University of Tasmania
A main concern of elementary algebra is the interplay between algorithms
and their associated functions. For example, the identity
While the theory is applicable to arbitrary (many-sorted) universal algebras, our presentation here focusses on real piecewise-defined polynomials, and is illustrated by simple algebraic proofs of theorems such as ||x|| = |x| and the triangle inequality. A prototype system has been implemented (in Mathematica), which supports both the evaluation of piecewise-defined algebraic functions and automatic reasoning about the properties of such functions. The trace of a session with this package is included.
 M. Bulmer, D. Fearnley-Sander and T. Stokes,
`Towards a Calculus of Algorithms', Bull. Austral. Math. Soc.,
50 (1994), pp. 81--89.
 H. Ehrig and B. Mahr, Fundamentals of algebraic specification, EATCS monographs on theoretical computer science, v. 6 (Springer-Verlag, Berlin, 1985).
 H. Lausch and W. Nobauer, Algebra of polynomials, North-Holland Mathematical Library 5 (North-Holland, Amsterdam, 1973).
 A.G. Pinus, `Boolean Constructions in Universal Algebra', Russ. Math. Surv. 47, 4 (1992), 157--198.
Key Words: algebraic computation, Boolean affine combination, Boolean power, piecewise polynomial, Mathematica.