We give an algorithm to compute term by term multivari-ate Puiseux series expansions of series arising as local parametrizations of zeroes of systems of algebraic equations at singular points. The algorithm is an extension of Newton's method for plane algebraic curves replacing the Newton polygon by the tropical variety of the ideal generated by the system.
We prove the existence of local Puiseux-type parameterizations of complex analytic sets via Laurent series convergent on wedges. We describe the wedges in terms of the Newton polyhedron of a function vanishing on the discriminant locus of a projection. The existence of a local parameterization of quasi-ordinary singularities of complex analytic sets of any… (More)
This paper describes an algorithmic method iterative method for searching power series solutions of a partial differential equation. Power series expansions considered have support in some convex cone of <b>R</b><sup>N</sup>. We do this by introducing a <i>N</i>-variables analog of the Newton polygon construction, used in the case of ordinary differential… (More)
SUMMARY Introduction Suicide is among the most prevalent causes of death in the world. A history of past suicide attempts is the most important of all the risk factors to show suicidal behavior (attempts and completed suicides). The objective of this study is to assess the effect of anxiety disorders, major depressive disorder, and comorbid major depression… (More)
The concepts of tropical semiring and tropical hypersurface, are extended to the case of an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator " tropicaliza-tion " we conclude with an extension of Kapranov's theorem to algebraically… (More)