Solving some overdetermined polynomial systems

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

Solving some overdetermined polynomial systems

Full text

Pdf (929 KB)

Source

International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1999 international symposium on Symbolic and algebraic computation table of contents

Vancouver, British Columbia, Canada

Pages: 1 - 8

Year of Publication: 1999

ISBN:1-58113-073-2

Authors

Marc Giusti	UMS MEDICIS, Laboratoire GAGE, École polytechnique, F-91128 Palaiseau, France
Éric Schost	UMS MEDICIS, Laboratoire GAGE, École polytechnique, F-91128 Palaiseau, France

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): 3, Downloads (12 Months): 16, 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/10.1145/309831.309838 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	BAUR, \~.. AND STRASSEN, V. The complcxity of' partial deriwitives. Theo. Comp. Sci. 22 (1983), 317-330.
	2	Didier Bondyfalat , Bernard Mourrain , Victor Y. Pan, Controlled iterative methods for solving polynomial systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation, p.252-259, August 13-15, 1998, Rostock, Germany [doi>10.1145/281508.281629]
	3	CIIISTOV. A.. AND G,~IGOaIEV, D. Subexpon(mtial time. solving systems of algebrai(: equations. LOMI preprint, 1983.
	4	DED~EU. J., AND SIIUB, M. Newton and predictorcorrector methods for overdetermined systems of eq~tations. Tech. rep., IBM Research Division, 1998.
	5	EGNER, S. Semi-m,merical solution to 6/6-Stewart platform kinematics based m, symmetry. Applicable Algebra in Engineering, Communication and Computing 7 (1996), 449 468.
	6	P. Gianni , T. Mora, Algebraic solution of systems of polynomial equations using Groebner bases, Proceedings of the 5th international conference, AAECC-5 on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.247-257, June 1987, Menorca, Spain
	7	GIUSTI, h'i., HAEGELE, K.. HE.INTZ, J., h'ION'I'ANA, Z., h'IORAIS, J., AND PARDO, L. Lower bounds for (tiophantine approximations. In .lournal of Pure and App. Algebra (Proc.eedings of MEGA '96) (1997), vol. 117, pp. 277-317.
	8	GIUST}, ~'I.. AND HEIN'FZ. Z. La ddtermination des points isold.s et de la dimension d'une varidt~ alg6brique peut se fair(: en temps polynomial. In Computational Algebraic Geometry and Commutative Algebra (1993), E. D. and R. L.. Eds.: vol. XXXIV of Symposia Matematica, Cambridge University Press, pp. 216--256.
	9	GIUSTI. h'I., HEINTZ, J., h:If)R.AIS, J., h.'IOR.(,ENSTEIIN, Z., AND PARD(), L. Straight-line l)rograms in geometric elitnination theory. Journal of Pure and App. Algebra 124 (1998), 101 146.
	10	Marc Giusti , Joos Heintz , Jose Enrique Morais , Luis M. Pardo, When Polynomial Equation Systems Can Be "Solved" Fast?, Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.205-231, July 17-22, 1995
	11	HEINTZ, J. Definability and fast quantifier elimination il, algebraically closed fieMs. Theor. Comput. Sci. 2~4, 3 (1983), 239--277.
	12	HEINTZ, ,1., KRICK, T., PL'I-)I')U, S., SARIA. J., AND x~VAISSBEIN. A. Delbrmation techniques for efficient, polynomial equation s()lvir, g. Subnlitted.
	13	HEINTZ. J., ANI) SCIINORll, C. Testing polynomials which are easy to c.ompute. In Logic and Al- .qorithmic, vol. 30 of Monograph, ie de l'ensei.qnement mathdmatiqv.e. 1980, pp. 237--254.
	14	T. Krick , L. M. Pardo, A computational method for diophantine approximation, Algorithms in algebraic geometry and applications, Birkhauser Verlag, Basel, Switzerland, 1996
	15	KR.ONECKER, L. Grundzfige einer arithmetische~, Theorie der algebraischen Gr5ssen. Journal f~r die re.ine und andcwandte Mathematik (1882).
	16	LAZARD: D. Stewart t)latform and GrSbner bases. In Proceedings of the third international workshop on advance.s of robot kinematics (1992), P.-C. V. and L. J., Eds., Ferrare, pp. 136-142.
	17	MERLET..J. Parallel manitmlators- 3rd part. research rep. no. 1003. Tech. re.'p., INRIA Sophia-Antipolis, 1988.
	18	MORALS, ,l. Resolucidn eficaz de sistemas de ecuaclones polinomiales. PhD thesis, University of Santander, Spain, 1998.
	19	B. Mourrain, Enumeration problems in geometry, robotics and vision, Algorithms in algebraic geometry and applications, Birkhauser Verlag, Basel, Switzerland, 1996
	20	RONGA. F.. AND \rlJS'l". T. Stewart I)latforms without computer '? In International Conference on Real Analytic and AIgebrnic Geometry (1995), F. Broglia, M. Galbiati, and A. Tognoli. Eds., W. de Gruyter.
	21	R.ot:lbLIER., F. Algorithmes efficaces pour l'dtude des zdros reSels des systb~mes polynomiaux. PhD thesis, Universitd R.ennes I, 1996.
	22	R.oulr.r.IEa. F. Solving zer~-dimensi~nal polynomial systems trough the rational univariate representation. Tcch. R.ep. 3:126, INRIA, Projet Polka, 1998.

CITED BY 5

	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	Luis Miguel Pardo , Jorge San Martín, Deformation techniques to solve generalised Pham systems, Theoretical Computer Science, v.315 n.2-3, p.593-625, 6 May 2004
	Yuzhen Huang , Wenda Wu , Hans J. Stetter , Lihong Zhi, Pseudofactors of multivariate polynomials, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.161-168, July 2000, St. Andrews, Scotland
	Guillaume Moroz, Complexity of the resolution of parametric systems of polynomial equations and inequations, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy
	Erich Kaltofen , Zhengfeng Yang , Lihong Zhi, On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms, Proceedings of the 2007 international workshop on Symbolic-numeric computation, July 25-27, 2007, London, Ontario, Canada