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Axiomatic Mathematics meets Object Oriented Programming

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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.

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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

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

Axiomatic definitions are implemented as abstract methods.

Ring

Example:

Rings, Polynomial Rings, Integers, Rational Functions, Algebraic Extensions, Cyclotomic Fields, Universal Rings, etc.

groups, metric spaces, topological spaces, group rings, etc.

But it can be applied to any mathematical structure, such as:

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)
Marc Conrad

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

Luton

Oxford

London

Contact