Algebraic Formula Manipulation in a Functional Language: A First Attempt

This paper represents the author's attempt to come to grips with some of the practical problems that arise out of conventional algebraic manipulation and leads to a discussion of the possibilities of generalising algebraic concepts such as commutativity and associativity to other algebraic systems. An account is given of a class instance providing manipulation and simplification of 'school' algebraic formulae. A concept of variability is introduced which controls the order in which terms and factors appear in sums and products. Rules based on the commutative, associative and distributive laws of algebra, for simplification of sums, products and a few basic operators are presented. Some discussion is given of how an advanced class system could possibly be of help in general algebraic simplification problems.