Axiomatic Mathematics meets Object Oriented Programming

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Presentation transcript:

Axiomatic Mathematics meets Object Oriented Programming

Use the GoF Mediator pattern for Implementing Abstract Mathematics. Ring * Ring Element R R[X] X:String Polynomial Integer Z

Abstract Structures are modelled as abstract classes. Abstract: An arbitrary (unspecified) ring Ring R Concrete: Ring of Integers, Polynomial Rings, … R[X] X:String Z

Axiomatic definitions are implemented as abstract methods. Ring Example: Abstract: addition negation multiplication inversion "zero" "one" check if zero Not abstract: subtraction exponentiation embedding of Z and Q Check for equality evaluation of polynomials

The mediator pattern is used in the Java com.perisic.ring package for: Rings, Polynomial Rings, Integers, Rational Functions, Algebraic Extensions, Cyclotomic Fields, Universal Rings, etc. But it can be applied to any mathematical structure, such as: groups, metric spaces, topological spaces, group rings, etc.

Further Reading The Java package com.perisic.ring is available at: http://ring.perisic.com M. Conrad, T. French, Exploring the synergies between the Object-Oriented paradigm and Mathematics: A Java led approach, to appear in Int. J. Math. Educ. Sci. Technol. M. Conrad, T. French, C. Maple, S. Pott, Mathematical Use Cases lead naturally to non-standard Inheritance Relationships – How to make them accessible in a mainstream language?, MASPEGHI 2004 (WS 12 of ECOOP)

Contact Marc Conrad Tim French Carsten Maple Luton Cambridge Oxford marc.conrad@luton.ac.uk Tim French tim.french@luton.ac.uk Carsten Maple carsten.maple@luton.ac.uk University of Luton Dept. of Computing and IT Park Square Luton LU1 3JU, UK Cambridge Oxford London Luton