Galois action on solutions of a differential equation
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A bound for the degree of the extension C ⊃ Q is given for the second-order differential equation y ″ + ay ′ + by = 0 with a, b ϵ Q ( x).About:
This article is published in Journal of Symbolic Computation.The article was published on 1995-06-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Algebraic differential equation & Universal differential equation.read more
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Galois theory of linear differential equations
TL;DR: In this paper, a large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, inverse problem and linear differential equations in positive characteristic.
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Factorization of Differential Operators with Rational Functions Coefficients
TL;DR: This method solves the main problem in Beke's factorization method, which is the use of splitting fields and/or Grobner basis.
Journal ArticleDOI
Liouvillian solutions of linear differential equations of order three and higher
TL;DR: This paper extends the algorithm in van Hoeij and Weil (1997) to compute semi-invariants and a theorem in Singer and Ulmer ( 1997) in such a way that, by computing one semi-Invariant that factors into linear forms, one gets all coefficients of the minimal polynomial of an algebraic solution of the Riccati equation, instead of only one coefficient.
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Formal Solutions and Factorization of Differential Operators with Power Series Coefficients
TL;DR: The notion of exponential parts is introduced to give a description of factorization properties and to characterize the formal solutions of linear differential equations with formal power series coefficients.
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TL;DR: Transliteration of Russian names has essentially followed the system adopted by the Library of Congress, but with no distinction between e and e or between Η and fi, and with yu used for κ> and ya for H .
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