On the parallel Risch Algorithm (II)

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On the parallel Risch Algorithm (II)

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 11 , Issue 4 (December 1985) table of contents

Pages: 356 - 362

Year of Publication: 1985

ISSN:0098-3500

Authors

J. H. Davenport	Univ. of Bath, UK
B. M. Trager	IBM Thomas J. Watson Research Center

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 3, Downloads (12 Months): 28, Citation Count: 6

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ABSTRACT

It is proved that, under the usual restrictions, the denominator of the integral of a purely logarithmic function is the expected one, that is, all factors of the denominator of the integrand have their multiplicity decreased by one. Furthermore, it is determined which new logarithms may appear in the integration.

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	James H. Davenport, The Parallel Risch Algorithm (I), Proceedings of the European Computer Algebra Conference on Computer Algebra, p.144-157, April 05-07, 1982
	2	John Fitch, User-based integration software, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.245-248, August 05-07, 1981, Snowbird, Utah, United States [doi>10.1145/800206.806404]
	3	A. C. Norman , James H. Davenport, Integration -- the dust settles? (invited), Proceedings of the International Symposiumon on Symbolic and Algebraic Computation, p.398-407, June 01, 1979
	4	NORMAN, A. C., AND MOORE, 1a. M.A. Implementing the new Risch integration algorithm. In Proceedings o{ 4th International Colloquium on Advanced Computing Methods in Theoretical Physics {Marseilles, 1977).
	5	R~SCH, R.H. The problem of integration in finite terms. Trans. Am. Math. Soc. 139 (1969}, 167-189.

CITED BY 6

	A. C. Norman, A Critical-pair/completion based integration algorithm, Proceedings of the international symposium on Symbolic and algebraic computation, p.201-205, August 20-24, 1990, Tokyo, Japan
	Anne Fredet, Linear differential equations, iterative logarithms and orderings on monomial differential extensions, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.121-128, July 2000, St. Andrews, Scotland
	K. O. Geddes , L. Y. Stefanus, On the risch-norman integration method and its implementation in MAPLE, Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation, p.212-217, July 17-19, 1989, Portland, Oregon, United States
	Carl G. Ponder, Parallelism and algorithms for algebraic manipulation: current work, ACM SIGSAM Bulletin, v.22 n.3, p.7-14, July 1988
	Manuel Bronstein, Structure theorems for parallel integration, Journal of Symbolic Computation, v.42 n.7, p.757-769, July, 2007
	R. Kragler, On mathematica program for "Poor Man's Integrator" implementing Risch-Norman algorithm, Programming and Computing Software, v.35 n.2, p.63-78, March 2009