Introduction

GRÖBNER is a library for computing Gröbner bases, based on the Computer Algebra library SACLIB and written in C language. Some of its features that

distinguish it from other Gröbner bases implementations are

• public availability of source code and
• a simple but efficient mechanism of polymorphism that makes the library applicable to a wide variety of combinations of coefficient domains, admissible term orderings, selection strategies for S-polynomials, etc. without the necessity of code duplication.

The availability of the source code is intended for those users who want to study the details of the Gröbner bases algorithm and need direct access to the code for experimenting. A basic knowledge about using SACLIB is a prerequisite in order to be able to modify the library appropriately, see [3]. Furthermore, a complete understanding of the methods used to establish polymorphism as well as a certain amount of knowledge in Gröbner basis theory is inevitable.

The concept of virtual domains as the key to polymorphic design and the its motivations are described in [5]. For an introduction to the Gröbner basis method we refer the reader to [1] and [2].

However, the library should also be a useful tool for those users who want to use GRÖBNER as a ``Black Box Gröbner Basis Solver'', without being concerned about the background in software design and algebraic matters. Still, they should be able to exploit the whole power of the library, namely its adjustability to several coefficient domains, term orderings, selection strategies, and data representations.

The present document is intended for the latter group of users, although we recommend [5] also for those users, since it might give some insight into the inner workings and the limitations of applicability of GRÖBNER.