Sturm-Habicht sequence

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Sturm-Habicht sequence

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation table of contents

Portland, Oregon, United States

Pages: 136 - 146

Year of Publication: 1989

ISBN:0-89791-325-6

Authors

L. Gonzalez
H. Lombardi
T. Recio
M.-F. Roy

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 44, Citation Count: 6

Additional Information:

references cited by index terms collaborative colleagues

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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	[Bar] Bareiss E. H.: Sylvester's identity and multistep integer preserving Gaussian elimination. Math. Comp. 22, 565-578 (1968).
	2	Michael Ben-Or , Dexter Kozen , John Reif, The complexity of elementary algebra and geometry, Journal of Computer and System Sciences, v.32 n.2, p.251-264, April 1986 [doi>10.1016/0022-0000(86)90029-2]
	3	M. Coste, Thoms's lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets, Journal of Symbolic Computation, v.5 n.1-2, p.121-129, February/April 1988 [doi>10.1016/S0747-7171(88)80008-7]
	4	[CGRS] Cucker F., Gonzalez L., Roy M.-F., Szpirglas A.: IF, a package for deciding systems of inequalities. Preprint.
	5	[GLRR] Gonzalez L., Lombardi H., Recio T., Roy M.- F.: Sous-résultants et spécialisation de la suite de Sturm. Submitted to RAIRO Informatique théorique.
	6	[H] Habicht W.: Eine Verallgemeinerung des Sturmschen Wurzelzählverfahrens. Comm. Math. Helvetici 21, 99-116 (1948).
	7	[HRS] Heintz J., Roy M.F., Solernò P.: Complexity of semialgebraic sets. To appear in IFIP-89 (San Francisco).
	8	[Lom] Lombardi Henri: Sous-résultants, suite de Sturm, spécialisation. Preprint. Besançon. 1988.
	9	[L] Loos R.: Generalized polynomial reminder sequences. In Computer Algebra, Symbolic and Algebraic Computation 115-138. Edited by Buchberger, Collins, Loos. Springer Verlag 1982.
	10	[M] Mignotte M.: Some useful bounds. In Computer Algebra, Symbolic and Algebraic Computation 259-263. Edited by Buchberger, Collins, Loos. Springer Verlag 1982.
	11	Marie-Françoise Roy , Aviva Szpirglas, Complexity of computation on real algebraic numbers, Journal of Symbolic Computation, v.10 n.1, p.39-51, July 1990 [doi>10.1016/S0747-7171(08)80035-1]
	12	[R S 2] Roy M.-F., Szpirglas A.: Complexity of cylindrical decomposition and topology of a real algebraic curve. Submitted to the Proceedings of Trento Conference on Real Algebraic Geometry.
	13	[Stu] Sturm C.: Mémoire sur la résolution des équations numériques. Inst. France Sc. Math. Phys. 6 (1835).
	14	[SYl] Sylvester J. T.: On a theory of syzygetic relations of two rational integral functions, comprising an appilication to the theory of Sturm's function. Trans. Roy. Soc. London (1853). Reprint in: Sylvester: Collected Math Papers. Chelsea Pub. Comp. NY 1983 vol 1 429- 586.

CITED BY 7

	Daniel Richardson, Towards computing non algebraic cylindrical decompositions, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.247-255, July 15-17, 1991, Bonn, West Germany
	E. Fortuna , P. Gianni , P. Parenti , C. Traverso, Algorithms to compute the topology of orientable real algebraic surfaces, Journal of Symbolic Computation, v.36 n.3-4, p.343-364, September 2003
	Carlos DAndrea , Hoon Hong , Teresa Krick , Agnes Szanto, An elementary proof of Sylvester's double sums for subresultants, Journal of Symbolic Computation, v.42 n.3, p.290-297, March, 2007
	Dimitrios I. Diochnos , Ioannis Z. Emiris , Elias P. Tsigaridas, On the complexity of real solving bivariate systems, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada
	Ioannis Z. Emiris , Elias P. Tsigaridas, Real algebraic numbers and polynomial systems of small degree, Theoretical Computer Science, v.409 n.2, p.186-199, December, 2008
	Dimitrios I. Diochnos , Ioannis Z. Emiris , Elias P. Tsigaridas, On the asymptotic and practical complexity of solving bivariate systems over the reals, Journal of Symbolic Computation, v.44 n.7, p.818-835, July, 2009
	Jinsan Cheng , Sylvain Lazard , Luis Peñaranda , Marc Pouget , Fabrice Rouillier , Elias Tsigaridas, On the topology of planar algebraic curves, Proceedings of the 25th annual symposium on Computational geometry, June 08-10, 2009, Aarhus, Denmark