Rational Solutions of First-Order Algebraic Ordinary Difference Equations

作者: Thieu N. Vo , Yi Zhang

DOI:

关键词:

摘要: We propose an algebraic geometric approach for studying rational solutions of first-order ordinary difference equations. For autonomous equations, we give upper bound the degrees its solutions, and thus derive a complete algorithm computing corresponding solutions.

参考文章(32)
J. Rafael Sendra, Franz Winkler, Sonia Prez-Diaz, Rational Algebraic Curves: A Computer Algebra Approach ,(2007)
Michael Karr, Summation in Finite Terms Journal of the ACM. ,vol. 28, pp. 305- 350 ,(1981) , 10.1145/322248.322255
Peter Paule, Greatest factorial factorization and symbolic summation Journal of Symbolic Computation. ,vol. 20, pp. 235- 268 ,(1995) , 10.1006/JSCO.1995.1049
Wolfram Koepf, Algorithms for m -fold hypergeometric summation Journal of Symbolic Computation. ,vol. 20, pp. 399- 417 ,(1995) , 10.1006/JSCO.1995.1056
Christoph Koutschan, Advanced applications of the holonomic systems approach ACM Communications in Computer Algebra. ,vol. 43, pp. 119- 119 ,(2010) , 10.1145/1823931.1823954
Manuel Bronstein, Marko Petkovšek, An introduction to pseudo-linear algebra Theoretical Computer Science. ,vol. 157, pp. 3- 33 ,(1996) , 10.1016/0304-3975(95)00173-5
S.A. Abramov, Rational solutions of linear differential and difference equations with polynomial coefficients Ussr Computational Mathematics and Mathematical Physics. ,vol. 29, pp. 7- 12 ,(1991) , 10.1016/S0041-5553(89)80002-3
Peter Paule, Markus Schorn, A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities Journal of Symbolic Computation. ,vol. 20, pp. 673- 698 ,(1995) , 10.1006/JSCO.1995.1071
J. M. Aroca, J. Cano, R. Feng, X. S. Gao, Algebraic general solutions of algebraic ordinary differential equations international symposium on symbolic and algebraic computation. pp. 29- 36 ,(2005) , 10.1145/1073884.1073891