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Tesis Doctoral
Métodos computacionales en los sistemas de ecuaciones en derivadas parciales
(2000)
"La memoria tiene dos partes: La primera está dedicada a la comparación entre los métodos clásicos de Riquier-Janet (para el estudio de los sistemas de ecuaciones en derivadas parciales) y los métodos modernos del álgebra ...
Artículo
Localization at hyperplane arrangements: combinatorics and D-modules
(Elsevier, 2007-10-15)
We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated by linear differential operators of order 1. The algorithm is ...
Artículo
Explicit calculations in rings of differential operators
(Société Mathématique de France, 2004)
We use the notion of a standard basis to study algebras of linear differential operators and finite type modules over these algebras. We consider the polynomial and the holomorphic cases as well as the formal case. Our ...
Tesis Doctoral
Métodos efectivos en anillos de operadores diferenciales y en sistemas hipergeométricos
(2002)
El Análisis Algebraico, o teoría de D-m&oa cute;dulos, trata el estudio de los sistemas de ecuaciones -- en derivadas parciales desde el punto de vista del álgebra y la geometría. Esta teoría generalizada la teoría clásica ...
Artículo
The Gröbner fan of an An-module
(Elsevier, 2000-06-14)
Let I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n→R be a linear form defined by L(α,β)=∑i=1neiαi+∑i=1nfiβi. If ei+fi≥0, then L defines a filtration F•L on An. Let grL(I) be the ...
Artículo
A flatness property for filtered D-modules
(European Mathematical Society, 2007)
Let M be a coherent module over the ring DX of linear differential operators on an analytic manifold X and let Z1, · · · , Zk be k germs of transverse hypersurfaces at a point x ∈ X. The Malgrange-Kashiwara V-filtrations ...
Artículo
Logarithmic cohomology of the complement of a plane curve
(Springer, 2002-03)
Let D, x be a plane curve germ. We prove that the complex Ω•(log D)x computes the cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial converse to a theorem of F.J. Castro-Jiménez, D. Mond ...
Artículo
The analytic standard fan of a D-module
(Elsevier, 2001-10-24)
We extend to the analytic D-module case our results in the algebraic case, namely, we associate with any monogeneous module over the ring D of germs of linear differential operators at the origin of Cn, with holomorphic ...
Artículo
The computation of the logarithmic cohomology for plane curves
(Elsevier, 2009-12-01)
We will give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables.
Artículo
Computational methods in algebra and analysis
(Sociedad Española de Matemática Aplicada, 2007-09)
This paper describes some applications of Computer Algebra to Algebraic Analysis also known as D-module theory, i.e. the algebraic study of the systems of linear partial differential equations. Gröbner bases for rings ...