Computing the algebraic relations of C-finite sequences and multisequences

Journal of Symbolic Computation

Volumn 43, Issue 11, 2008, Pages 787-803

  Kauers, Manuel ^a   Zimmermann, Burkhard ^a  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

Author keywords

Algebraic relations; C finite sequences; Recurrence equations

Indexed keywords

EID: 45649085341     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2008.03.002     Document Type: Article

References (20)

1. Adams W.W., and Loustaunau P. An Introduction to Gröbner Bases. Graduate Studies in Math. vol. 3 (1994), Amer. Math. Soc., New York
2. Becker T., Weispfenning V., and Kredel H. Gröbner Bases (1993), Springer
3. Buchberger, B., 1965. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal. Ph.D. Thesis, Universität Innsbruck
4. Cohen H. A Course in Computational Algebraic Number Theory (1993), Springer
5. Everest G., van der Poorten A., Shparlinski I., and Ward T. Recurrence Sequences. Mathematical Surveys and Monographs vol. 104 (2003), American Mathematical Society
6. Friendman J. Problem B-785. The Fibonacci Quarterly 33 2 (1995)
7. Furdui O. Problem B-931. The Fibonacci Quarterly 40 1 (2002) 85
8. Ge, G., 1993. Algorithms related to multiplicative representations of algebraic numbers. Ph.D. Thesis, U.C. Berkeley
9. Graham R.L., Knuth D.E., and Patashnik O. Concrete Mathematics. 2nd edition (1994), Addison-Wesley
10. Hoggatt V.E. Fibonacci and Lucas Numbers (1979), The Fibonacci Association
11. Karr M. Summation in finite terms. Journal of the ACM 28 (1981) 305-350
12. Kauers, M., Zimmermann, B., 2007. Dependencies - A Mathematica package for computing algebraic dependencies of C-finite sequences. Tech. Rep., SFB F013, Johannes Kepler Universität (in preparation)
13. Milne-Thomson L.M. The Calculus of Finite Differences (1933), Macmillan and Co., ltd
14. Nemes I., and Petkovšek M. RComp: A mathematica package for computing with recursive sequences. Journal of Symbolic Computation 20 5-6 (1995) 745-753
15. Salvy B., and Zimmermann P. Gfun: A Maple package for the manipulation of generating and holonomic functions in one variable. ACM Transactions on Mathematical Software 20 2 (1994) 163-177
16. Schneider, C., 2001. Symbolic summation in difference fields. Ph.D. Thesis, RISC-Linz, Johannes Kepler Universität Linz
17. Sloane N.J.A., and Plouffe S. The Encyclopedia of Integer Sequences (1995), Academic Press. http://research.att.com/~njas/sequences/
18. Stanley R.P. Enumerative Combinatorics. Cambridge Studies in Advanced Mathematics 62 vol. 1 (1997), Cambridge University Press
19. Sturmfels B., Weismantel R., and Ziegler G.M. Gröbner bases of lattices, corner polyhedra, and integer programming. Contributions to Algebra and Geometry 36 2 (1995) 281-298
20. Zeilberger D. A holonomic systems approach to special function identities. Journal of Computational and Applied Mathematics 32 (1990) 321-368