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 Copyright © Maplesoft, a division of Waterloo Maple Inc. 2011 Maple Programming Guide by 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, and S. M. Vorkoetter Copyright Maplesoft, Maple, MapleNet, MaplePrimes, Maplet, Maple T.A., and OpenMaple are all trademarks of Waterloo Maple Inc. © Maplesoft, a division of Waterloo Maple Inc. 1996-2011. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transcribed, in any form or by any means — electronic, mechanical, photocopying, recording, or otherwise. Information in this document is subject to change without notice and does not represent a commitment on the part of the vendor. 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Printed in Canada ISBN 978-1-926902-08-1 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 Defining a Simple Procedure ..................................................................... 4 Entering a Procedure Definition ................................................................. 4 Adding Comments to a Procedure .............................................................. 7 Calling a Procedure ................................................................................. 8 Maple Library Commands, Built-In Commands, and User-Defined Proced- ures ....................................................................................................... 8 Full Evaluation and Last Name Evaluation .................................................. 9 Viewing Procedure Definitions 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 iv • Contents 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 Simplification 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 ................................................................................