Programs for applying symmetries

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Programs for applying symmetries

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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: 7 - 15

Year of Publication: 1995

ISBN:0-89791-699-9

Author

Thomas Wolf

School of Mathematical Sciences, Queen Mary and Westfield College, University of London, London, E1 4NS

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

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Downloads (6 Weeks): 7, Downloads (12 Months): 20, Citation Count: 2

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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	W. Hereman, Chapter 13 in vol 3 of the CRC Handbook of Lie Group Analysis of Differential Equations, Ed.: N.H. Ibragimov, CRC Press, Boca Raton, Florida (1995). Systems described in this paper are among others: DELIA (Alexei Bocharov et.al.) Pascal DIFFGROB2 (Liz Mansfield) Maple DIMSYM (James Sherring and Geoff Prince) REDUCE HSYM (Vladimir Gerdt) Reduce LIE (V. Eliseev, R.N. Fedorova and V.V. Kornyak) Reduce LIE (Alan Head) muMath Lie (Gerd Baumann) Mathematica LIEDF/INFSYM (Peter Gragert and Paul Kersten) Reduce Liesymm (John Carminati, John Devitt and Greg Fee) Maple MathSym (Scott Herod) Mathematica NUSY (Clara Nucci) Reduce PDELIE (Peter Vafeades) Macsyma SPDE (Fritz Schwarz) Reduce and Axiom SYM_DE (Stanly Steinberg) Macsyma Symmgroup.c (Dominique Berube and Marc de Montigny) Mathematica STANDARD FORM (Gregory Reid and Alan Wittkopf) Maple SYMCAL (Gregory Reid) Macsyma and Maple SYMMGRP.MAX (Benoit Champagne, Willy Hereman and Pavel Winternitz) Macsyma LIE package (Khai Vu) Maple Toolbox for symmetries (Mark Hickman) Maple Lie symmetries (Jeffrey Ondich and Nick Coult) Mathematica.
	2	S. Lie, Sophus Lie's 1880 Transformation Group Paper, Translated by M. Ackerman, comments by R. Hermann, Mathematical Sciences Press, Brookline, (1975).
	3	S. Lie, Differentialgleichungen, Chelsea Publishing Company, New York, (1967).
	4	T. Wolf, An efficiency improved program LIEPDE for determining Lie - symmetries of PDEs, Proceedings of the workshop on Modern group theory methods in Acireale (Sicily) Nov. (1992)
	5	A.V. Bocharov and M.L. Bronstein, Efficiently Implementing Two Methods of the Geometrical Theory of Differential Equations: An Experience in Algorithm and Software Design, Acta. Appl. Math. 16 (1989) 143- 166.
	6	P.J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag New York (1986).
	7	E. Kamke, Differentialgleichungen, LSsungs- methoden und LSsungen, Band 2, PartielIe Differentialgleichungen, 6.Aufl., Teubner, Stuttgart:Teubner, 1979.
	8	T. Wolf, A. Brand, The Computer Algebra Package CRACK for Investigating PDEs, Manual for the package CRACK in the REDUCE network library and in Proceedings of ERCIM School on Partial Differential Equations and Group Theory, April 1992 in Bonn, GMD Bonn.
	9	H. Stephani, Differential equations, Their solution using symmetries, Cambridge University Press (1989).
	10	V.I. Karpman, Phys. Lett. A 136, 216 (1989)
	11	B. Champagne, W. Hereman, P. Winternitz, The computer calculation of Lie point symmetries of large systems of differential equations, Comp. Phys. Comm. 66, 319-340 (1991)
	12	M. Kubitza, private communication
	13	M.j. Prelle, M.F. Singer, Elementary First Integrals of Differential Equations. Trans. AMS 279, 215-229 (1983).
	14	Yiu-Kwong Man, Computing closed form solutions of first order ODEs using the Prelle-Singer procedure, Journal of Symbolic Computation, v.16 n.5, p.423-443, Nov. 1993 [doi>10.1006/jsco.1993.1057]
	15	L. Goldman, Integrals of multinomial systems of ordinary differential equations, J. of Pure and Applied Algebra, vol 45, 225-240 (1987).
	16	William Y. Sit, On Goldman's Algorithm for Solving First-Order Multinomial Autonomous Systems, Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.386-395, July 04-08, 1988
	17	Fritz Schwarz, Existence theorems for polynomial first integrals, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.256-264, July 15-17, 1991, Bonn, West Germany [doi>10.1145/120694.120733]

CITED BY 2

	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	Thomas Wolf , Andreas Brand, Investigating DEs with CRACK and related programs, ACM SIGSAM Bulletin, v.29 n.SI, p.1-8, June 1995