Información del autor
Documentos disponibles escritos por este autor (18)
Añadir el resultado a su cesta Hacer una sugerencia Refinar búsqueda
texto impreso
An algorithm to give an explicit description of all the solutions to any tropical linear system A x=B x is presented. The given system is converted into a finite (rather small) number p of pairs (S,T) of classical linear systems: a system S of e[...]texto impreso
We correct a previously published theorem by proving a criterion to decide whether the fibration given by a real polynomial function f : R-2 --> R is locally trivial at infinity. The algorithmical nature of this criterion provides a test that c[...]texto impreso
The Baer-Krull theorems deal with the relationship between orderings of a valued field compatible with the valuation, and orderings of the residue class field. For these theorems it is necessary that the valuation ring should be convex with resp[...]texto impreso
texto impreso
Let p' and q' be points in R-n. Write p' similar to q' if p' - q' is a multiple of (1,...,1). Two different points p and q in R-n/ similar to uniquely determine a tropical line L(p, q) passing through them and stable under small perturbations. T[...]texto impreso
Let f : R(2) --> R be an open polynomial function. Then, f changes sign across V(f) (alternatively around a singular point of V(f)) and the function c : R --> N expressing the number c(lambda) of connected components of the lambda-level curve [...]texto impreso
Consider the space Mnnor of square normal matrices X=(xij) over R?{-?}, i.e., -??xij?0 and ;bsupesup&=0. Endow Mnnor with the tropical sum ? and multiplication. Fix a real matrix A?Mnnor and consider the set ?(A) of matrices in Mnnor which commu[...]texto impreso
En este art´?culo se demuestra que la multiplicidad de intersecci´on de dos curvas algebraicas planas complejas definida usando resultantes no depende del sistema proyectivo de coordenadas elegido. La clave de la demostraci´on consiste en descom[...]texto impreso
Puente Muñoz, María Jesús de la ; Ansola Fernández-Enríquez, Maria Macarena | Springer Verlag | 2009-11We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically independ[...]texto impreso
“Let A be the coordinate ring of the real plane, i.e., A = R[X, Y ], where X, Y are algebraically independent over the field of real numbers R. The purpose of this paper is to describe all the valuation rings of A which are compatible with some [...]texto impreso
In this paper we give a short, elementary proof of a known result in tropical mathematics, by which the convexity of the column span of a zero-diagonal real matrix $A$ is characterized by $A$ being a Kleene star. We give applications to alcoved [...]texto impreso
We study real algebraic plane curves, at an elementary level, using as little algebra as possible. Both cases, affine and projective, are addressed. A real curve is infinite, finite or empty according to the fact that a minimal polynomial for th[...]texto impreso
This paper provides an elementary exposition of affine and projective real plane curves. Where possible, elementary proofs are given, but to some extent, one must make use of results from algebraic geometry (over the complex numbers) and real al[...]texto impreso
Let phi : k --> A and f : A --> R be ring morphisms, R a real ring. We prove that if f : A --> R is etale, then the corresponding mapping between real Riemann surfaces S-r(f) : S-r(R/k) --> S-r(A/k) is a local homeomorphism. Several preparat[...]texto impreso
Let a polynomial function f of two real variables be given. We prove the existence of a finite number of unbounded regions of the real plane along which the tangent planes to the graph of f tend to horizontal position, when moving away from the [...]
