A product formula for minimal polynomials and degree bounds for inverses of polynomial automorphisms
HTML articles powered by AMS MathViewer
- by Jie Tai Yu PDF
- Proc. Amer. Math. Soc. 123 (1995), 343-349 Request permission
Abstract:
By means of Galois theory, we give a product formula for the minimal polynomial G of $\{ {f_0},{f_1}, \ldots ,{f_n}\} \subset K[{x_1}, \ldots ,{x_n}]$ which contains n algebraically independent elements, where K is a field of characteristic zero. As an application of the product formula, we give a simple proof of Gabber’s degree bound inequality for the inverse of a polynomial automorphism.References
- Shreeram S. Abhyankar, Algebraic geometry for scientists and engineers, Mathematical Surveys and Monographs, vol. 35, American Mathematical Society, Providence, RI, 1990. MR 1075991, DOI 10.1090/surv/035
- Hyman Bass, Edwin H. Connell, and David Wright, The Jacobian conjecture: reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 287–330. MR 663785, DOI 10.1090/S0273-0979-1982-15032-7
- Wei Li and Jie Tai Yu, Computing minimal polynomials and the degree of unfaithfulness, Comm. Algebra 21 (1993), no. 10, 3557–3569. MR 1231617, DOI 10.1080/00927879308824749
- Wei Li and Jie Tai Yu, Reconstructing birational maps from their face functions, Manuscripta Math. 76 (1992), no. 3-4, 353–366. MR 1185025, DOI 10.1007/BF02567766
- James H. McKay and Stuart Sui Sheng Wang, An inversion formula for two polynomials in two variables, J. Pure Appl. Algebra 40 (1986), no. 3, 245–257. MR 836651, DOI 10.1016/0022-4049(86)90044-7
- David Mumford, Algebraic geometry. I, Grundlehren der Mathematischen Wissenschaften, No. 221, Springer-Verlag, Berlin-New York, 1976. Complex projective varieties. MR 0453732 P. Pederson and B. Sturmfels, Product formulas for sparse resultants, J. Algebra (to appear) (1993).
- Bernd Sturmfels, Sparse elimination theory, Computational algebraic geometry and commutative algebra (Cortona, 1991) Sympos. Math., XXXIV, Cambridge Univ. Press, Cambridge, 1993, pp. 264–298. MR 1253995
- Bernd Sturmfels and Jie Tai Yu, Minimal polynomials and sparse resultants, Zero-dimensional schemes (Ravello, 1992) de Gruyter, Berlin, 1994, pp. 317–324. MR 1292495
- Stuart Sui Sheng Wang, A Jacobian criterion for separability, J. Algebra 65 (1980), no. 2, 453–494. MR 585736, DOI 10.1016/0021-8693(80)90233-1
- Jie Tai Yu, Face polynomials and inversion formula, J. Pure Appl. Algebra 78 (1992), no. 2, 213–219. MR 1161345, DOI 10.1016/0022-4049(92)90099-2
- Jie Tai Yu, Computing minimal polynomials and the inverse via GCP, Comm. Algebra 21 (1993), no. 7, 2279–2294. MR 1218498, DOI 10.1080/00927879308824677
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 343-349
- MSC: Primary 12E05; Secondary 12F05, 12Y05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1216829-4
- MathSciNet review: 1216829