Algebraic general solutions of algebraic ordinary differential equations
作者： J. M. Aroca , J. Cano , R. Feng , X. S. Gao
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摘要: In this paper, we give a necessary and sufficient condition for an algebraic ODE to have general solution. For first order autonomous ODE, optimal bound the degree of its solutions polynomial-time algorithm compute solution if it exists. Here means that given by differential polynomial.
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iss.ac.cn 参考文章(22)
Barry Marshall Trager, Integration of algebraic functions Massachusetts Institute of Technology. ,(1984)
Serge Lang, Introduction to Algebraic and Abelian Functions ,(1972)
James Harold Davenport, On the integration of algebraic functions ,(1981)
Marius van der Put, Michael F. Singer, Galois theory of linear differential equations Springer. pp. 1- 82 ,(2003) , 10.1007/978-3-642-55750-7
Joachim Von Zur Gathen, Jurgen Gerhard, Modern Computer Algebra ,(1999)
Manuel M. Carnicer, The Poincaré problem in the nondicritical case Annals of Mathematics. ,vol. 140, pp. 289- 294 ,(1994) , 10.2307/2118601
Evelyne Hubert, The general solution of an ordinary differential equation international symposium on symbolic and algebraic computation. pp. 189- 195 ,(1996) , 10.1145/236869.237073
Ellis Kolchin, Differential Algebra and Algebraic Groups ,(2012)
F. Ulmer, J. Calmet, On Liouvillian solutions of homogeneous linear differential equations Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '90. pp. 236- 243 ,(1990) , 10.1145/96877.96936
Robert H. Risch, The solution of the problem of integration in finite terms Bulletin of the American Mathematical Society. ,vol. 76, pp. 605- 609 ,(1970) , 10.1090/S0002-9904-1970-12454-5