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Issue No.02 - March (1995 vol.15)
pp: 60-69
Part 2 of this tutorial concerns methods for constructing multivariate resultants, including methods for bidegree and equal-degree polynomial equations. It also describes u-resultants, a powerful use of standard resultants.
Chionh Eng Wee, Ronald N. Goldman, "Elimination and Resultants", IEEE Computer Graphics and Applications, vol.15, no. 2, pp. 60-69, March 1995, doi:10.1109/38.365007
1. G. Salmon, Lessons Introductory to the Modern Higher Algebra, G.E. Stechert&Co., New York, 1924.
2. F.S. Macaulay, “Some Formulae in Elimination,” Proc. London Math. Soc., Vol. 35, May 1902, pp. 3-27.
3. F.S Macaulay, “Note on the Resultant of a Number of Polynomials of the Same Degree,” Proc. London Math. Soc., Vol. 21, June 1921, pp. 14-21.
4. A.L. Dixon, “The Eliminant of Three Quantics in Two Independent Variables,” Proc. London Math. Soc., Vol. 7, Nov. 1908, pp. 49-69, 473-492.
5. T. Muir, A Treatise on the Theory of Determinants, revised and enlarged by W.H. Metzler, Longmans, Green&Co., New York, 1933.
6. E.W. Chionh and R.N. Goldman, “Degree, Multiplicity, and Inversion Formulas for Rational Surfaces Usingu‐Resultants,” Computer Aided Geometric Design, Vol. 9, No. 2, June 1992, pp. 93‐108.
7. A.L. Dixon, “On a Form of the Elimination of Two Quantics,” Proc. London Math. Soc., Vol. 6, June 1908, pp. 468-478.
8. A.L. Dixon, “Symbolical Expressions for the Eliminant of Two Binary Quantics,” Proc. London Math. Soc., Vol. 8, June 1909, pp. 265-276.
9. A.L. Dixon, “The Eliminant of the Equations of Four Quadric Surfaces,” Proc. London Math. Soc., Vol. 8, Dec. 1909, pp. 340-352.
10. J.F. Canny, “Generalized Characteristic Polynomials,” J. Symbolic Computation, Vol. 9, No. 3, Mar. 1990, pp. 241-250.
11. E.W. Chionh, “Base Points, Resultants, and the Implicit Representation of Rational Surfaces,” doctoral dissertation, Computer Science Dept., University of Waterloo, 1989.
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