Download An Introduction to Programming with Mathematica by Richard J. Gaylord PDF

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 publication was once released, major adjustments have happened in Mathematica and its use around the world. holding 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 insurance to the most recent good points as much as, and together with, Mathematica 5.1 Mathematica notebooks, on hand from, comprise examples, courses, and ideas to routines within the e-book. also, fabric to complement later models of the software program might be made to be had. this is often definitely the right textual content for all medical scholars, researchers, and programmers wishing to deepen their realizing of Mathematica, or maybe these willing to software utilizing an interactive language that comprises programming paradigms from all significant programming languages: procedural, sensible, recursive, rule-based, and object-oriented.

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In mathematics, this is a b c. In Mathematica this could be known as associativity and is written as a b c indicated by saying that the two expressions Plus[a, Plus[b, c]] and Plus[ Plus[a, b], c] are equivalent to the flattened form Plus[a, b, c]. When Mathematica knows that a function has the attribute Flat, it writes it in flattened form. In[2]:= Out[2]= Plus Plus a, b , c a b c The Orderless attribute indicates that the function is commutative; that is, a b b a. This allows Mathematica to write such an expression in an order that is useful for computation.

43 2 The Mathematica language Functions with multiple definitions When you make an assignment, the symbol associated with the evaluation rule is called an assignment tag. Assignment tags are used to specify the structure of expressions. So, for example, the expression {a,b,c} is represented internally by List[a,b,c]. Its assignment tag is List. List does not really do anything except serve as a wrapper to specify the structure of this expression. Similarly, the expression 1+2 is represented internally by Plus[1,2]; its assignment tag is Plus.

In[10]:= rand2 : Random Notice that the delayed assignment does not return a value when the assignment is made. In fact, the right-hand side will not be evaluated until the function rand2 is called. 40 An Introduction to Programming with Mathematica Let us call the function rand1 five times. 668693. Each subsequent call to rand1 returns that value. In[12]:= ? 668693 On the other hand, creating a table of values using rand2 produces a very different result. 600252 Each of the five times that rand2 is called in the Table, Mathematica looks up the definition of rand2 (which does not have a numeric value), and sees that it should evaluate Random[].

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