Séminaire Marelle : Le théorème des trois cercles

Lundi 08/07/2013, à partir de 14h30, en salle Byron Blanc.

Oratrice : Julianna Zsido.

Titre : Le théorème des trois cercles.

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, allowing us to formalise the proof from an algebraic point of view.