FRAC: A Maple Package for Computing in the Rational Function Field K(X)

Abstract

In this paper we present the programs package FRAC (= Funciones RACionales) which is designed for performing computations in the rational function field. The main objects in FRAC are rational functions over the field of rational numbers, but extensions to other computable fields can be done in a “natural” way. The key tool is using functional decomposition algorithms. We motivate the interest to work with rational function decomposition by presenting applications to computer science, engineering (CAD), pure mathematics or robotics. We also present some simple examples in order to illustrate the use of FRAC. Finally, we include the synopsis of the main procedures of FRAC.