The importance of the continuing and growing need in the systems and control community for reliable algorithms and robust numerical software for increasingly challenging applications is well known and has already been reported elsewhere (IEEE Control Systems Magazine, Vol. 24, Issue 1). However, we have all had the experience of working on a mathematical project where an increased number of symbolic manipulations was needed. In a simple case, the required computation might have been to compute the Laplace transform or the inverse Laplace transform of a function, or to find the transfer function matrix for a given system topology where parameters are included. In a more demanding situation the required computation might have been to find the parametric family of solutions of a polynomial matrix Diophantine equation resulting from a variety of control problems such as those associated with stabilization, decoupling, model matching, tracking and regulation, or to compute the Smith McMillan form of a rational transfer function matrix in order to obtain a better insight into a number of structural properties of a system. The desire to use a computer to perform long and tedious mathematical computations such as the above led to the establishment of a new area of research whose main objective is the development: (a) of systems (software and hardware) for symbolic mathematical computations, and (b) of efficient symbolic algorithms for the solution of mathematically formulated problems. This new subject area is referred to by a variety of terms such as symbolic computations, computer algebra, algebraic algorithms to name a few. During the last four decades this subject area has accomplished important steps and it is still continuing its evolution process.