TYBES OFRESULTANT MATRICES FOR MULTIGRADED POLYNOMIAL SYSTEMS
DOI:
https://doi.org/10.59743/jbs.v33i2.194Abstract
Resultant computation eliminates variables is an important tool to answer posed by the given polynomial system. Dating back from as much as 200 years ago, it has become a classical algebraic tool to determine whether a given polynomial system has a common root without explicitly solving for the roots. The study of resultant goes back to the classical work of Bezout, Sylvester, Cayley, Macaulay and Dixon.
References
Igor Shafarevich (1995). Basic Algebraic Geometry I: Varieties in projective Space (2nded.). Springer-Verlag.
I. Z. Emiris (1995). Efficient Inceremtal Algorithms for the Sparse Resultant and the Mixed Volume. Journal of Complexity, Volume 20, Pages 117-149.
Weiming Wang and Xinze Lain (2005). Computations of Multi-resulant with mechanization. Jpurnal of Applied Mathematics and Compution. Volume 1710, Issue 1. Pages 237-257.
David, John, D. O, Shea (1998). Using Algebraic Gemoetry. Springer VerlagNewtwork, Inc.
J. F. Canny and I. Z. Emiris (2000). A subdivision based algorithm for the sparse resultant. Journal of ACM. Volume 47. Issue 3.
D. Cox, J. Little and D. O. Shea (2006). Ideal, Varieties and algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (3rd ed.). Springer- Verlag. New York- berlin- Heidelberg.
Grigoriev, D.,Karpinski, M., and Singer, M., (1990) Fast Parallel Algorithms for sparse Multivariate polynomial interpolation Over Finite Field. Slam J. Computation. Volume 19, No. 6, Pages 1059-1063
D. Kapur and T. Sexena (1996). SparsityConsederations in Dixon Resultants. ACM Press Proc. IssAc. Pages 187.
I. Z. Emiris and Victor Y.Pan (1997). The Structure of Sparse Resultant Matricies. ACM Inter. Symposium On Symbolic and Algebraic Computation. Pages 183-192.
D. Manocha (1992). Algebraic and Numeric Techniques for Modeleling and Robotics. National Science Fiundation.
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