Gröbner bases in Geometry and Robotics
We will present a computational method in Commutative Algebra, together with its applications to some interesting problems in Geometry and Robotics, which require no more than the basic operations with multivariate polynomials. According to the theory of Gröbner basis, one can replace any system of n polynomial equations in m variables, by an equivalent system where variables can be 'eliminated' in succession, thereby greatly simplifying its resolution. In fact, this method generalizes the Gaussian elimination method for linear systems of equations. Some problems in Robotics and Systems Theory, as well as in Algebraic Geometry, require the consideration of systems of polynomial equations. Therefore, the algorithms to compute Gröbner bases, implemented nowadays in almost every symbolic manipulation computer system, can be especially useful.
