Picard-Vessiot rings
Enhances understanding of differential Galois theory
Abstract
In this note, we describe a method to construct the Picard-Vessiot ring of a given linear differential equation.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems · Advanced Algebra and Geometry