Por motivos de mantenimiento se ha deshabilitado el inicio de sesión temporalmente. Rogamos disculpen las molestias.
Article
The Newton Procedure for several variables
Author/s | Soto Prieto, Manuel Jesús
Vicente Córdoba, José Luis |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2011-07-15 |
Deposit Date | 2016-10-17 |
Published in |
|
Abstract | Let us consider an equation of the form P(x, z) = zm + w1(x)zm−1 + · · · + wm−1(x)z + wm(x) = 0, where m>1, n>1, x=(x1⋯xn) is a vector of variables, k is an algebraically closed field of characteristic zero, View the ... Let us consider an equation of the form P(x, z) = zm + w1(x)zm−1 + · · · + wm−1(x)z + wm(x) = 0, where m>1, n>1, x=(x1⋯xn) is a vector of variables, k is an algebraically closed field of characteristic zero, View the MathML source and wm(x)≠0. We consider representations of its roots as generalized Puiseux power series, obtained by iterating the classical Newton procedure for one variable. The key result of this paper is the following: Theorem 1.The iteration of the classical Newton procedure for one variable gives rise to representations of all the roots of the equation above by generalized Puiseux power series in x1/d, d∈Z>0, whose supports are contained in an n-dimensional, lex-positive strictly convex polyhedral cone (see Section 5). We must point out that the crucial result is not the existence of these representations, which is a well-known fact; but the fact that their supports are contained in such a special cone. We achieve the proof of this theorem by taking a suitable affine chart of a toric modification of the affine space. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Project ID. | MTM-2010-19298 |
Citation | Soto Prieto, M.J. y Vicente Córdoba, J.L. (2011). The Newton Procedure for several variables. Linear Algebra and its Applications, 435 (2), 255-269. |
Files | Size | Format | View | Description |
---|---|---|---|---|
The Newton Procedure for several ... | 226.8Kb | [PDF] | View/ | |