A modular algorithm for computing greatest common right divisors of Ore polynomials

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

A modular algorithm for computing greatest common right divisors of Ore polynomials

Full text

Pdf (1.00 MB)

Source

International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1997 international symposium on Symbolic and algebraic computation table of contents

Kihei, Maui, Hawaii, United States

Pages: 282 - 289

Year of Publication: 1997

ISBN:0-89791-875-4

Authors

Ziming Li	Mathematics-Mechanization Research Center, Institute of Systems Science, Beijing 100084, China
István Nemes	Research Institute for Symbolic Computation, Johannes Kepler University, A-4040 Linz, Austria

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

Bibliometrics

Downloads (6 Weeks): 2, Downloads (12 Months): 18, Citation Count: 5

Additional Information:

references cited by index terms collaborative colleagues

Tools and Actions:	Request Permissions Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/258726.258812 What is a DOI?

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	M. Bronstein and M. Petkovgek. On Ore Rings, Linear Operators and Factorization. Programming and Corn. put. Software, 20, pp. 14-26, 1994.
	2	Manuel Bronstein , Marko Petkovšek, An introduction to pseudo-linear algebra, Theoretical Computer Science, v.157 n.1, p.3-33, April 9, 1996
	3	W. S. Brown, On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors, Journal of the ACM (JACM), v.18 n.4, p.478-504, Oct. 1971 [doi>10.1145/321662.321664]
	4	George E. Collins , Mark J. Encarnación, Efficient rational number reconstruction, Journal of Symbolic Computation, v.20 n.3, p.287-297, Sept. 1995 [doi>10.1006/jsco.1995.1051]
	5	Mark J. Encarnación, Computing GCDs of polynomials over algebraic number fields, Journal of Symbolic Computation, v.20 n.3, p.299-313, Sept. 1995 [doi>10.1006/jsco.1995.1052]
	6	Keith O. Geddes , Stephen R. Czapor , George Labahn, Algorithms for computer algebra, Kluwer Academic Publishers, Norwell, MA, 1992
	7	D. Yu. Grigor'ev, Complexity of factoring and calculating the GCD of linear ordinary differential operators, Journal of Symbolic Computation, v.10 n.1, p.7-37, July 1990 [doi>10.1016/S0747-7171(08)80034-X]
	8	Z. Li. A Subresultant Theory for Ore Polynomials and its Applications. PhD Thesis, Research Institute for Symbolic Computation, Johannes Kepler University, Linz, A-4040, Austria, 1996.
	9	R. Loos. Generalized Polynomial Remainder Sequences. Computer Algebra, Symbolic and Algebraic Computation, B. Buchberger, G. E. Collins and R. Loos (eds.), Springer-Verlag, Wien-New York, pp. 115-137, 1982.
	10	Bhubaneswar Mishra, Algorithmic algebra, Springer-Verlag New York, Inc., New York, NY, 1993
	11	O. Ore. Theory of Non-Commutative Polynomials. Annals of Math, 34, pp. 480-508, 1933.
	12	Bruno Salvy , Paul Zimmerman, GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable, ACM Transactions on Mathematical Software (TOMS), v.20 n.2, p.163-177, June 1994 [doi>10.1145/178365.178368]
	13	Paul S. Wang, A p-adic algorithm for univariate partial fractions, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.212-217, August 05-07, 1981, Snowbird, Utah, United States [doi>10.1145/800206.806398]
	14	Paul S. Wang , M. J. T. Guy , J. H. Davenport, P-adic reconstruction of rational numbers, ACM SIGSAM Bulletin, v.16 n.2, p.2-3, May 1982 [doi>10.1145/1089292.1089293]
	15	H. S. Wilf and D. Zeilberger. An Algorithmic Proof of Theory for Hypergeometric (Ordinary and "q") Multisum / Integral identities, lnventiones Mathernaticae, 108, pp. 575-633, 1992.

CITED BY 5

	Ziming Li, A subresultant theory for Ore polynomials with applications, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.132-139, August 13-15, 1998, Rostock, Germany
	Howard Cheng , George Labahn, Output-sensitive modular algorithms for polynomial matrix normal forms, Journal of Symbolic Computation, v.42 n.7, p.733-750, July, 2007
	Ziming Li , Martin Ondera , Huaifu Wang, Simplifying skew fractions modulo differential and difference relations, ACM Communications in Computer Algebra, v.42 n.3, September 2008
	Mark W. Giesbrecht , Ilias Kotsireas , Austin Lobo, ISSAC 2007 poster abstracts, ACM Communications in Computer Algebra, v.41 n.1-2, p.38-72, March-June 2007 issues 159-160
	Miroslav Halás , Ülle Kotta , Ziming Li , Huaifu Wang , Chunming Yuan, Submersive rational difference systems and their accessibility, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, July 28-31, 2009, Seoul, Republic of Korea