Algebraic structures as typed objects

Abstract

Following the research direction of strongly typed, generic, object oriented computer algebra software, we examine the modeling of algebraic structures as typed objects in this paper. We discuss the design and implementation of algebraic and transcendental extension fields together with the modeling of real algebraic and complex algebraic extension fields. We will show that the modeling of the relation between algebraic and real algebraic extension fields using the delegation design concept has advantages over the modeling as sub-types using sub-class implementation. We further present a summary of design problems, which we have encountered so far with our implementation in Java and present possible solutions in Scala. © 2011 Springer-Verlag.