Chapter 18 - Programs

Abstract

Mathematica supports many styles of programming, such as procedural, functional, rule-based, and recursive. In addition, the use of graphics primitives and directives leads us to graphics programming. Even object-oriented programming can be approached with Mathematica . Functional and rule-based programming make up the heart of programming in Mathematica . Programs built with traditional programming languages, such as Fortran and C, are called procedures, hence the term procedural programming. Mathematica has similar commands (such as for, while, and if) to those used in procedural programming, so one can program in the procedural style with Mathematica . With functional programming, one can apply functions to arguments. The functions are applied to the arguments by special powerful commands, such as Map, Apply, Nest, Fixed Point, and Fold. Functional programming is effective especially in list manipulations and iterative calculations. Rule-based programming uses rules and patterns . In addition, rule-based programming gives several rules for the same function. These rules cover several different situations or several patterns of argument. Recursive programming naturally arises by programming recursive mathematical formulas: the program calls itself with another argument. Many list manipulation tasks can also be programmed recursively.