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math.AG2018
A new general formula for the Cauchy Index on an interval with Subresultants
Daniel Perrucci, Marie-Françoise Roy
We present a new formula for the Cauchy index of a rational function on an interval using subresultant polynomials. There is no condition on the endpoints of the interval and the f…
math.AG2018
A version of Putinar's Positivstellensatz for cylinders
Paula Escorcielo, Daniel Perrucci
We prove that, under some additional assumption, Putinar's Positivstellensatz holds on cylinders of type with $S = \{x \in {\mathbb R}^n | g_1(x) \ge 0, ...,…
math.AG2018
Quantitative Fundamental Theorem of Algebra
Daniel Perrucci, Marie-Françoise Roy
Using subresultants, we modify a recent real-algebraic proof due to Eisermann of the Fundamental Theorem of Algebra ([FTA]) to obtain the following quantitative information: in ord…