Daniel Perrucci

activity

20032023

most citedAn elementary recursive bound for effective Positivstellensatz and Hilbert 17-th problem

18 citations · 28 across the 13 of their papers we have counts for

collaborators

18 papers

math.AG2023

Algebraic Winding Numbers

Daniel Perrucci, Marie-Françoise Roy

In this paper, we propose a new algebraic winding number and prove that it computes the number of complex roots of a polynomial in a rectangle, including roots on edges or vertices…

math.AG2023

Rational certificates of non-negativity on semialgebraic subsets of cylinders

Gabriela Jeronimo, Daniel Perrucci

Let $g_{1}, \dots, g_{s} \in R [X_{1}, \dots, X_{n}, Y]$ and $S = {(x ˉ, y) \in R^{n + 1} ∣ g_{1} (x ˉ, y) \geq 0, \dots, g_{s} (x ˉ, y) \geq 0}$ be a non-empty, possibly…

math.AG2022

Topology of real multi-affine hypersurfaces and a homological stability property

Saugata Basu, Daniel Perrucci

Let $R$ be a real closed field. We prove that the number of semi-algebraically connected components of a real hypersurface in $R^{n}$ defined by a multi-affine poly…

math.AG2021

A few more extensions of Putinar's Positivstellensatz to non-compact sets

Paula Escorcielo, Daniel Perrucci

We extend previous results about Putinar's Positivstellensatz for cylinders of type $S \times R$ to sets of type $S \times R^{r}$ in some special cases taking int…

math.AG2019

On sum of squares certificates of non-negativity on a strip

Paula Escorcielo, Daniel Perrucci

A well-known result of Murray Marshall states that every $f \in R [X, Y]$ non-negative on the strip $[0, 1] \times R$ can be written as $f = σ_{0} + σ_{1} X (1 - X)$ with $…

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…