Efficient and certified algorithms for solving polynomial system of equalities and inequalities

This paper is of mostly of expository nature and has to be considered as a support for the author’s lecture at JNRR’05. We mainly describe some efficient strategies for studying real roots of zero- dimensional systems (with a finite number of complex roots) as well as parametric sys-tems, with or without inequations or inequalities. As an ex-ample we give a new computational proof of the existence of a parallel robot with real roots in less than 1 sec on a PC. An application of solving parametric systems is given in the paper: the classification of -revolute-jointed manipulators based on the cuspidal behavior