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A practical method for the sparse resultant

Authors:

Ioannis Emiris,

John CannyAuthors Info & Claims

ISSAC '93: Proceedings of the 1993 international symposium on Symbolic and algebraic computation

Pages 183 - 192

https://doi.org/10.1145/164081.164122

Published: 01 August 1993 Publication History

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References

[1]

D.N. Bernstein. The number of roots of a system of equations. Funktszonal'nyz Anahz Ego Pmlozheniya, 9(3):1-4, aul-Sep 1975.

Google Scholar

[2]

C. Bajaj, T. Garrity, and a. Warren. On the applications of multi-equational resultants. Technical Report 826, Purdue Univ., 1988.

Google Scholar

[3]

J.F. Ca,nny. The Complexity of Robot Motion Planning. M.I.T. Press, Cambridge, 1988.

Digital Library

Google Scholar

[4]

J. Canny and I. Emiris. An efficient algorithm for the spa.rse mixed resultant. In Proc. AAEEC '93. Springer Verlag, May 1993. To Appear.

Digital Library

Google Scholar

[5]

M. Chardin. The resultant via a Koszul complex. In F. Eyssette and A. Galligo, editors, Proc. of MEGA '92, pages 29-39, Nice, April 1992.

Google Scholar

[6]

I. Emiris and J. Canny. An efficient approach to removing geometric degeneracies. In Proc. 8th A CM Syrup. on ComputatzoT~al Geometry, pages 74-82, June 1992.

Digital Library

Google Scholar

[7]

B. Huber and B. Sturmfels. Homotopies preserving the Newton polytopes. Manuscript, Cornel Univ., presented at the "Workshop on Real Algebraic Geometry", August 1992.

Google Scholar

[8]

A.G. Khovanskii. Newton polyhedra, a.nd the genus of complete intersections. Funkts,tonal'- nyi Anahz z Ego Pr, lozhenzya, 12(1)'51-61, Jan-Mar 1978.

Google Scholar

[9]

M.M. Kapranov, B. Sturmfels, and A.V. Zelevinsky. Chow polytopes and general resultants. Duke Math. J., 67:237-254, 1992.

Crossref

Google Scholar

[10]

A.G. Kushnirenko. The Newton polyhedron and the number of solutions of a system of k equations in k unknowns. Uspekh~ Mal. Nauk., 30:266-267, 1975.

Google Scholar

[11]

D. Lazard. R~solution des syst~mes d'dquations alg~briques. Theor. Co~np. Scence, 15:77-110, 1981.

Crossref

Google Scholar

[12]

F.S. Macaulay. Some formulaein elimination. Proc. London Math. Soc., 1(33)'3-27, 1902.

Google Scholar

[13]

E. Mahalingam. A way to compute mixed volumes. Master's thesis, UC Berkeley, October 1992.

Google Scholar

[14]

D. Manocha and J. Canny. The impicit representation of rationa.1 parametric surfaces. J. Symb. Computatzon, 13"485-510, 1992.

Digital Library

Google Scholar

[15]

D. Manocha and J. Canny. Multipolynomial resultants and linear algebra. In Proc. ISSAC '92, Berkeley, July 1992.

Digital Library

Google Scholar

[16]

D. Manocha and J. Canny. Real time inverse kinematics for general 6R manipulators. In Proc. IEEE I~tern. Conf. Robotzcs and Aulomat~on, Nice, May 1992.

Crossref

Google Scholar

[17]

P. Pedersen and B. Sturmfels. Product formulas for sparse resultants. Ma.nuscript, Cornell Univ., 1991.

Google Scholar

[18]

G. Salmon. Modern H~.gher Algebra. G.E. Stechert and Co., New York, 1885. reprinted 1924.

Google Scholar

[19]

J.T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. J. ACM, 27(4)701-717, 1980.

Digital Library

Google Scholar

[20]

B. Sturmfels. Sparse elimination theory. In D. Eisenbud and L. Robbiano, editors, Proc. Computat. Algebraic Geom. and Commut. Algebra, Cortona, Italy, June 1991. Cambridge Univ. Press. To appear.

Google Scholar

[21]

B. Sturmfels. Combinatorics of the sparse resultant. Technical Report 020-93, MSRI, Berkeley, November 1992.

Google Scholar

[22]

B. Sturmfels and A. Zelevinsky. Multigraded resultants of Sylvester type. J. of Algebra. To appear. Also, Manuscript, Cornell Univ., i991.

Google Scholar

[23]

B.L. van der Waerden. Modern Algebra. Ungar Publishing Co., New York, 3rd edition, 1950.

Google Scholar

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Bhayani SHeikkilä JKukelova Z(2024)Sparse Resultant-Based Minimal Solvers in Computer Vision and Their Connection with the Action MatrixJournal of Mathematical Imaging and Vision10.1007/s10851-024-01182-166:3(335-360)Online publication date: 23-Mar-2024
https://doi.org/10.1007/s10851-024-01182-1
Bhayani SKukelova ZHeikkila J(2021)Computing stable resultant-based minimal solvers by hiding a variable2020 25th International Conference on Pattern Recognition (ICPR)10.1109/ICPR48806.2021.9411957(6104-6111)Online publication date: 10-Jan-2021
https://doi.org/10.1109/ICPR48806.2021.9411957
Bhayani SKukelova ZHeikkila J(2020)A Sparse Resultant Based Method for Efficient Minimal Solvers2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR42600.2020.00184(1767-1776)Online publication date: Jun-2020
https://doi.org/10.1109/CVPR42600.2020.00184
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A practical method for the sparse resultant

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Published In

ISSAC '93: Proceedings of the 1993 international symposium on Symbolic and algebraic computation

August 1993

321 pages

ISBN:0897916042

DOI:10.1145/164081

Editor:
Manuel Bronstein

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 1993

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SIGSAM

ISSAC93: International Symposium on Symbolic and Algebraic

July 6 - 8, 1993

Kiev, Ukraine

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Bhayani SHeikkilä JKukelova Z(2024)Sparse Resultant-Based Minimal Solvers in Computer Vision and Their Connection with the Action MatrixJournal of Mathematical Imaging and Vision10.1007/s10851-024-01182-166:3(335-360)Online publication date: 23-Mar-2024
https://doi.org/10.1007/s10851-024-01182-1
Bhayani SKukelova ZHeikkila J(2021)Computing stable resultant-based minimal solvers by hiding a variable2020 25th International Conference on Pattern Recognition (ICPR)10.1109/ICPR48806.2021.9411957(6104-6111)Online publication date: 10-Jan-2021
https://doi.org/10.1109/ICPR48806.2021.9411957
Bhayani SKukelova ZHeikkila J(2020)A Sparse Resultant Based Method for Efficient Minimal Solvers2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR42600.2020.00184(1767-1776)Online publication date: Jun-2020
https://doi.org/10.1109/CVPR42600.2020.00184
Telen S(2020)Numerical Root Finding via Cox RingsJournal of Pure and Applied Algebra10.1016/j.jpaa.2020.106367(106367)Online publication date: Mar-2020
https://doi.org/10.1016/j.jpaa.2020.106367
Ahmad SAris N(2015)The implementation of a hybrid resultant matrix formulation10.1063/1.4932424(020015)Online publication date: 2015
https://doi.org/10.1063/1.4932424
Ahmad SAris NKanafiah S(2010)The mechanization of multires algorithm and computation of mixed volume using mixed subdivision for sparse resultants2010 International Conference on Science and Social Research (CSSR 2010)10.1109/CSSR.2010.5773883(74-79)Online publication date: Dec-2010
https://doi.org/10.1109/CSSR.2010.5773883
Hahmann SBelyaev ABusé LElber GMourrain BRössl C(2008)Shape InterrogationShape Analysis and Structuring10.1007/978-3-540-33265-7_1(1-51)Online publication date: 2008
https://doi.org/10.1007/978-3-540-33265-7_1
Peters JSitharam MZhou YFan J(2006)Elimination in generically rigid 3D geometric constraint systemsAlgebraic Geometry and Geometric Modeling10.1007/978-3-540-33275-6_13(205-216)Online publication date: 2006
https://doi.org/10.1007/978-3-540-33275-6_13
Li TLi X(2001)Finding Mixed Cells in the Mixed Volume ComputationFoundations of Computational Mathematics10.1007/s1020800100051:2(161-181)Online publication date: 1-Jan-2001
https://dl.acm.org/doi/10.1007/s102080010005
Hirukawa HMourrain BPapegay Y(2000)A symbolic-numeric silhouette algorithmProceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113)10.1109/IROS.2000.895320(2358-2365)Online publication date: 2000
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