Abstract
We discuss some changes of the traditional scheme for finding rational solutions of linear difference equations (homogeneous or inhomogeneous) with rational coefficients. These changes in some cases allow one to detect the absence of rational solutions in an early stage of computation and to stop the work. The corresponding strategy may be useful for the algorithms based on finding rational solutions of equations of considered form, e.g., for some symbolic summation algorithms.
- S. Abramov. Rational solutions of linear difference and q-difference equations with polynomial coefficients. Programming and Comput. Software 21, 273--278 (1995). Transl. from Programmirovanie No 6, 3--11 (1995).Google Scholar
- S. Abramov, M. Barkatou. Rational solutions of first order linear difference systems, ISSAC'98 Proceedings, 124--131 (1998). Google ScholarDigital Library
- S.A. Abramov, A. Gheffar, D.E. Khmelnov. Factorization of polynomials and gcd computations for finding universal denominators, CASC'2010 Proceedings , 4--18, (2010). Google ScholarDigital Library
- S. Abramov, M. van Hoeij. Integration of solutions of linear functional equations, Integral Transforms Spec. Funct. 8, 3--12 (1999).Google ScholarCross Ref
- A. Gheffar. Linear differential, difference and q-difference homogeneous equations having no rational solutions. ACM Comm. in Computer Algebra, 44, No 3, 77--83 (2010). Google ScholarDigital Library
- R.W. Gosper, Decision procedure for indefinite hypergeometric summation. Proc. Natl. Acad. Sci. USA 75, 40--42 (1978).Google ScholarCross Ref
- M. van Hoeij. Rational solutions of linear difference equations. ISSAC'98 Proceedings, 120--123 (1998). Google ScholarDigital Library
- Y.K. Man, F.J. Wright. Fast polynomial dispersion computation and its application to indefinite summation. Proc. ISSAC'94, 175--180 (1994). Google ScholarDigital Library
- D. Zeilberger. The method of creative telescoping. J. Symb. Comput. 11, 195--204 (1991). Google ScholarDigital Library
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