Arithmetic of Polynomials, Rational Functions, and Power Series

Abstract

In Chapter 2 we introduced the basic algebraic domains which are of interest to computer algebra. This was followed by the representation problem, that is, the problem of how elements of these algebras are to be represented in a computer environment. Having described the types of objects along with the various representation issues, there follows the problem of implementing the various algebraic operations that define the algebras. In this chapter we describe the arithmetic operations of addition, subtraction, multiplication, and division for these domains. In particular, we describe these fundamental operations in the ring of integers modulo n, the ring of formal power series over a field, and the ring of polynomials over an integral domain along with their quotient fields. The latter includes the domain of multiprecision integers and rational numbers.