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: [failed]	This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.