On polynomial solutions of linear operator equations

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On polynomial solutions of linear operator equations

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1995 international symposium on Symbolic and algebraic computation table of contents

Montreal, Quebec, Canada

Pages: 290 - 296

Year of Publication: 1995

ISBN:0-89791-699-9

Authors

Sergei A. Abramov	Computer Center of the Russian Academy of Science, Vavilova 40, Moscow 117967, Russia
Manuel Bronstein	Institute for Scientific Computation, ETH Zentrum IFW,, CH-8092 Zürich, Switzerland
Marko Petkovšek	Department of Mathematics, University of Ljubljana, Jadranska 19, 61111 Ljubljana, Slovenia

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 7, Downloads (12 Months): 35, Citation Count: 23

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	Abr89a	S. A. Abramov (1989): Problems of computer algebra involved in the search for polynomial solutions of linear differential and difference equations, Moscow Univ. Comput. Math. and Cybernet., no. 3, 63-68.
	Abr89b	S. A. Abramov, Rational solutions of linear differential and difference equations with polynomial coefficients, USSR Computational Mathematics and Mathematical Physics, v.29 n.6, p.7-12, 1989 [doi>10.1016/S0041-5553(89)80002-3]
	Abr95	S. A. Abramov, Rational solutions of linear difference and q-difference equations with polynomial coefficients, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.285-289, July 10-12, 1995, Montreal, Quebec, Canada [doi>10.1145/220346.220383]
	Abr&Kva91	S. A. Abramov , K. Yu. Kvansenko, Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.267-270, July 15-17, 1991, Bonn, West Germany [doi>10.1145/120694.120735]
	Abr&Pet95	Sergei A. Abramov , Peter Paule , Marko Petkovšek, q-hypergeometric solutions of q-difference equations, Proceedings of the 7th conference on Formal power series and algebraic combinatorics, p.3-22, February 1998, France
	Bach&al94	Olaf Bachmann , Paul S. Wang , Eugene V. Zima, Chains of recurrences—a method to expedite the evaluation of closed-form functions, Proceedings of the international symposium on Symbolic and algebraic computation, p.242-249, July 20-22, 1994, Oxford, United Kingdom [doi>10.1145/190347.190423]
	Bro&Pet94	M. Bronstein, M. Petkovgek (1994): On Ore rings, linear operators and factorisation, Programmirovanie 20, N.1, 27-45 (also Research Report 200, Informatik, ETH Ziirich).
	Gos78	R. W. Gosper, Jr. (1978): Decision procedure for indefinite hypergeometric summation, Proc. Natl. Acad. Sci. USA 75, 40-42.
	Pet92	Marko Petkovšek, Hypergeometric solutions of linear recurrences with polynomial coefficients, Journal of Symbolic Computation, v.14 n.2-3, p.243-264, Aug./Sept. 1992 [doi>10.1016/0747-7171(92)90038-6]
	Sin91	Michael F. Singer, Liouvillian solutions of linear differential equations with Liouvillian coefficients, Journal of Symbolic Computation, v.11 n.3, p.251-273, March 1991 [doi>10.1016/S0747-7171(08)80048-X]
	Zei91	Doron Zeilberger, The method of creative telescoping, Journal of Symbolic Computation, v.11 n.3, p.195-204, March 1991 [doi>10.1016/S0747-7171(08)80044-2]
	Zima84	E V Zima, Automatic construction of systems of recurrence relations, USSR Computational Mathematics and Mathematical Physics, v.24 n.11-12, p.193-197, March 1986

CITED BY 23

	Jürgen Gerhard, High degree solutions of low degree equations (extended abstract), Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.284-289, August 13-15, 1998, Rostock, Germany
	Sergei A. Abramov , Eugene V. Zima, D'Alembertian solutions of inhomogeneous linear equations (differential, difference, and some other), Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.232-240, July 24-26, 1996, Zurich, Switzerland
	Joachim von zur Gathen , Jürgen Gerhard, Fast algorithms for Taylor shifts and certain difference equations, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.40-47, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	S. P. Tsarev, An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.226-231, July 24-26, 1996, Zurich, Switzerland
	Mark van Hoeij, Rational solutions of linear difference equations, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.120-123, August 13-15, 1998, Rostock, Germany
	S. A. Abramov , M. A. Barkatou, Rational solutions of first order linear difference systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.124-131, August 13-15, 1998, Rostock, Germany
	Eugene V, Zima, Mixed representation of polynomials oriented towards fast parallel shift, Proceedings of the second international symposium on Parallel symbolic computation, p.150-155, July 20-22, 1997, Maui, Hawaii, United States
	Manuel Bronstein , Anne Fredet, Solving linear ordinary differential equations over C (x, e^{∫ f(x)dx}), Proceedings of the 1999 international symposium on Symbolic and algebraic computation, p.173-179, July 28-31, 1999, Vancouver, British Columbia, Canada
	Mark van Hoeij, Rational solutions of the mixed differential equation and its application to factorization of differential operators, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.219-225, July 24-26, 1996, Zurich, Switzerland
	S. A. Abramov, Rational solutions of linear difference and q-difference equations with polynomial coefficients, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.285-289, July 10-12, 1995, Montreal, Quebec, Canada
	Anne Fredet, Linear differential equations, iterative logarithms and orderings on monomial differential extensions, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.121-128, July 2000, St. Andrews, Scotland
	Sergei A. Abramov , Manuel Bronstein, On solutions of linear functional systems, Proceedings of the 2001 international symposium on Symbolic and algebraic computation, p.1-6, July 2001, London, Ontario, Canada
	Delphine Boucher, About the polynomial solutions of homogeneous linear differential equations depending on parameters, Proceedings of the 1999 international symposium on Symbolic and algebraic computation, p.261-268, July 28-31, 1999, Vancouver, British Columbia, Canada
	George Labahn , Ziming Li, Hyperexponential solutions of finite-rank ideals in orthogonal ore rings, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.213-220, July 04-07, 2004, Santander, Spain
	Alin Bostan , Thomas Cluzeau , Bruno Salvy, Fast algorithms for polynomial solutions of linear differential equations, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.45-52, July 24-27, 2005, Beijing, China
	S. A. Abramov, A direct algorithm to compute rational solutions of first order linear q-difference systems, Discrete Mathematics, v.246 n.1-3, p.3-12, 6 March 2002
	Ruyong Feng , Xiao-Shan Gao , Zhenyu Huang, Rational solutions of ordinary difference equations, Journal of Symbolic Computation, v.43 n.10, p.746-763, October, 2008
	D. E. Khmelnov, Basis Selection in Solving Linear Functional Equations, Programming and Computing Software, v.28 n.2, p.102-105, March-April 2002
	D. Behloul , S. S. Cheng, Computation of all polynomial solutions of a class of nonlinear differential equations, Computing, v.77 n.2, p.163-177, April 2006
	A. Bostan , F. Chyzak , B. Salvy , T. Cluzeau, Low complexity algorithms for linear recurrences, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
	A. A. Ryabenko, Symbolic solution of nonhomogeneous linear ordinary differential equations in terms of power series, Programming and Computing Software, v.32 n.2, p.120-122, March 2006
	D. E. Khmelnov, Search for Polynomial Solutions of Linear Functional Systems by Means of Induced Recurrences, Programming and Computing Software, v.30 n.2, p.61-67, March-April 2004
	Alin Bostan , Éric Schost, Fast algorithms for differential equations in positive characteristic, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, July 28-31, 2009, Seoul, Republic of Korea