The Axiom computer algebra system applied to computational category theory
(joint work with W. Dreckmann(Bangor and Stockholm))
Date: July 18th (Thursday)
Time: 16:25-16:45
Abstract
The Axiom language is based on what are called: (Axiom) categories, domains,
packages, objects.
An `Axiom category' consists essentially of a signature. The representation of objects,
implementation of operations, and expression as output form, is carried out in the domain
constructors. The advantages of the Axiom language and system are discussed, and
illustrated in terms of the code for directed graphs, free categories, and the category of finite
sets. It is argued that this type of system allows for the development of code for the
interaction of examples and abstract algebraic systems, and code which is relatively easily
modified, and sufficiently general to cope with new examples. That is, the code
approximates more than is usual to the standard ways of writing mathematics.
