Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients

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Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1991 international symposium on Symbolic and algebraic computation table of contents

Bonn, West Germany

Pages: 267 - 270

Year of Publication: 1991

ISBN:0-89791-437-6

Authors

S. A. Abramov	Computer Center of the USSR Acad. of Sci.
K. Yu. Kvansenko	Computer Center of the USSR Acad. of Sci.

Sponsors

GMD : German Natl Research Ctr for Information Tech. - Gesellschft
German Comp Soc : GI - Gesellshaft for Informatik
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 2, Downloads (12 Months): 16, Citation Count: 16

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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.

	1	Singer, M. F. Algebraic solutions of n-th order linear differential equations Proc. of the 1979 Queens Univ. Conf. on Number Theory.
	2	Abramov, S. A. Problems of computer algebra connected with the search of polynomial solutions of linear differential and difference equations Moscow University Computational Mathematics and Cybernetics, {translation of Soviet journal}, Seria. XV: Vychislitel'naya Matema.tica i Cibernetica., 3(1989), 56-60.
	3	F. Schwarz, A factorization algorithm for linear ordinary differential equations, Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation, p.17-25, July 17-19, 1989, Portland, Oregon, United States [doi>10.1145/74540.74544]
	4	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]
	5	Kvashenko, K. Yu. Program in REDUCE/or the ages. Computer algebra" {in Russian}.
	6	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
	7	Kamke, E. DifferentiaIgIeichungen Akademische Verlagsgesetlschaft, Leipzig, 1962.

CITED BY 16

	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
	Sergei A. Abramov , Mark van Hoeij, A method for the integration of solutions of Ore equations, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.172-175, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Manuel Bronstein, Linear ordinary differential equations: breaking through the order 2 barrier, Papers from the international symposium on Symbolic and algebraic computation, p.42-48, July 27-29, 1992, Berkeley, California, 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
	Jacques-Arthur Weil, The use of the special semi-groups for solving differential equations, Proceedings of the international symposium on Symbolic and algebraic computation, p.341-347, July 20-22, 1994, Oxford, United Kingdom
	Sergei A. Abramov , Marko Petkovšek, D'Alembertian solutions of linear differential and difference equations, Proceedings of the international symposium on Symbolic and algebraic computation, p.169-174, July 20-22, 1994, Oxford, United Kingdom
	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
	Manuel Bronstein, An improved algorithm for factoring linear ordinary differential operators, Proceedings of the international symposium on Symbolic and algebraic computation, p.336-340, July 20-22, 1994, Oxford, United Kingdom
	Manuel Bronstein, The Risch differential equation on an algebraic curve, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.241-246, July 15-17, 1991, Bonn, West Germany
	Sergei A. Abramov , Eugene V. Zima, Minimal completely factorable annihilators, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.290-297, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	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
	Sergei A. Abramov , Manuel Bronstein , Marko Petkovšek, On polynomial solutions of linear operator equations, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.290-296, July 10-12, 1995, Montreal, Quebec, Canada
	S. A. Abramov, On d'Alembert substitution, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.20-26, July 06-08, 1993, Kiev, Ukraine
	Ruyong Feng , Xiao-shan Gao, Rational general solutions of algebraic ordinary differential equations, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.155-162, 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
	Manuel Kauers, Solving difference equations whose coefficients are not transcendental, Theoretical Computer Science, v.401 n.1-3, p.217-227, July, 2008