Chapter 12 - Numbers

Abstract

Publisher Summary Mathematica has a richer assortment of numbers than is usually found in computer applications. One can use arbitrarily large integers, calculate with exact rational numbers, and calculate with real numbers containing as many digits as one wants. Mathematica has four types of numbers: integers such as 38254, rationals such as 41/7, reals such as 58.723, and complexes such as 9.45 + 3i. Variable-precision arithmetic is what arithmetic should be: The precision of the result is what can be justified from the input and calculations. Only significant digits are then included in the result. The precision of such numbers varies—thus the name variable-precision arithmetic. This arithmetic is implemented in the software of Mathematica. Variable-precision arithmetic has two remarkable properties. First, all digits returned by Mathematica are correct if this arithmetic is used. Second, one can ask for the result to whatever precision is wanted. Advantages of variable-precision arithmetic include arbitrary precision in the calculations; no round-off errors are introduced by the arithmetic itself; and results contain only correct digits.