Automatic computation of limits

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Automatic computation of limits

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Symposium on Symbolic and Algebraic Manipulation archive
Proceedings of the second ACM symposium on Symbolic and algebraic manipulation table of contents

Los Angeles, California, United States

Pages: 458 - 464

Year of Publication: 1971

Author

Paul S. Wang

Sponsors

SIGNUM: ACM Special Interest Group on Numerical Mathematics
SIGART: ACM Special Interest Group on Artificial Intelligence
SIAM : Society for Industrial and Applied Mathematics
SIGPLAN: ACM Special Interest Group on Programming Languages
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 0, Downloads (12 Months): 14, Citation Count: 6

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ABSTRACT

This paper describes a program designed and implemented for the MACSYMA system for the computation of limits of single-valued functions of a real variable. The classes of expressions handled by this program include rational, radical, logarithmic and exponential expressions, and also the trigonometric functions sine, cosine and tangent. The first few sections of this paper contain an outline of the algorithm used and some examples of solutions of limit problems by the MACSYMA system. A number of more important methods used in the program are discussed in detail in the later sections. Among these methods are: a fast method for the limit of a rational function, L'Hospital's rule, a method for a class of expressions called RP-expressions and comparison of orders of infinity.

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	Fenichel, Robert R., "An On-line System for Algebraic Manipulation" Ph. D. thesis M. I. T., December 1966.
	2	Iturriaga Jose R., "Contributions to Mechanical Mathematics", Ph. D. thesis, Carnegie Institute of Technology, 1967.
	3	W. A. Martin , R. J. Fateman, The MACSYMA system, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.59-75, March 23-25, 1971, Los Angeles, California, United States [doi>10.1145/800204.806267]
	4	Moses, Joel, "Symbolic Integration", Ph. D. thesis, M. I. T., December 1967.

CITED BY 6

	Paul S. Wang, Application of MACSYMA to an asymptotic expansion problem, Proceedings of the ACM annual conference, p.844-850, August 01-01, 1972, Boston, Massachusetts, United States
	W. A. Martin , R. J. Fateman, The MACSYMA system, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.59-75, March 23-25, 1971, Los Angeles, California, United States
	Jacques Cohen , Carl Zuckerman, Two languages for estimating program efficiency, Communications of the ACM, v.17 n.6, p.301-308, June 1974
	Paul S. Wang, Implications of symbolic computation for the teaching of mathematics, ACM SIGSAM Bulletin, v.10 n.3, p.15-18, August 1976
	Joel Moses, MACSYMA - the fifth year, ACM SIGSAM Bulletin, v.8 n.3, p.105-110, August 1974
	Steven J. Harrington, A symbolic limit evaluation program in REDUCE, ACM SIGSAM Bulletin, v.13 n.1, p.27-31, February 1979