Count the Number of Complex Roots

Wenda Li 🌐

October 17, 2017


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

Change history

October 26, 2021

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


Theories of Count_Complex_Roots