TOPOLOGIE DES ($M - 2$)-COURBES RÉELLES SYMÉTRIQUES

Approximations fonctionnelles des courbes des espaces projectifs

Calcul effectif de la topologie de courbes et surfaces algébriques réelles. (On the Computation of The Topology of Real Algebraic Curves and Surfaces)

In this thesis, we got interested into the Effective Computation of the Topology of Real Algebraic Curves and Surfaces. One can distinguish three main new algorithms in the field of shape representation. Our first algorithm is a certified symbolic-numerical based on sub-resultants properties and computes the topology of a plane algebraic curve with the best known complexity. The second algorith...

Algorithmes pour l'étude des solutions réelles des systèmes polynomiaux

This presentation summarizes a set of general methods for solving systems of polynomial equations (with or without inequalities), mainly centered on the study of their real roots; The main subject is the “resolution” of systems with an arbitrary number of solutions (finite or infinite), depending or not on parameters. Since the field is vast, one constrains it by imposing it that the algorithms...

Algorithmique des courbes algébriques pour la cryptologie

In this memoir, we present various works on the theme of algorithms for algebraic curveswith a view towards cryptology. We describe algorithms for computing discrete logarithms,which is a problem whose difficulty is the key to the security of curve-based cryptosystems.A first class of algorithms contains «index-calculus»-like techniques ; a second class containsmethods relying o...

La Limite des Theories de Courbes Generiques

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