Count the Number of Complex Roots

Wenda Li

17 October 2017

Abstract

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

[2021-10-26] resolved the roots-on-the-border problem in the rectangular case (revision 82a159e398cf).

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