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[PDF] Maple 7 Programming Guide

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Maple 7

Programming Guide

M. B. Monagan K. O. Geddes K. M. Heal

G. Labahn S. M. Vorkoetter J. McCarron

P. DeMarco

c ?2001 by Waterloo Maple Inc. ii•

Waterloo Maple Inc.

57 Erb Street West

Waterloo, ON N2L 6C2

Canada

Maple and Maple V are registered trademarks of Waterloo Maple Inc. c ?2001, 2000, 1998, 1996 by Waterloo Maple Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the copyright holder, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

Contents

1 Introduction 1

1.1 Getting Started........................ 2

Locals and Globals...................... 7

Inputs, Parameters, Arguments............... 8

1.2 Basic Programming Constructs............... 11

The Assignment Statement................. 11

TheforLoop......................... 13

The Conditional Statement................. 15

ThewhileLoop ....................... 19

Modularization........................ 20

Recursive Procedures..................... 22

Exercise............................ 24

1.3 Basic Data Structures.................... 25

Exercise............................ 26

Exercise............................ 28

AMEMBERProcedure..................... 28

Exercise............................ 29

Binary Search......................... 29

Exercises........................... 30

Plotting the Roots of a Polynomial............. 31

1.4 Computing with Formulae.................. 33

The Height of a Polynomial................. 34

Exercise............................ 36

The Chebyshev Polynomials,T

n (x)............. 36

Exercise............................ 37

Integration by Parts..................... 37

Exercises........................... 39

Computing with Symbolic Parameters........... 39

Exercise............................ 42

1.5 Conclusion.......................... 42

iii iv•Contents

2 Fundamentals 45

2.1 Evaluation Rules....................... 46

Parameters.......................... 47

Local Variables........................ 50

Global Variables....................... 51

Exceptions.......................... 52

2.2 Nested Procedures...................... 54

Local Versus Global Variables................ 55

The Quick-Sort Algorithm.................. 56

Creating a Uniform Random Number Generator..... 59

2.3 Types ............................. 62

Types that Modify Evaluation Rules............ 62

Structured Types....................... 66

Type Matching........................ 68

2.4 Choosing a Data Structure: Connected Graphs...... 70

Exercises........................... 75

2.5 Remember Tables....................... 76

TherememberOption.................... 76

Adding Entries Explicitly.................. 77

Removing Entries from a Remember Table......... 78

2.6 Conclusion.......................... 79

3 Advanced Programming 81

3.1 Procedures Which Return Procedures........... 82

Creating a Newton Iteration................. 82

A Shift Operator....................... 85

3.2 When Local Variables Leave Home............. 86

Creating the Cartesian Product of a Sequence of Sets . . 89

Exercises........................... 94

3.3 Interactive Input....................... 94

Reading Strings from the Terminal............. 95

Reading Expressions from the Terminal.......... 95

Converting Strings to Expressions............. 97

3.4 Extending Maple....................... 98

Defining New Types..................... 99

Exercises........................... 100

Neutral Operators...................... 100

Exercise............................ 104

Extending Certain Commands............... 106

3.5 Conclusion.......................... 109

Contents•v

4 The Maple Language 111

4.1 Language Elements...................... 113

The Character Set...................... 113

Tokens............................. 114

Token Separators....................... 118

4.2 Escape Characters...................... 122

4.3 Statements.......................... 122

The Assignment Statement................. 123

Unassignment: Clearing a Name.............. 128

The Selection Statement................... 130

The Repetition Statement.................. 133

ThereadandsaveStatements............... 138

4.4 Expressions.......................... 139

Expression Trees: Internal Representation......... 140 The Types and Operands of Integers, Strings, Indexed

Names, and Concatenations............. 144

Fractions and Rational Numbers.............. 147

Floating-Point (Decimal) Numbers............. 148

Complex Numerical Constants............... 151

Labels............................. 153

Sequences........................... 154

Sets and Lists......................... 158

Functions........................... 160

The Arithmetic Operators.................. 165

Non-Commutative Multiplication.............. 168

The Composition Operators................. 169

The Ditto Operators..................... 170

The Factorial Operator................... 170

ThemodOperator...................... 171

The Neutral Operators.................... 172

Relations and Logical Operators.............. 173

Tables............................. 178

Series............................. 180

Ranges............................. 182

Unevaluated Expressions................... 184

Constants........................... 186

Structured Types....................... 187

4.5 Useful Looping Constructs.................. 190

Themap,select,remove, andselectremoveCommands 191

ThezipCommand...................... 194

Theseq,add, andmulCommands............. 195

vi•Contents

4.6 Substitution.......................... 197

4.7 Conclusion.......................... 200

5 Procedures 201

5.1 Procedure Definitions.................... 201

Mapping Notation...................... 202

Unnamed Procedures and Their Combinations...... 203

Procedure Simplification................... 204

5.2 Parameter Passing...................... 204

Declared Parameters..................... 206

The Sequence of Arguments................. 207

5.3 Local and Global Variables................. 208

Evaluation of Local Variables................ 210

5.4 Procedure Options and the Description Field....... 212

Options............................ 212

The Description Field.................... 214

5.5 The Value Returned by a Procedure............ 215

Assigning Values to Parameters............... 215

Explicit Returns....................... 218

Error Returns......................... 219

Trapping Exceptions..................... 221

Returning Unevaluated.................... 225

Exercise............................ 227

5.6 The Procedure Object.................... 227

Last Name Evaluation.................... 227

The Type and Operands of a Procedure.......... 228

Saving and Retrieving Procedures............. 231

5.7 Explorations......................... 232

Exercises........................... 232

5.8 Conclusion.......................... 233

6 Programming with Modules 235

About This Chapter..................... 238

6.1 Syntax and Semantics.................... 238

The Module Body...................... 239

Module Parameters...................... 240

Named Modules....................... 240

Declarations.......................... 242

Exported Local Variables.................. 244

Module Options........................ 249

Implicit Scoping Rules.................... 249

Contents•vii

Lexical Scoping Rules.................... 249

Modules and Types...................... 251

Example: A Symbolic Differentiator............ 252

6.2 Records............................ 263

6.3 Packages............................ 266

What Is a Package?..................... 266

Example: TheLinkedListPackage............. 268

Example: A Code Coverage Profiling Package....... 275

Example: The Shapes Package............... 282

6.4 TheuseStatement...................... 291

Operator Rebinding..................... 294

6.5 Modeling Objects....................... 297

Example: Priority Queues.................. 300

An Object-oriented Shapes Package............ 304

6.6 Interfaces and Implementations............... 306

Interfaces........................... 307

Example: Generic Graph Algorithms............ 312

Example: Quotient Fields.................. 318

Example: A Generic Group Implementation........ 327

6.7 Conclusion.......................... 348

7 Debugging Maple Programs 349

7.1 A Tutorial Example..................... 349

Numbering the Procedure Statements I.......... 350quotesdbs_dbs17.pdfusesText_23