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References
D.N. Bernstein, “The number of roots of a system of equations,” Functional Anal. Appl. 9 (1975), 183–185.
U. Betke, “Mixed volumes of polytopes,” Archiv der Mathematik 58 (1992), 388–391.
L.J. Billera and B. Sturmfels, “Fiber polytopes,” Ann. Math. 135 (1992), 527–549.
R.C. Buck, “Partitions of space,” Amer. Math. Monthly 50 (1943), 541–544.
J. Canny and I. Emiris, “An efficient algorithm for the sparse mixed resultant,” Proc. AAECC, Puerto Rico, May 1993, Springer Lect. Notes in Comput. Science 263 (1993), pp. 89–104.
I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, “Discriminants of polynomials in several variables and triangulations of Newton polytopes,” Algebra i analiz (Leningrad Math. J.) 2 (1990), 1–62.
I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, “Discriminants and Resultants,” Birkhäuser, Boston, 1994.
I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, “Generalized Euler integrals and A-hypergeometric functions,”Adv. Math. 84 (1990), 255–271.
I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, “Newton polytopes of the classical resultant and discriminant,” Adv. Math. 84 (1990), 237–254.
B. Huber and B. Sturmfels, “Homotopies preserving the Newton polytopes,” presented at the Workshop on Real Algebraic Geometry, MSI Cornell, August 1992.
M. Kapranov, B. Sturmfels, and A Zelevinsky, “Chow polytopes and general resultants,” Duke Math. J. 67 (1992), 189–218.
C. Lee, “Regular triangulations of convex polytopes,” in Applied Geometry and Discrete Mathematics — The Victor Klee Festschrift, [P. Gritzmann and B. Sturmfels, eds.], American Mathematical Society, DIMACS Series 4, Providence, RI, 1991, pp. 443–456.
F.S. Macaulay, “Some formulae in elimination,” Proc. London Math. Soc. 33 1, (1902), 3–27.
P. Pedersen and B. Sturmfels, “Product formulas for resultants and Chow forms,” Mathematische Zeitschrift, 214 (1993), 377–396.
B. Sturmfels, “Sparse elimination theory,” in Computational Algebraic Geometry and Commutative Algebra Proc. Cortona, D. Eisenbud and L. Robbiano, eds., Cambridge University Press, 1993, pp. 377–396.
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Sturmfels, B. On the Newton Polytope of the Resultant. Journal of Algebraic Combinatorics 3, 207–236 (1994). https://doi.org/10.1023/A:1022497624378
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DOI: https://doi.org/10.1023/A:1022497624378