Programming in Mathematics

Programming in Mathematics

by Roman E. Maeder

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ISBN-10: 0201510022

ISBN-13: 9780201510027

Pub. Date: 12/01/1989

Publisher: Addison-Wesley

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Table of Contents

1. Introduction.
From Calculations to Programs.
Basic Ingredients of a Package.
A Second Function in the Package.
Defaults for Positional Arguments.
Parameter Type Checking.

2. Packages.
Packages that Use Other Packages.
Protection of Symbols in a Package.
Package Framework and Documentation.
Loading Packages.
Large Projects.

3. Defaults and Options.
Default Values.
Options for Your Functions.
Setting Options of Several Commands.

4. Functional and Procedural Programming.
Procedures and Local Variables.
Structured Iteration.
Iterated Function Application.
Map and Apply.
Application: The Platonic Solids.
Operations on Lists and Matrices.

5. Evaluation.
Evaluation of the Body of a Rule.
Pure Functions.
Nonstandard Evaluation.
Nonlocal Flow of Control.
Advanced Topic: Scopes of Names.

6. Transformation Rules.
Simplification Rules and Normal Forms.
Application: Trigonometric Simplifications.
Globally Defined Rules.
Pattern Matching for Rules.
Traversing Expressions.

7. Numerical Computations.
Numerical Evaluation.
Numeric Quantities.
Application: Differential Equations.

8. Interaction with Built-In Rules.
Modifying the Main Evaluation Loop.
User-Defined Rules Take Precedence.
Modifying System Function.
Advanced Topic: A New Mathematical Function.

9. Input and Output.
Input and Output Formatting.
Input from Files and Programs.
Running Mathematica Unattended.
Session Logging.
Advanced Topic: Typesetting Mathematics.

10. Graphics Programming.
Graphics Packages.
Animated Graphics.
The Chapter Pictures.

11. Notebooks.
Packages and Notebooks.
The Structure of Notebooks.
Frontend Programming.

12. Application: Iterated Function Systems.
Affine Maps.
Iterated Function Systems.
Examples of Invariant Sets.
Documentation: Help Notebooks and Manuals.

Appendix A. Exercises.
Programming Exercises.

Appendix B. Bibliography.
Background Information and Further Reading.

Subjects and Names.

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