Symbolic Computation Group

Connected components of real algebraic sets are semi-algebraic sets, i.e. they are described by a boolean formula whose atoms are polynomial constraints with real coefficients. Computing such descriptions finds topical applications in optical system design and robotics.

In this talk, I will describe a new algorithm for computing such semi-algebraic descriptions for real algebraic curves. Notably, its complexity is significantly smaller than the best known one for computing a graph which is isotopic to the real space curve under study (by a factor close to $\delta^2$ where $\delta$ is the degree of the curve).

This is joint work with Elisabetta Rocchi.