Mathematica programming: an advanced introduction Leonid Shifrin Copyright © Leonid Shifrin, 2008 The application of a rule can be controlled by the function Condition (/ ).MathematicaÒ programming: an advanced introduction Leonid The point here is that the second rule never gets applied successfully since the b in the list is removed before the second rule “gets a chance to look at it.” Finally, we mention conditional statements. The final application of the list of rules finds no matches and hence the evaluation terminates, returning yes. The next time the rules are applied, neither the first nor the second rule find a match and so the third rule is applied and returns yes. For example, consider the function defined by applying the following pair of rules: In:=ĭelta:=. Sometimes we can use this fact to our advantage by placing a more general rule after a more specific one. When using Replace or ReplaceAll (/.), the order that the rules appear in the list is important, since each rule is tried in turn beginning with the first.

Although we often talk about a set of rules, Mathematica stores rules in lists.

If the rhs contains expressions that depend on values in the lhs and that may change from case to case, we must use :>. Hence, for simple re-arrangements we can use ->. First, what is the difference between Rule (->) and RuleDelayed (:>)? The statement lhs -> rhs causes Mathematica to evaluate rhs immediately, while lhs :> rhs evaluates rhs only when the rule is applied. We begin by discussing some important generalities concerning rules in Mathematica. The idea is to demonstrate the power and flexibility of this style of programming. In this work, we present three more examples of rule-based programs: an implementation of a Turing machine, a function to solve tri-diagonal systems of linear equations by Gaussian elimination, and an implementation of a finite group from a presentation. Selig In the first edition of Stephen Wolfram’s Mathematica book is an example of a rule-based program that implements the bubble sort algorithm. The diversity of the applications demonstrates the power and flexibility of this approach to programming. Some Rule Based Programming Examples Three examples are given of Mathematica programs that use replacement rules rather than procedural constructs.

Mathematica programming an advanced introduction