Programming in Mathematica - 3rd Ed.

✍ Scribed by Roman Maeder

• Publisher: Addison-Wesley Publishing Company
• Year: 1997
• Tongue: English
• Leaves: 384
• Edition: 3
• Category: Library

✦ Synopsis

The programming examples in this book serve two purposes. First, they help explain
concepts and show how things fit together to make up complete programs. Second, they are
designed to be more than mere toy programs and should prove useful in their own right. In
developing an example we always use the same method. We start out with a few commands
or definitions that could be entered directly into Mathematica. We then extract the parts
of the computation that are the same regardless of the input and define some functions or
procedures that automate these steps. Then we apply standard techniques to these functions
to make them into a package, adding documentation and certain programming constructs
that make such a package easier to use. The goal is to write a program that would be
useful not only to its author, who knows how it works, but also to other people. Finally,
we might add a few more functions to the package or look at alternatives to what we did so
far. In Chapter 1 these steps are described in full detail. Later on, when we concentrate on
other aspects, we assume that you are familiar with these basic concepts and we shall not
mention all the steps in detail. All the programs developed in this book are either part of
the standard Mathematica distribution from Wolfram Research, or they are available free
in electronic form.
This book is no replacement for the Mathematica manual "The Mathematica Book"
[40]. I do not expect that you have read everything in the Mathematica book, but you
should have some basic experience with Mathematica before reading this book. Single
commands are usually used without detailed explanation. You can use the index in the
Mathematica book to look up a description of a command that you did not know about. We
also give references to places in the Mathematica book where you can find explanations of
concepts that are particularly relevant to a topic in this book. You should always tum to the
Mathematica book for explanations of features that are assumed known here, but that you
have not used yet. The place to look for an explanation of all variants, defaults, or options
for a particular command is the reference guide in the back of the Mathematica book. All
this information is also available in electronic form and can be accessed through the Help
Browser of Mathematica.

✦ Table of Contents

Title Page
Preface
Contents
About This Book
Chapter Overview
About the Examples
Notation and Terminology
The Programming in Mathematica Web Site
Teaching Mathematica Programming
1 Introduction
1.1 From Calculations to Programs
1.2 Basic Ingredients of a Package
1.3 A Second Function in the Package
1.4 Options
1.5 Defaults for Positional Arguments
1.6 Parameter Type Checking
2 Packages
2.1 Contexts
2.2 Packages That Use Other Packages
2.3 Protection of Symbols in a Package
2.4 Package Framework and Documentation
2.5 Loading Packages
2.6 Large Projects
3 Defaults and Options
3.1 Default Values
3.2 Options for Your Functions
3.3 Setting Options of Several Commands
4 Functional and Procedural Programming
4.1 Procedures and Local Variables
4.2 Loops
4.3 Structured Iteration
4.4 Iterated Function Application
4.5 Map and Apply
4.6 Application: The Platonic Solids
4.7 Operations on Lists and Matrices
5 Evaluation
5.1 Evaluation of the Body of a Rule
5.2 Pure Functions
5.3 Nonstandard Evaluation
5.4 Nonlocal Flow of Control
5.5 Definitions
5.6 Advanced Topic: Scopes of Names
6 Transformation Rules
6.1 Simplification Rules and Normal Forms
6.2 Application: Trigonometric Simplifications
6.3 Globally Defined Rules
6.4 Pattern Matching for Rules
6.5 Traversing Expressions
7 Numerical Computations
7.1 Numbers
7.2 Numerical Evaluation
7.3 Numeric Quantities
7.4 Application: Differential Equations
8 Interaction with Built-in Rules
8.1 Modifying the Main Evaluation Loop
8.2 User-Defined Rules Take Precedence
8.3 Modifying System Function
8.4 Advanced Topic: A New Mathematical Function
9 Input and Output
9.1 Input and Output Formatting
9.2 Input from Files and Programs
9.3 Running Mathematica Unattended
9.4 Session Logging
9.5 Advanced Topic: Typesetting Mathematics
10 Graphics Programming
10.1 Graphics Packages
10.2 Animated Graphics.
10.3 The Chapter Pictures
11 Notebooks
11.1 Packages and Notebooks
11.2 The Structure of Notebooks
11.3 Frontend Programming
12 Application: Iterated Function Systems
12.1 Affine Maps
12.2 Iterated Function Systems
12.3 Examples of Invariant Sets
12.4 Documentation: Help Notebooks and Manuals
Appendix A Exercises
A.1 Programming Exercises
A.2 Solutions
Appendix B Bibliography
B.1 Background Information and Further Reading
B.2 References
Index
Programs
Subjects and Names