# Count the Number of Complex Roots

 Title: Count the Number of Complex Roots Author: Wenda Li Submission date: 2017-10-17 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 a rectangle box or a 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). BibTeX: @article{Count_Complex_Roots-AFP, author = {Wenda Li}, title = {Count the Number of Complex Roots}, journal = {Archive of Formal Proofs}, month = oct, year = 2017, note = {\url{https://isa-afp.org/entries/Count_Complex_Roots.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Sturm_Tarski, Winding_Number_Eval Used by: Linear_Recurrences Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.