TABLE OF CONTENTS The automatic simplification process is defined as a collection of algebraic and trigonometric simplification transformations that is applied to an expression as part of the evaluation process. In this chapter we take an in-depth look at the algebraic component of this process.
In Section 3.1 we describe the automatic simplification process in an informal way, focusing on which transformations should be included in the process and which ones are best handled by other operators. Next, we give a precise definition of an automatically simplified algebraic expression which includes an order relation that describes actions of the additive and multiplicative commutative transformations.
In Section 3.2 we describe the basic automatic simplification algorithm. Although the algorithm is based only on the rules of elementary algebra, it is quite involved. To handle a large variety of expressions, the automatic simplification process includes over 30 rules (or rule groups), some of which are recursive. The problem addressed in this section is how to organize this involved process into a coherent algorithm.
The transformation rules in automatic simplification are motivated by the field axioms (which are assumed to hold for expressions as well as for number fields) and by the transformations that are logical consequences of these axioms. We begin by examining the role of each of the axioms in the automatic simplification process.
The (right) distributive property (field axiom F-8) has the form
This transformation is applied during automatic simplification in a right to...
