Array Computing and Curve Plotting

Abstract

Lists are introduced in Chapter 2 to store “tabular data” in a convenient way. An array is an object that is very similar to a list, but less flexible and computationally much more efficient. When using the computer to perform mathematical calculations, we often end up with a huge amount of numbers and associated arithmetic operations. Storing numbers in lists may in such contexts lead to slow programs, while arrays can make the programs run much faster. This may not be very important for the mathematical problems in this book, since most of the programs usually finish execution within a few seconds. Nevertheless, in more advanced applications of mathematics, especially the applications met in industry and science, computer programs may run for weeks and months. Any clever idea that reduces the execution time to days or hours is therefore paramount¹.

Many may argue that programmers of mathematical software have traditionally paid too much attention to efficiency and smart program constructs. The resulting software often becomes very hard to maintain and extend. In this book we advocate a focus on clear, well-designed, and easy-to-understand programs that work correctly. Optimization for speed should always come as a second step in program development.