By Richard J. Gaylord
An advent to Programming with Mathematica® is designed to introduce the Mathematica programming language to a large viewers. because the final variation of this booklet used to be released, major adjustments have happened in Mathematica and its use all over the world. protecting speed with those alterations, this considerably higher, up to date model contains new and revised chapters on numerics, procedural, rule-based, and front-end programming, and offers major insurance to the most recent beneficial properties as much as, and together with, Mathematica 5.1 Mathematica notebooks, on hand from www.cambridge.org/0521846781, comprise examples, courses, and recommendations to workouts within the ebook. also, fabric to complement later types of the software program might be made on hand. this is often the perfect textual content for all medical scholars, researchers, and programmers wishing to deepen their realizing of Mathematica, or perhaps these willing to software utilizing an interactive language that includes programming paradigms from all significant programming languages: procedural, sensible, recursive, rule-based, and object-oriented.
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Extra resources for An Introduction to Programming with Mathematica
Sample text
But oftentimes, when you set up definitions for functions, those functions may depend upon the values of previously defined functions or constants. In such instances it us useful to delay the assignment until the function is actually used in a computation. This is the basic difference between immediate and delayed assignments. An immediate assignment is written Set[lhs,rhs] or, more commonly: lhs = rhs where lhs is an abbreviation for “left-hand side” and rhs abbreviates “right-hand side”. As an example, consider defining rand1 to be an immediate assignment that generates a uniformly distributed random number between 0 and 1.
1 In[4]:= f x_ 1 Out[4]= x 1 1 x The expression f[x_] on the left side of this assignment is a pattern. It indicates the class of expressions for which this definition should be used. We will have much more to say about patterns and pattern matching in Mathematica in Chapter 6, but, for now, it is enough to say that the pattern f[x_] matches f[any expression]. You can evaluate f at different values by replacing x with the value you wish to use. These values can be numeric, exact, or symbolic. 909091 f 1 1 2 f 2 1 1 2 2 The Mathematica language 39 We clear the symbols that are no longer needed.
The built-in functions are designed to usually warn you of such errors in input. In the first example below, we have supplied the Log function with an incorrect number of arguments (it expects one or two arguments only). In the second example, FactorInteger operates on integers only and so the real number argument causes the error condition. In[38]:= Log 2, 16, 3 Log::argt : Log called with 3 arguments; 1 or 2 arguments are expected. 5 is not an exact number. 5 Getting help Mathematica contains a vast array of documentation that you can access in a variety of ways.