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 version of this booklet was once released, major adjustments have happened in Mathematica and its use world wide. retaining velocity with those adjustments, 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 newest positive aspects as much as, and together with, Mathematica 5.1 Mathematica notebooks, to be had from www.cambridge.org/0521846781, comprise examples, courses, and ideas to workouts within the e-book. also, fabric to complement later types of the software program can be made to be had. this can be the right textual content for all clinical scholars, researchers, and programmers wishing to deepen their realizing of Mathematica, or perhaps these prepared to software utilizing an interactive language that comprises programming paradigms from all significant programming languages: procedural, practical, recursive, rule-based, and object-oriented.
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Extra info for An Introduction to Programming with Mathematica
3. Create a ten-element list of random 1s and 1s. This table can be viewed as a list of the steps taken in a random walk along the x-axis, where a step can be taken in either the positive x direction (corresponding to 1) or the negative x direction (corresponding to 1) with equal likelihood. The random walk in one, two, three (and even higher) dimensions is used in science and engineering to represent phenomena that are probabilistic in nature. We will use a variety of random walk models throughout this book to illustrate specific programming points.
In:= FullForm a b Out//FullForm= Plus a, b So Part[a+b,1] is another way of asking for the first element of Plus[a,b], which is just a. In general Part[expr,n] gives the nth element of expr. 36 An Introduction to Programming with Mathematica It is worth noting that the 0th part is the Head of the expression. In:= Out= Part a b, 0 Plus As we stated above, atomic expressions have no parts. In:= Part "read my lips", 1 Part::partd : Part specification read my lips 1 is longer than depth of object.
Similarly, the expression 1+2 is represented internally by Plus[1,2]; its assignment tag is Plus. Occasionally you will encounter the Tag expression when you try to evaluate some incorrect input. In:= 1 2 4 Set::write : Tag Plus in 1 Out= 2 is Protected. More… 4 For user-defined functions, the tag basically refers to the name of the function. So, for example, the following assignment associates the rule 1 x x2 with the tag f. In:= f x_ : 1 x x2 There can be many evaluation rules associated with one tag.