CALCULATION OF FUNCTIONS Using hand calculations, a hand calculator, or a com- Summary: CALCULATION OF FUNCTIONS Using hand calculations, a hand calculator, or a com- puter, what are the basic operations of which we are capable? In essence, they are addition, subtraction, multiplication, and division (and even this will usually require a truncation of the quotient at some point). In addition, we can make logical decisions, such as deciding which of the following are true for two real numbers a and b: a > b, a = b, a < b Furthermore, we can carry out only a finite number of such operations. If we limit ourselves to just addi- tion, subtraction, and multiplication, then in evaluat- ing functions f(x) we are limited to the evaluation of polynomials: p(x) = a0 + a1x + · · · anxn In this, n is the degree (provided an 6= 0) and {a0, ..., an} are the coefficients of the polynomial. Later we will discuss the efficient evaluation of polynomials; but for now, we ask how we are to evaluate other functions Collections: Computer Technologies and Information Sciences