Factored rational expressions in ALTRAN

Abstract

In this paper we present detailed algorithms for the basic arithmetic operations on symbolic rational expressions represented by formal quotients of factored polynomials. These algorithms are currently implemented in the ALTRAN system for symbolic algebra but the descriptions given in this paper are system independent.First we describe the representation and examine the need for options to permit control over the amount of effort expended in the search for factors or in canonicalizing results. We then present algorithms in the form of programs for equality-test, exponentiation, multiplication, and addition, and mention the modifications required for division and subtraction.We conclude by presenting the results of several benchmark tests comparing the performance of these algorithms with others previously used.