25 citations · 73 across the 14 of their papers we have counts for
17 papers
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…
A data analysis of women's trails among ICM speakers
Helena Mihaljević, Marie-Françoise Roy
The International Congress of Mathematicians (ICM), inaugurated in 1897, is the greatest effort of the mathematical community to strengthen international communication and connecti…
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…
Bounds for polynomials on algebraic numbers and application to curve topology
Daouda Niang Diatta, Sény Diatta, Fabrice Rouillier +2
Let be a given square-free polynomial of total degree with integer coefficients of bitsize less than , and let $V_{\mathbb{R}} (P) := \{ (x,y) \in…
Sylvester double sums, subresultants and symmetric multivariate Hermite interpolation
Marie-Françoise Roy, Aviva Szpirglas
Sylvester doubles sums, introduced first by Sylvester are symmetric expressions of the roots of two polynomials. Sylvester's definition of double sums makes no sense in the presenc…
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…