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 ebook used to be released, major adjustments have happened in Mathematica and its use world wide. retaining velocity with those alterations, this considerably greater, up to date model comprises new and revised chapters on numerics, procedural, rule-based, and front-end programming, and provides major assurance to the most recent positive aspects as much as, and together with, Mathematica 5.1 Mathematica notebooks, to be had from www.cambridge.org/0521846781, include examples, courses, and recommendations to routines within the booklet. also, fabric to complement later models of the software program might be made to be had. this can be the proper textual content for all clinical scholars, researchers, and programmers wishing to deepen their realizing of Mathematica, or maybe these willing to application 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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**Example text**

For the simple examples above, the crucial difference between rewrite rules created with the SetDe layed and Set functions becomes apparent by querying the rule base for the rewrite rules associated with the symbols rand1 and rand2. In[16]:= ? 668693 A rewrite rule created using the Set function has the same left-hand side as the function that created it but the right-hand side of the rule may differ from the right-hand side of the function. This is because the right-hand side of the rule was evaluated at the moment the rule was first evaluated.

In[5]:= Out[5]= In[6]:= Out[6]= NumericQ True NumericQ False This is distinct from a related function, NumberQ, which evaluates to True whenever its argument is an explicit number (that is, has head one of Integer, Rational, Real, Complex). 2 True NumberQ False Many other predicates are available for testing if an expression is an atom, a list, a matrix, a polynomial, and much more. In[9]:= AtomQ "string" Out[9]= True In[10]:= ListQ Out[10]= In[11]:= Out[11]= In[12]:= Out[12]= In[13]:= Out[13]= a, b, c True MatrixQ 1 0 0 0 1 0 0 0 1 True 1 1 1 x x2 x3 PolynomialQ ,x False IntervalMemberQ Interval 3, 4 , True Relational and logical operators Another type of predicate that is commonly used in programming are relational operators.

A/b)[[2, 2]] 4. What is the part specification of the b in the expression a x^2 + b x + c? 2 Definitions Defining variables and functions One of the most common tasks in any programming environment is to define functions, constants, and procedures to perform various tasks. Sometimes a particular function that you need is not part of the built-in set of functions. Other times, you may need to use an expression over and over again and so it would be useful to define it once and have it available for future reference.