TABLE OF CONTENTS This chapter is concerned with the manipulation of algebraic expressions that contain exponential or trigonometric functions. In Section 7.1 we describe expansion algorithms that expand these functions with respect to their arguments. These algorithms obtain the transformations
In Section 7.2 we describe contraction algorithms that invert the transformations in (7.1) and (7.2). In addition, we describe a simplification algorithm that can verify a large class of trigonometric identities.
In this section we describe algorithms that expand the exponential and trigonometric functions that appear in an expression.
Let u, v, and w be algebraic expressions. The exponential function satisfies the following properties [1]:
The operation that applies these transformations in a left to right manner is called exponential expansion, and the operation that applies the transformations in a right to left manner is called exponential contraction [2]. In this section we describe procedures for exponential expansion. Procedures for exponential contraction are described in Section 7.2.
The goal of exponential expansion is described in the next definition.
Definition 7.1. An algebraic expression u is in exponential-expanded form if the argument of each exponential function in u
is not a sum;
is not a product with an operand that is an integer.
Although Equation (7.4) provides a way to remove any operand of a product from the argument of an exponential function, it doesn t specify which operand should be removed. To eliminate this ambiguity, we only remove an integer...
