Maeder The Mathematica® Programmer

1. Auflage 2014
ISBN: 978-1-4832-1415-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 216 Seiten, Web PDF

The Mathematica Programmer covers the fundamental programming paradigms and applications of programming languages. This book is organized into two parts encompassing 10 chapters. Part 1 begins with an overview of the programming paradigms. This part also treats abstract data types, polymorphism and message passing, object-oriented programming, and relational databases. Part 2 looks into the practical aspects of programming languages, including in lists and power series, fractal curves, and minimal surfaces. This book will prove useful to mathematicians and computer scientists.

Autoren/Hrsg.

Maeder, Roman E.

Inhaltsverzeichnis

1;Front Cover;1
2;The Mathematica Programmer;4
3;Copyright Page;5
4;Table of Contents;6
5;Foreword;10
6;Preface;12
7;About This Book;14
8;Contents of the Chapters;14
9;About the Programs;14
10;Notation and Terminology;16
11;Colophon;16
12;Part 1: Paradigms of Programming;18
12.1;Chapter One.
Introduction;20
12.1.1;1.1 Mathematical's
Programming Language;22
12.1.2;1.2 Pattern Matching and Term Rewriting;25
12.1.3;1.3 Programming Styles;27
12.2;Chapter
Two. Abstract Data Types;34
12.2.1;2.1 Data Types as a Programming Tool;36
12.2.2;2.2 The Definition of Abstract Data Types;36
12.2.3;2.3 A Practical Approach;40
12.2.4;2.4 Design Principles for Abstract Data Types;42
12.2.5;2.5 An Example: LISP in Mathematica;45
12.2.6;2.6 Built-in Functions and Data Types;48
12.2.7;2.7 An Exercise;48
12.2.8;2.8 Conclusions and Further Reading;49
12.3;Chapter Three. Polymorphism and Message Passing;52
12.3.1;3.1 Polymorphic Operations;54
12.3.2;3.2 Three Implementation Methods;55
12.3.3;3.3 Data-Driven Programming and Rules;63
12.3.4;3.4 A Better Interface for Objects;64
12.3.5;3.5 Objects with Local State;66
12.3.6;3.6 Conclusions;68
12.4;Chapter Four. Object-Oriented Programming;70
12.4.1;4.1 The Object-Oriented Paradigm;72
12.4.2;4.2 An Implementation in
Mathematica;77
12.4.3;4.3 Abstract Classes and Polymorphic Data;80
12.4.4;4.4 An Advanced Example: Collections from SMALLTALK;82
12.4.5;4.5 Conclusions and Further Reading;88
12.4.6;4,6 The Complete Code of Classes.m;89
12.5;Chapter Five. Databases;92
12.5.1;5.1 Database Design;94
12.5.2;5.2 Relational Databases;96
12.5.3;5.3 Fundamental Operations on Relations;99
12.5.4;5.4 Data Entry;104
12.5.5;5.5 Other Functions;106
12.5.6;5.6 Conclusions;107
12.5.7;5,7 The Complete Code of Databases.m;108
13;Part 2: Applications;124
13.1;Chapter Six. Computations with Infinite Structures;126
13.1.1;6.1 Infinite Sets and Infinite Lists;128
13.1.2;6.2 Streams, Like Lists;129
13.1.3;6.3 Infinity at Last;132
13.1.4;6.4 More Applications;133
13.1.5;6.5 Really Taking Off;135
13.1.6;6.6 Conclusions and Further Reading;137
13.1.7;6.7 The Complete Code of Streams.m;138
13.2;Chapter Seven. Fibonacci on the Fast Track;142
13.2.1;7.1 Fibonacci Numbers;144
13.2.2;7.2 Complexity Measures;145
13.2.3;7.3 A Closed Formula;146
13.2.4;7.4 The Matrix Method;148
13.2.5;7.5 Conclusions and Further Reading;153
13.3;Chapter Eight. Fractal Curves;156
13.3.1;8.1 Self-Similarity;158
13.3.2;8,2 A Language for Polygons;159
13.3.3;8.3 Displaying Fractals;160
13.3.4;8.4 Variations on the Theme;163
13.3.5;8.5 The Fractal Dimension;164
13.3.6;8.6 Examples;165
13.3.7;8.7 Conclusions and Further Reading;167
13.3.8;8.8 The Complete Code of FractalCurves.m;169
13.4;Chapter Nine. Minimal Surfaces;172
13.4.1;9.1 A Formula for Minimal Surfaces;174
13.4.2;9.2 A Package for Plotting Minimal Surfaces;177
13.4.3;9.3 Analytic Continuations;179
13.4.4;9.4 Complex Contortions;181
13.4.5;9.5 Bonus Pictures;182
13.4.6;9.6 Further Reading;183
13.4.7;9.7 The Complete Code of MinimalSurfaces.m;184
13.5;Chapter Ten. System Programming;188
13.5.1;10.1 Working with Symbols;190
13.5.2;10.2 Housekeeping;191
13.5.3;10.3 Applying Functions to Symbols;194
13.5.4;10.4 A Crash Test;196
13.5.5;10.5 Options;197
13.5.6;10.6 Conclusions;198
13.5.7;10.7 The Complete Code of SystemProgramming.m;199
14;Appendices;202
15;Bibliography;204
16;Additional Program Listings;206
17;Index of Programs;218
18;Index;220