The Mathematica® Programmer

The Mathematica® Programmer

1st Edition - December 8, 1993

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  • Author: Roman E. Maeder
  • eBook ISBN: 9781483214153

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Description

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.

Table of Contents


  • Foreword

    Preface

    About This Book

    Contents of the Chapters

    About the Programs

    Notation and Terminology

    Colophon

    Part 1: Paradigms of Programming

    1 Introduction

    1.1 Mathematica's Programming Language

    1.2 Pattern Matching and Term Rewriting

    1.3 Programming Styles

    2 Abstract Data Types

    2.1 Data Types as a Programming Tool

    2.2 The Definition of Abstract Data Types

    2.3 A Practical Approach

    2.4 Design Principles for Abstract Data Types

    2.5 An Example: LISP in Mathematica

    2.6 Built-in Functions and Data Types

    2.7 An Exercise

    2.8 Conclusions and Further Reading

    3 Polymorphism and Message Passing

    3.1 Polymorphic Operations

    3.2 Three Implementation Methods

    3.3 Data-Driven Programming and Rules

    3.4 A Better Interface for Objects

    3.5 Objects with Local State

    3.6 Conclusions

    4 Object-Oriented Programming

    4.1 The Object-Oriented Paradigm

    4.2 An Implementation in Mathematica

    4.3 Abstract Classes and Polymorphic

    4.4 An Advanced Example: Collections from SMALLTALK

    4.5 Conclusions and Further Reading

    4.6 The Complete Code of Classes.m

    5 Databases

    5.1 Database Design

    5.2 Relational Databases

    5.3 Fundamental Operations on Relations

    5.4 Data Entry

    5.5 Other Functions

    5.6 Conclusions

    5.7 The Complete Code of Databases.m

    Part 2: Applications

    6 Computations with Infinite Structures

    6.1 Infinite Sets and Infinite Lists

    6.2 Streams, Like Lists

    6.3 Infinity at Last

    6.4 More Applications

    6.5 Really Taking Off

    6.6 Conclusions and Further Reading

    6.7 The Complete Code of Streams.m

    7 Fibonacci on the Fast Track

    7.1 Fibonacci Numbers

    7.2 Complexity Measures

    7.3 A Closed Formula

    7.4 The Matrix Method

    7.5 Conclusions and Further Reading

    8 Fractal Curves

    8.1 Self-Similarity

    8.2 A Language for Polygons

    8.3 Displaying Fractals

    8.4 Variations on the Theme

    8.5 The Fractal Dimension

    8.6 Examples

    8.7 Conclusions and Further Reading

    8.8 The Complete Code of FractalCurves.m

    9 Minimal Surfaces

    9.1 A Formula for Minimal Surfaces

    9.2 A Package for Plotting Minimal Surfaces

    9.3 Analytic Continuations

    9.4 Complex Contortions

    9.5 Bonus Pictures

    9.6 Further Reading

    9.7 The Complete Code of MinimalSurfaces.m

    10 System Programming

    10.1 Working with Symbols

    10.2 Housekeeping

    10.3 Applying Functions to Symbols

    10.4 A Crash Test

    10.5 Options

    10.6 Conclusions

    10.7 The Complete Code of SystemProgramming.m

    Appendices

    Bibliography

    Additional Program Listings

    Index of Programs

    Index

Product details

  • No. of pages: 216
  • Language: English
  • Copyright: © Academic Press 1993
  • Published: December 8, 1993
  • Imprint: Academic Press
  • eBook ISBN: 9781483214153

About the Author

Roman E. Maeder

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