### Abstract

The Descartes test based on Bernstein coefficients and Descartesâ€™ 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.

BSD License