Mathematica Cookbook

Chapter 4. Patterns and Rule-Based Programming

You are an obsession I cannot sleep I am your possession Unopened at your feet There’s no balance No equality Be still I will not accept defeat

I will have you Yes, I will have you I will find a way and I will have you Like a butterfly A wild butterly I will collect you and capture you

—Animation, “Obsession”

4.0 Introduction

In Chapter 2, I argue that the functional style of programming is the preferred way to solve problems in Mathematica. Although functions form much of the brawn, pattern matching provides the brains. In fact, functions and patterns should be thought of as partners rather than competitors. By mastering both functional programming and pattern-based programming, you will be able to use Mathematica to its fullest potential. In fact, once you get the hang of pattern-based solutions they may become a bit of an obsession.

If you have done any programming that involves text manipulation, you have no doubt been exposed to regular expressions, a concise syntax for describing patterns in text and manipulating text. Mathematica’s pattern syntax generalizes regular expressions to the domain of symbolic processing, which allows you to manipulate arbitrary symbolic structures. Patterns and rules are at the foundation of Mathematica’s symbolic processing capabilities. Symbolic integration, differentiation, equation solving, and simplification are all driven by the pattern primitives explained in this chapter.

In the context of Mathematica, ...