On the Newton Polytope of the Resultant
Bernd Sturmfels
DOI: 10.1023/A:1022497624378
Pages: 207–236
Keywords: elimination theory; mixed subdivision; resultant; polytope
Full Text: PDF
References
1. D.N. Bernstein, "The number of roots of a system of equations," Functional Anal. Appl. 9 (1975), 183-185.
2. U. Betke, "Mixed volumes of polytopes," Archiv der Mathematik 58 (1992), 388-391.
3. L.J. Billera and B. Sturmfels, "Fiber polytopes," Ann. Math. 135 (1992), 527-549.
4. R.C. Buck, "Partitions of space," Amer. Math. Monthly 50 (1943), 541-544.
5. 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.
6. 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.
7. I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, "Discriminants and Resultants," Birkhauser, Boston, 1994.
8. I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, "Generalized Euler integrals and A-hypergeometric functions," Adv. Math. 84 (1990), 255-271.
9. I.M. Gelfand, M.M. Kapranov, and A.V Zelevinsky, "Newton polytopes of the classical resultant and discriminant," Adv. Math. 84 (1990), 237-254.
10. B. Huber and B. Sturmfels, "Homotopies preserving the Newton polytopes," presented at the Workshop on Real Algebraic Geometry, MSI Cornell, August 1992.
11. M. Kapranov, B. Sturmfels, and A Zelevinsky, "Chow polytopes and general resultants," Duke Math. J. 67 (1992), 189-218.
12. 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.
13. F.S. Macaulay, "Some formulae in elimination," Proc. London Math. Soc. 33 1, (1902), 3-27.
14. P. Pedersen and B. Sturmfels, "Product formulas for resultants and Chow forms," Mathematische Zeitschrift, 214 (1993), 377-396.
15. 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.
2. U. Betke, "Mixed volumes of polytopes," Archiv der Mathematik 58 (1992), 388-391.
3. L.J. Billera and B. Sturmfels, "Fiber polytopes," Ann. Math. 135 (1992), 527-549.
4. R.C. Buck, "Partitions of space," Amer. Math. Monthly 50 (1943), 541-544.
5. 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.
6. 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.
7. I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, "Discriminants and Resultants," Birkhauser, Boston, 1994.
8. I.M. Gelfand, M.M. Kapranov, and A.V. Zelevinsky, "Generalized Euler integrals and A-hypergeometric functions," Adv. Math. 84 (1990), 255-271.
9. I.M. Gelfand, M.M. Kapranov, and A.V Zelevinsky, "Newton polytopes of the classical resultant and discriminant," Adv. Math. 84 (1990), 237-254.
10. B. Huber and B. Sturmfels, "Homotopies preserving the Newton polytopes," presented at the Workshop on Real Algebraic Geometry, MSI Cornell, August 1992.
11. M. Kapranov, B. Sturmfels, and A Zelevinsky, "Chow polytopes and general resultants," Duke Math. J. 67 (1992), 189-218.
12. 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.
13. F.S. Macaulay, "Some formulae in elimination," Proc. London Math. Soc. 33 1, (1902), 3-27.
14. P. Pedersen and B. Sturmfels, "Product formulas for resultants and Chow forms," Mathematische Zeitschrift, 214 (1993), 377-396.
15. 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.