Maple_programmingGuide

maple

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这是一本相当好的Maple编程书，从介绍最新版本的maple15基本功能到编程，该书介绍详细且画面清晰，是一本很难得的maple教材！

Maple Programming Guide

L. Bernardin

P. Chin

P. DeMarco

K. O. Geddes

D. E. G. Hare

K. M. Heal

G. Labahn

J. P. May

J. McCarron

M. B. Monagan

D. Ohashi

S. M. Vorkoetter

2011

Contents

Preface ....................................................................................................... xxi

1 Introduction to Programming in Maple .............................................................. 1

1.1 In This Chapter ...................................................................................... 1

1.2 The Maple Software ................................................................................ 1

The User Interface .................................................................................. 1

The Computation Engine .......................................................................... 1

1.3 Maple Statements ................................................................................... 2

Getting Help .......................................................................................... 2

Displaying a Text String ........................................................................... 2

Performing an Arithmetic Operation ........................................................... 3

Assigning to a Name ............................................................................... 3

Using Maple Library Commands .............................................................. 3

1.4 Procedures ............................................................................................ 4

Dening a Simple Procedure ..................................................................... 4

Entering a Procedure Denition ................................................................. 4

Adding Comments to a Procedure .............................................................. 7

Calling a Procedure ................................................................................. 8

Maple Library Commands, Built-In Commands, and User-Dened Proced-

ures ....................................................................................................... 8

Full Evaluation and Last Name Evaluation .................................................. 9

Viewing Procedure Denitions and Maple Library Code ............................... 10

1.5 Interrupting Computations and Clearing the Internal Memory ........................ 11

Interrupting a Maple Computation ............................................................ 11

Clearing the Maple Internal Memory ........................................................ 12

1.6 Avoiding Common Problems ................................................................... 12

Unexpected End of Statement .................................................................. 12

Missing Operator .................................................................................. 13

Invalid, Wrong Number or Type of Arguments ........................................... 14

Unbalanced Parentheses ......................................................................... 14

Assignment Versus Equality .................................................................... 14

1.7 Exercises ............................................................................................. 16

2 Maple Language Elements ............................................................................ 17

2.1 In This Chapter ..................................................................................... 17

2.2 Character Set ....................................................................................... 17

2.3 Tokens ................................................................................................ 18

Reserved Words .................................................................................... 18

Programming-Language Operators ........................................................... 19

Names ................................................................................................ 22

2.4 Natural Integers .................................................................................... 23

2.5 Strings ................................................................................................ 24

Length of a String ................................................................................. 24

iii

Substrings ............................................................................................ 24

Searching a String ................................................................................. 25

String Concatenation ............................................................................. 25

Mutability of Strings .............................................................................. 26

Special Characters in Strings ................................................................... 27

Parsing Strings ..................................................................................... 27

Converting Expressions to Strings ............................................................ 28

2.6 Using Special Characters ........................................................................ 29

Token Separators .................................................................................. 29

Blank Spaces, New Lines, Comments, and Continuation ............................... 29

Punctuation Marks ................................................................................ 30

Escape Characters ................................................................................. 33

2.7 Types and Operands .............................................................................. 34

DAGs ................................................................................................. 34

Maple Types ........................................................................................ 35

Operands and op ................................................................................... 36

2.8 Avoiding Common Problems ................................................................... 40

Attempting to Assign to a Protected Name ................................................. 40

Invalid Left-Hand Assignment ................................................................. 41

Incorrect Syntax in Parse ........................................................................ 41

White Space Characters within a Token ..................................................... 41

Incorrect Use of Double and Single Quotes ................................................ 41

Avoid Using Maple Keywords as Names ................................................... 42

2.9 Exercises ............................................................................................. 43

3 Maple Expressions ....................................................................................... 45

3.1 In This Chapter ..................................................................................... 45

3.2 Introduction ......................................................................................... 45

Expressions and Statements .................................................................... 45

Automatic Simplication and Evaluation ................................................... 45

Syntax and Constructors ........................................................................ 45

3.3 Names ................................................................................................ 47

Creating Names: Lexical Conventions ....................................................... 48

3.4 Unevaluated Expressions ........................................................................ 52

Protecting Names and Options ................................................................. 53

Generic Expressions .............................................................................. 54

Pass by Reference ................................................................................. 54

Displaying the Original Command ............................................................ 55

Unassigning Names ............................................................................... 55

Evaluation and Automatic Simplication ................................................... 56

Example: Dening a Procedure that Is Returned Unevaluated ........................ 57

3.5 Numbers ............................................................................................. 59

Integers ............................................................................................... 59

Fractions ............................................................................................. 60

iv • Contents

Floats .................................................................................................. 61

Complex Numbers ................................................................................ 65

3.6 Indexed Expressions .............................................................................. 69

3.7 Member Selection ................................................................................. 74

3.8 Functions ............................................................................................ 75

Calls to Procedures ................................................................................ 77

3.9 Arithmetic Expressions .......................................................................... 77

Arithmetic Operators ............................................................................. 77

Noncommutative Multiplication ............................................................... 90

Factorials ............................................................................................. 92

Forming Sums and Products .................................................................... 93

3.10 Boolean and Relational Expressions ........................................................ 94

Boolean Constants ................................................................................. 94

Boolean Operators ................................................................................. 94

Relational Operators .............................................................................. 98

Efcient Boolean Iteration .................................................................... 102

3.11 Expressions for Data Structures ............................................................ 103

Sequences .......................................................................................... 103

Lists .................................................................................................. 105

Sets .................................................................................................. 107

Tables ............................................................................................... 107

Rectangular Tables .............................................................................. 108

3.12 Set-Theoretic Expressions ................................................................... 109

Membership ....................................................................................... 110

Set Inclusion ....................................................................................... 110

Other Binary Operators for Sets ............................................................. 111

3.13 Other Expressions .............................................................................. 113

Functional Operators ............................................................................ 113

Composition ....................................................................................... 114

Neutral Operators ................................................................................ 116

Ranges .............................................................................................. 116

The Concatenation Operator .................................................................. 119

The Double Colon Operator ................................................................... 121

Series ................................................................................................ 122

3.14 Attributes ......................................................................................... 124

3.15 Using Expressions ............................................................................. 126

Evaluating and Simplifying Expressions .................................................. 126

Substituting Subexpressions .................................................................. 127

Structured Types ................................................................................. 130

3.16 Exercises ......................................................................................... 134

4 Basic Data Structures ................................................................................. 135

4.1 In This Chapter ................................................................................... 135

4.2 Introduction ....................................................................................... 135

Contents • v

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