The Risch differential equation on an algebraic curve

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The Risch differential equation on an algebraic curve

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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: 241 - 246

Year of Publication: 1991

ISBN:0-89791-437-6

Author

Manuel Bronstein

Informatik, ETH - Zentrum, CH-8092 Zürich, Switzerland

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

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Downloads (6 Weeks): 9, Downloads (12 Months): 27, Citation Count: 3

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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	S.A. Abramov, Problems of Computer Algebra involved in lhe Search for Polynomial Solutions of Linear Differential and Difference Equalions (in russian), MGU Num. Math and Cybernetics, vol. 15, No.3, pp. 56-60, 1989.
	2	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]
	3	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]
	4	Manuel Bronstein, The transcendental Risch differential equation, Journal of Symbolic Computation, v.9 n.1, p.49-60, Jan. 1990 [doi>10.1016/S0747-7171(08)80006-5]
	5	Manuel Bronstein, Integration of elementary functions, Journal of Symbolic Computation, v.9 n.2, p.117-173, Feb. 1990 [doi>10.1016/S0747-7171(08)80027-2]
	6	M.Bronstein, On Solutions of Linear Ordinary Differenlial Equations in their Coejficient Field, Research Report 152, Informatik, ETH Zfirich, 1991.
	7	J.It. Davenport, Intdgration Algorithmique des Fonctions Eldmentairement Transcendantes sur une Courbe Algdbrique, Annales de l'Institut Fourier, vol. 34, fast.2, pp. 271-276, 1984.
	8	E.G.C. Poole, Introduction to the Theory of Linear Differential Equations, Dover Publications Inc., New York, 1960.
	9	1%. Risch, On the Integration of Elemenlary Functions which are built up using Algebraic Operations, Report SP-2801/002/00, System Development Corp., Santa Monica, CA., 1968.
	10	R. Risch, The Problem of Integration In Finite Terms, Trans. Amer. Math. Sot., vol. 139, pp. 167- 189, 1969.
	11	M. Rothstein, A New Algorithm for the Integration of Exponential and Logarithmic Functions in "Proceedings 1977 MACSYMA Users Conference", NASA Pub. CP-2012, pp. 263-274, 1977.
	12	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]
	13	B. Trager, integration of Algebraic Functions, Ph.D. thesis, Dpt. of EECS, Massachusetts Institute of Technology, 1984.

CITED BY 3

	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
	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
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003