Branch cuts in computer algebra

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Branch cuts in computer algebra

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

Oxford, United Kingdom

Pages: 250 - 257

Year of Publication: 1994

ISBN:0-89791-638-7

Authors

Adam Dingle	Computer Science Division, EECS Dep't, University of California at Berkeley
Richard J. Fateman	Computer Science Division, EECS Dep't, University of California at Berkeley

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 5, Downloads (12 Months): 21, Citation Count: 5

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ABSTRACT

Most computer algebra systems provide little assistance in working with expressions involving functions with complex branch cuts. Worse, by their ignorance of the existence of branch cuts, algebra systems sometimes simplify complex expressions incorrectly. We propose a computer representation for branch cuts; we show how a complex expression's branch cuts may be mechanically computed, and how an expression with branch cuts may sometimes be algebraically simplified within each of its branches.

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	G. F. Carrier, M. Krook, and C. E. Pearson. Functions of a Complez Variable: Theory and Techniques, McGraw-Hill, 1966.
	2	B. W. Char, K. 0. Geddes, et al. Maple V Library Reference Manual, (and other volumes) Springer-Verlag, 1991.
	3	Richard D. Jenks , Robert Sutor, AXIOM: the scientific computation system, Springer-Verlag New York, Inc., New York, NY, 1992
	4	A. Dingle. "Branch Cuts in Computer Algebra," Master's Thesis, Department of Electrical Engineering and Computer Science, University of California at Berkeley, 1991.
	5	W. Kahan. "instead of UNLN', unpublished paper, April 1991.
	6	H. Kober. Dictionary of Conformal Representations, Dover, 1957.
	7	Macsyma Inc. Macsyma Be/erence Manual, Version 14, 1991.
	8	Z. Nehari. Gonformal Mapping, McGraw-Hill, 1952.
	9	H. Seymour. "Conform: A Conformal Mapping System", Master's Thesis, Department of Electrical Engineering and Computer Science, University of California at Berkeley, 1985.
	10	Stephen Wolfram, Mathematica: a system for doing mathematics by computer (2nd ed.), Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, 1991

CITED BY 5

	Martin Dunstan , Tom Kelsey , Steve Linton , Ursula Martin, Lightweight formal methods for computer algebra systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.80-87, August 13-15, 1998, Rostock, Germany
	T. H. Einwohner , Richard J. Fateman, Searching techniques for integral tables, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.133-139, July 10-12, 1995, Montreal, Quebec, Canada
	D. J. Jeffrey , A. C. Norman, Not seeing the roots for the branches: multivalued functions in computer algebra, ACM SIGSAM Bulletin, v.38 n.3, September 2004
	James C. Beaumont , Russell J. Bradford , James H. Davenport , Nalina Phisanbut, A poly-algorithmic approach to simplifying elementary functions, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.27-34, July 04-07, 2004, Santander, Spain
	James C. Beaumont , Russell J. Bradford , James H. Davenport , Nalina Phisanbut, Adherence is better than adjacency: computing the Riemann index using CAD, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.37-44, July 24-27, 2005, Beijing, China