Comparison of various multivariate resultant formulations

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Comparison of various multivariate resultant formulations

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1995 international symposium on Symbolic and algebraic computation table of contents

Montreal, Quebec, Canada

Pages: 187 - 194

Year of Publication: 1995

ISBN:0-89791-699-9

Authors

Deepak Kapur	Institute for Programming and Logics, Department of Computer Science, State University of New York at Albany, Albany, NY
Tushar Saxena	Institute for Programming and Logics, Department of Computer Science, State University of New York at Albany, Albany, NY

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): 18, Citation Count: 12

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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	Bayer D., Stillman M., Macaulay User's Manual, Cornell University, Ithaca, NY.
	2	Bernshtein D.N., The Number of Roots of a System of Equations, FunktsionaI'nyi AnaIiz i Ego Prilozheniya, 9(3):1-4.
	3	Buchberger B., GrSbner bases: An Algorithmic Method in Polynomial Ideal Theory, Multidimensional Systems Theory, N.K. Bose, ed., D. ReideI PubI. Co., 1985.
	4	John Canny, Generalised characteristic polynomials, Journal of Symbolic Computation, v.9 n.3, p.241-250, March 1990 [doi>10.1016/S0747-7171(08)80012-0]
	5	John F. Canny , Ioannis Z. Emiris, An Efficient Algorithm for the Sparse Mixed Resultant, Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.89-104, May 10-14, 1993
	6	John Canny , Paul Pedersen, An Algorithm for the Newton Resultant, Cornell University, Ithaca, NY, 1993
	7	Cayley A., On the Theory of Elimination. Cambridge and Dublin Mathematical Journal, III, 1865, 210-270.
	8	Eng-wee Chionh, Base points, resultants, and the implicit representation of rational surfaces, University of Waterloo, Waterloo, Ont., Canada, 1990
	9	George E. Collins, The Calculation of Multivariate Polynomial Resultants, Journal of the ACM (JACM), v.18 n.4, p.515-532, Oct. 1971 [doi>10.1145/321662.321666]
	10	Dixon A.L., The Eliminant of Three Quantics in Two Independent Variables. Proc. London Mathematical Society, 6, 1908, 468-478.
	11	Ioannis Emiris , John Canny, A practical method for the sparse resultant, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.183-192, July 06-08, 1993, Kiev, Ukraine [doi>10.1145/164081.164122]
	12	Ioannis Z. Emiris , John F. Canny, Efficient Incremental Algorithms for the, University of California at Berkeley, Berkeley, CA, 1994
	13	Faug~re J.C., Gb Reference Manual, PoSSo project, Institut Blaise Pascal, France.
	14	Gantmatcher F.R., Matrix Theory, vol. 1. Chelsea Publishing, 1959, Chap. 2.
	15	Grigoryev D.Yu. and Chistov A.L., Sub-exponential Time Solving of Systems of Algebraic Equations. LOMI Preprints E-9-83 and E-10-83, Leningrad, 1983.
	16	Gelfand I.M., Kapranov M.M. and Zelevinsky A.V., Discriminants, Resuitants and Multidimensional Determinants, Birkh~user, Boston, 1994.
	17	Kapur D. and Lakshman Y.N., Elimination Methods: an Introduction. Symbolic and Numerical Computation for Artificial Intelligence B. Donald et. al. (eds.), Academic Press, 1992.
	18	Deepak Kapur , Tushar Saxena , Lu Yang, Algebraic and geometric reasoning using Dixon resultants, Proceedings of the international symposium on Symbolic and algebraic computation, p.99-107, July 20-22, 1994, Oxford, United Kingdom [doi>10.1145/190347.190372]
	19	Kapur D and Saxena T., Spaxsity Considerations in the Dixon Resultant Formulation, manuscript under preparation.
	20	Macaulay F.S., The Algebraic Theory of Modular Systerns, Cambridge Tracts in Math. and Math. Phys., 19, 1916.
	21	Thomas W. Sederberg , Ronald N. Goldman, Algebraic geometry for computer-aided geometric design, IEEE Computer Graphics and Applications, v.6 n.6, p.52-59, June 1986 [doi>10.1109/MCG.1986.276742]
	22	Sturmfels B., Sparse Elimination Theory, Proc. Computat. Algebraic Geom. and Commut. Algebra, D. Eisenbud and L. Robbiano, eds., Cortona, Italy, June 1991.
	23	Sturmfels B. and Zelevinsky A., Multigraded resultants of the Sylvester type, Journal of Algebra, 1992.
	24	Weyman J. and Zelevinsky A., Determinantal Formulas for Multigraded Resultants, Journal of Algebraic Geometry, pp 569-597, 1994.
	25	Zippel R. Effective Polynomial Computation, Kluwer Academic Publishers, Boston, 1993.

CITED BY 12

	Robert H. Lewis, Heuristics to accelerate the Dixon resultant, Mathematics and Computers in Simulation, v.77 n.4, p.400-407, April, 2008
	Deepak Kapur , Tushar Saxena, Sparsity considerations in Dixon resultants, Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, p.184-191, May 22-24, 1996, Philadelphia, Pennsylvania, United States
	Arthur D. Chtcherba , Deepak Kapur, Conditions for exact resultants using the Dixon formulation, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.62-70, July 2000, St. Andrews, Scotland
	Deepak Kapur , Tushar Saxena, Extraneous factors in the Dixon resultant formulation, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.141-148, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Ana Marco , José-Javier Martínez, Structured matrices in the application of bivariate interpolation to curve implicitization, Mathematics and Computers in Simulation, v.73 n.6, p.378-385, February, 2007
	Arthur D. Chtcherba , Deepak Kapur, Support hull: relating the cayley-dixon resultant constructions to the support of a polynomial system, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.95-102, July 04-07, 2004, Santander, Spain
	Arthur D. Chtcherba , Deepak Kapur, On the efficiency and optimality of Dixon-based resultant methods, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.29-36, July 07-10, 2002, Lille, France
	Yongli Sun , Jianping Yu, Implicitization of Parametric Curves via Lagrange Interpolation, Computing, v.77 n.4, p.379-386, June 2006
	Arthur D. Chtcherba , Deepak Kapur, Exact resultants for corner-cut unmixed multivariate polynomial systems using the Dixon formulation, Journal of Symbolic Computation, v.36 n.3-4, p.289-315, September 2003
	Bernard Mourrain , Philippe Trebuchet, Solving projective complete intersection faster, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.234-241, July 2000, St. Andrews, Scotland
	John F. Canny , Ioannis Z. Emiris, A subdivision-based algorithm for the sparse resultant, Journal of the ACM (JACM), v.47 n.3, p.417-451, May 2000
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003