ABSTRACT
The idea of using Grobner bases for solving equations which arise from a given polynomial ideal is relatively new. Grobner bases have been introduced by B.Buchberger in his dissertation in 1965, but only about ten years ago has the computer algebra community become aware of them and packages for computing and using Grobner bases have only recently been added to existing computer algebra systems. The problems, however, which can be attacked via Grobner bases have a long history. Grobner bases are useful in computer algebra systems at least in two different ways. First, they allow to find solutions to a number of algebraic problems which are important in their own right. Secondly, Grobner bases can be used to simplify complicated partial results with respect to polynomial side relations. Simplification is one of the main problems in computer algebra.
