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