# The Theorem of Three Circles

 Title: The Theorem of Three Circles Authors: Fox Thomson (foxthomson0 /at/ gmail /dot/ com) and Wenda Li Submission date: 2021-08-21 Abstract: The Descartes test based on Bernstein coefficients and Descartes’ rule of signs effectively (over-)approximates the number of real roots of a univariate polynomial over an interval. In this entry we formalise the theorem of three circles, which gives sufficient conditions for when the Descartes test returns 0 or 1. This is the first step for efficient root isolation. BibTeX: @article{Three_Circles-AFP, author = {Fox Thomson and Wenda Li}, title = {The Theorem of Three Circles}, journal = {Archive of Formal Proofs}, month = aug, year = 2021, note = {\url{https://isa-afp.org/entries/Three_Circles.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Budan_Fourier, Polynomial_Interpolation 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.