Computer algebra applied to itself

Abstract

This paper explains how computer algebra (Reduce) was used to analyse the expressions resulting from the complexity analysis of a family of algorithms for the isolation of real roots of polynomials. The expressions depend on sufficiently many parameters, and are sufficiently complex, that manual analysis would have been almost impossible. In addition, by analysing constant factors as well as the 0 form of the expressions, we obtain more information about the relative costs of algorithms with the same 0 complexity.