A new general formula for the Cauchy Index on an interval with Subresultants

Daniel Perrucci (1) , Marie-Françoise Roy (2)

1 Departamento de Matemática [Buenos Aires]
2 IRMAR - Institut de Recherche Mathématique de Rennes

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 formula also involves in some cases less subresultant polynomials.

Mots clés: Cauchy Index; Subresultant Polynomials

Domaines: Informatique [cs]; Géométrie algorithmique [cs.CG]

Daniel Perrucci, Marie-Françoise Roy. A new general formula for the Cauchy Index on an interval with Subresultants. Journal of Symbolic Computation, 2022, 109, pp.465-481. ⟨10.1016/j.jsc.2020.07.016⟩. ⟨hal-02912353⟩