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Towards a calculus of algorithms

Published online by Cambridge University Press:  17 April 2009

M. Bulmer ,
D. Fearnley-Sander  and
T. Stokes
M. Bulmer
Affiliation:
Department of MathematicsUniversity of Tasmania Hobart, Tas 7000, Australia
D. Fearnley-Sander
Affiliation:
Department of MathematicsUniversity of Tasmania Hobart, Tas 7000, Australia
T. Stokes
Affiliation:
Department of MathematicsUniversity of Tasmania Hobart, Tas 7000, Australia
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Abstract

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We develop a generalised polynomial formalism which captures the concept of an algebra of piece-wise denned polynomials. The formalism is based on the Boolean power construction of universal algebra. A generalisation of the theory of substitution homomorphisms is developed. The abstract operation of composition of generalised polynomials in one variable is denned and shown to correspond to function composition.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 81 - 89
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Lausch, H. and Nobauer, W., Algebra of polynomials, North-Holland mathematical library 5 (North-Holland, Amsterdam, 1973).CrossRefGoogle Scholar
[2]Pinus, A.G., ‘Boolean Constructions in Universal Algebra’, Russian Math. Surveys 47 (1992), 157–198.CrossRefGoogle Scholar