1 citations · 2 across the 10 of their papers we have counts for
10 papers
Sparse systems and algorithmic equidimensional decomposition
Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with pre…
Decision problem for a class of univariate Pfaffian functions
Maria Laura Barbagallo, Gabriela Jeronimo, Juan Sabia
We address the decision problem for sentences involving univariate functions constructed from a fixed Pfaffian function of order . We present a new symbolic procedure solving th…
On degree bounds for the sparse Nullstellensatz
Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We prove new upper bounds for the degrees in Hilbert's Nullstellensatz and for the Noether exponent of polynomial ideals in terms of the monomial structure of the polynomials invol…
On the multiplicity of isolated roots of sparse polynomial systems
María Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We give formulas for the multiplicity of any affine isolated zero of a generic polynomial system of n equations in n unknowns with prescribed sets of monomials. First, we consider…
Zero counting for a class of univariate Pfaffian functions
María Laura Barbagallo, Gabriela Jeronimo, Juan Sabia
We present a new procedure to count the number of real zeros of a class of univariate Pfaffian functions of order . The procedure is based on the construction of Sturm sequences…
Puiseux expansions and non-isolated points in algebraic varieties
Maria Isabel Herrero, Gabriela Jeronimo, Juan Sabia
We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given truncated Puiseux se…