Journal of Automated Reasoning

, Volume 53, Issue 2, pp 105–127 | Cite as

Theorem of Three Circles in Coq

  • Julianna ZsidóEmail author


The theorem of three circles in real algebraic geometry guarantees the termination and correctness of an algorithm of isolating real roots of a univariate polynomial. The main idea of its proof is to consider polynomials whose roots belong to a certain area of the complex plane delimited by straight lines. After applying a transformation involving inversion this area is mapped to an area delimited by circles. We provide a formalisation of this rather geometric proof in Ssreflect, an extension of the proof assistant Coq, that supports a variety of algebraic tools. They allow us to formalise the proof from an algebraic point of view.


Formalisation Coq Three circles Bernstein coefficients Normal polynomial Real root isolation 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.INRIA Sophia AntipolisSophia Antipolis CedexFrance

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