Product representations in Π∑-fields

Annals of Combinatorics

Volumn 9, Issue 1, 2005, Pages 75-99

  Schneider, Carsten ^a  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Difference fields; Simplification of products; Symbolic summation

Indexed keywords

EID: 15844383473     PISSN: 02180006     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00026-005-0242-2     Document Type: Article

References (27)

1. S. Abramov and M. Petkovšek, Rational normal forms and minimal decompositions of hypergeometric terms, J. Symbolic Comput. 33(5) (2002) 521-543.
2. S.A. Abramov and M. Bronstein, Hypergeometric dispersion and the orbit problem, In: Proc. ISSAC'00, C. Traverso, Ed., ACM Press, 2000.
3. S.A. Abramov, H.Q. Le, and M. Petkovsek, Rational canonical forms and efficient representations of hypergeometric terms, In: Proc. ISSAC'03, J.R. Sendra, Ed., ACM Press, 2003, pp. 7-14.
4. M. Bronstein, On solutions of linear ordinary difference equations in their coefficient field, J. Symbolic Comput 29 (6) (2000) 841-877.
5. J. Cai, R.J. Lipton, and Y. Zalcstein, The complexity of the A B C problem, SIAM J. Comput. 29 (6) (2000) 1878-1888.
6. K. Driver, H. Prodinger, C. Schneider, and A. Weideman, Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation, to appear.
7. K. Driver, H. Prodinger, C. Schneider, and A. Weideman, Padé approximations to the logarithm III: Alternative methods and additional results, to appear.
8. G. Ge, Algorithms related to the multiplicative representation of algebraic numbers, Ph. D. thesis, Department of Mathematics, University of California at Berkeley, Berkeley, CA, 1993.
9. G. Ge, Testing equalities of multiplicative representations in polynomial time, In: Proceedings Foundation of Computer Science, 1993, pp. 422-426.
10. R. Kannan and R. Lipton, Polynomial-time algorithm for the orbit problem, J. ACM 33 (4) (1986) 808-821.
11. M. Karr, Summation in finite terms, J. ACM 28 (1981) 305-350.
12. M. Karr, Theory of summation in finite terms, J. Symbolic Comput. (1) (1985) 303-315.
13. Y.K. Man and F.J. Wright, Fast polynomial dispersion computation and its applications to indefinite summation, In: Proc. ISSAC'94, J. von zur Gathen and M. Giesbrecht, Eds., ACM Press, 1994, pp.175-180.
14. D.W. Masser, Linear relations on algebraic groups, New Advances in Transcendence Theory, A. Baker, Ed., Cambridge University Press, UK, 1988.
15. P. Paule and C. Schneider, Computer proofs of a new family of harmonic number identities, Adv. in Appl. Math. 31 (2) (2003) 359-378.
16. M. Petkovšek, H. S. Wilf, and D. Zeilberger, A = B, A.K. Peters, Wellesley, MA, 1996.
17. M. Pohst and H. Zassenhaus, Algorithmic algebraic number theory, Encyclopedia of mathematics and its applications, G.C. Rota, Ed., Cambridge University Press, 1989.
18. C. Schneider, An implementation of Karr's summation algorithm in Mathematica, Sém. Lothar. Combin. S43b (2000) 1-10.
19. C. Schneider, Symbolic summation in difference fields, Technical Report 01-17, RISC-Linz, Ph. D. Thesis, J. Kepler University, November 2001.
20. C. Schneider, Degree bounds to find polynomial solutions of parameterized linear difference equations in ∏Σ-fields, to appear.
21. C. Schneider, Solving parameterized linear difference equations in ∏Σ-fields, SFB-Report 02-19, J. Kepler University, Linz, November 2002.
22. C. Schneider, A collection of denominator bounds to solve parameterized linear difference equations in ∏Σ-extensions, In: Proc. SYNASC04, D. Petcu et al., Eds., Mirton Publishing, 2004, pp. 269-282.
23. C. Schneider, The summation package Sigma: Underlying principles and a rhombus tiling application, Discrete Math. Theor. Comput. Sci. 6 (2) (2004) 365-386.
24. Symbolic summation with single-nested sum extensions, In: Proc. ISSAC'04, 2004, pp. 282-289.
25. C. C. Sims, Abstract algebra, A computational approach, John Wiley & Sons, New York, 1984.
26. F. Winkler, Polynomial Algorithms in Computer Algebra, Texts and Monographs in Symbolic Computation, B. Buchberger, G.E. Collins, Eds., Springer, Wien, 1996.
27. D. Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (2) (1990) 207-211.