Abstract:
In this paper, we will give a leisurely introduction to the theory of Grobner bases.First we will see how to determine whether a polynomial f is contained in an idealand how an answer to this problem leads to a method to determine whether two ideals are equal. We will use Euclidian Algorithem for solving this problems. After that will be introduced what we mean by the leading term of a polynomial in nvariables. So we will explain Grobner bases notion and will present the algorithem due to Bruno Buchberger wich transform the abstract notion of a Grobner basis in a fondamental tool in computational algebra. And in the end we will give some applications of Grobner bases.
