Semialgebraic sets are a generalization of polyhedra, where instead of linear constraints we take polynomial inequalities. As the fundamental object of real algebraic geometry and capable of modeling diverse real-world phenomena, they are of interest to both pure and applied mathematicians. We'll begin with an introduction to the motivations and definitions surrounding real algebraic geometry, after which we will discuss the Tarski-Seidenberg Principle and see an illustrative application to robotics. With computer algebra!
