Generic Programming Techniques in Aldor

Certain problems in mathematical computing present unusual challenges in structuring software libraries. Although generics, or templates as they are sometimes called, have been in wide use now for many years, new ways to use them to improve library architecture continue to be discovered. We find mathematical software to be particularly useful in exploring these ideas because the domain is extremely rich while being well-specified. In this paper we present two techniques for using generics in mathematical computation: The first allows efficient formulation of generic algorithms for modular computations. The second allows mathematical domains to be endowed with additional algorithms after they are defined and to have these algorithms used in generic libraries.