Toward a formal implementation of computer algebra

Abstract

We consider in this paper the task of synthesizing an algebraic system. Today the task is significantly simpler than in the pioneer days of symbol manipulation, mainly because of the work done by the pioneers in our area, but also because of the progress in other areas of Computer Science. There is now a considerable collection of algebraic algorithms at hand and a much better understanding of data structures and programming constructs than only a few years ago.