Count the Number of Complex Roots

Wenda Li 🌐

October 17, 2017

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


Based on evaluating Cauchy indices through remainder sequences, this entry provides an effective procedure to count the number of complex roots (with multiplicity) of a polynomial within various shapes (e.g., rectangle, circle and half-plane). Potential applications of this entry include certified complex root isolation (of a polynomial) and testing the Routh-Hurwitz stability criterion (i.e., to check whether all the roots of some characteristic polynomial have negative real parts).


BSD License


October 26, 2021
resolved the roots-on-the-border problem in the rectangular case (revision 82a159e398cf).


Session Count_Complex_Roots