On solving systems of algebraic equations via ideal bases and elimination theory

The determination of solutions of a system of algebraic equations is still a problem for which an efficient solution does not exist. In the last few years several authors have suggested new or refined methods, but none of them seems to be satisfactory. In this paper we are mainly concerned with exploring the use of Buchberger's algorithm for finding Groebner ideal bases [2] and combine/compare it with the more familiar methods of polynomial remainder sequences (pseudo-division) and of variable elimination (resultants) [4].