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Essential Maple 7: An Introduction for Scientific Programmers Robert M. Corless Springer Essential Maple 7 Springer NewYork Berlin Heidelberg Barcelona HongKong London Milan Paris Singapore Tokyo Robert M. Corless Essential Maple 7 An Introduction for Scientific Programmers With76Illustrations 1 Springer RobertM.Corless DepartmentofAppliedMathematics UniversityofWesternOntario London,OntarioN6A5B7 Canada [email protected] MathematicsSubjectClassification(2000):68-04 LibraryofCongressCataloging-in-PublicationData Corless,RobertM. EssentialMaple7:anintroductionforscientificprogrammers/RobertM.Corless. p. cm. Includesbibliographicalreferencesandindex. ISBN0-387-95352-3(alk.paper) 1. Maple(Computerfile) 2. Mathematics—Dataprocessing. I. Title. QA76.95.C6782001 (cid:1) 510.2855369—dc21 2001048432 Printedonacid-freepaper. (cid:2)c 2002Springer-VerlagNewYork,Inc. Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher (Springer-VerlagNewYork,Inc.,175FifthAvenue,NewYork,NY10010,USA),exceptforbriefexcerptsinconnectionwith reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch, isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights. ProductionmanagedbyMichaelKoy;manufacturingsupervisedbyJacquiAshri. TypesetbyIntegreTechnicalPublishingCompany,Inc.,Albuquerque,NM. PrintedandboundbyEdwardsBrothers,Inc.,AnnArbor,MI. PrintedintheUnitedStatesofAmerica. 9 8 7 6 5 4 3 2 1 ISBN0-387-95352-3 SPIN10850813 Springer-Verlag NewYork Berlin Heidelberg AmemberofBertelsmannSpringerScience+BusinessMediaGmbH For my parents: JohnD. Corlessand MarionL. Corless and M.AlyHassan and Galima Hassan This page intentionally left blank What’s in This Book ThisbookcontainsanacceleratedintroductiontoMaple,acomputeralgebralan- guage.Itisintendedforscientificprogrammerswhohaveexperiencewithother computer languages such as C, FORTRAN, or Pascal. If you want a longer and moredetaileddescriptionofhowtoprograminMaple,see[44]. Themathematicalprerequisitesarecalculus,linearalgebra,andsomediffer- entialequations.Acourseinnumericalanalysiswillalsohelp.Anyextramathe- maticsneededwillbedevelopedinthebook. ThisbookwasoriginallypreparedusinganearlierversionofMaple,buthas been revised for Maple Release 7, with an eye towards changes for the next re- leaseafterthat.Maplecontinuestobeanevolvingsystem.Newfeatureswillbe describedinthedocumentationforupdates(?updatesinMaple),andanynec- essaryupdatesofthetextofthisbookwillbemadeavailableovertheWeb.See mywebpagehttp://www.apmaths.uwo.ca/(cid:1)rcorlessforapointer. Indeed,onereasonthattherewassomuchtimebetweenthefirstandsecond editionsof thisbookis preciselythat Maple hasbeen evolvingso rapidlyin the last few years, too rapidly for me to revise this book (much less complete my others) while coping with my other duties. Maple is now a substantially better productthanitwas,withimportantimprovementstotheprogramminglanguage itself(particularly,nestedlexicalscopesandmodules)andtothelibraryof“black boxes” (particularly LinearAlgebra). This book takes complete account of these improvements: All the programs and examples and exercises in this book have been revised, many quite substantially. The former Chapter 4, which was asubject-orientedkeywordsummaryofMaple,hasbeen supplantedcompletely by the on-line help system, and therefore cut from the book. In spite of cutting that chapter, the total number of pages in the book has increased for the second edition, because much new material has been added, including an appendix on complexvariablesinacomputeralgebracontext. viii WHAT’SINTHISBOOK In spite of the additions, this book does not provide complete coverage of Maple. For example, I don’t talk about so-called “smart” plots, or about the fa- cilities for exact solution of partial differential equations. Without doubt, some readerswould find it useful for me to write about some of these omitted topics. Ontheotherhand,alsowithoutdoubt,Ihaveincludedsometopicsthatareonly neededbysomereaders,notall.Thetopicselectionisacompromise,andIhope thatyoudon’tmindthoseselectionsIhavemadethatdon’tfityourneeds.Please sendmeyoursuggestionsfortopicstoincludeinthenextedition,orintheelec- tronicupdates. Thisbookdoesnotrequireanyparticularhardware.ThesystemsIhaveused in developing the book are machines running Windows 98 and Windows NT, Linux machines, and X-windowssystems. There should be no adjustmentsnec- essaryforreadersequippedwithMacintoshesorotherhardware. How to Read This Book ThesuggestedwaytoreadthisbookistoreadSections1.1–1.3atasitting,while youhave Maplerunninginfrontofyousoyoucantrythingsout.Read therest ofthebookatyourleisure,andinanyorderyoulike. There are many small programs scattered throughout this book, and I hope thatyoumayfindthemusefulinthemselves,andasguidesforwritingyourown. The exercises are intendedto give you practice in what hasjust been shown andtodeveloptheideasfurther.Theyvaryindifficultyfromtrivialtoquitedif- ficult. They have been used as assignments in an introductory graduate course in applied computer algebra here at the University of Western Ontario. It is not necessarytodothemtobenefitfromthisbook,butitisprobablymorefunthan justreading.Iplan,withthehelpofsomeofmystudents,toprovideasolutions manual;seemywebpagehttp://www.apmaths.uwo.ca/(cid:1)rcorlessfordetails. Acknowledgements The most significant help I received for this book was from my wife, Sumaya. Byhardworkinawidevarietyofcapacitiesshehasmadewritingthisbookboth possibleandverypleasant.Shedeservesmuchmorecreditthanshegetsfromthis onelittleparagraph.Thisremainstrueforthesecondedition. Intheacknowledgmentsforthefirsteditionofthisbook,Iwrote: MydaughterShamila,ontheotherhand,hasn’treallybeenhelp- fulatall—butshealwayswantstohelp,andsomehowthat’sjustas good,fromsomeonewho’sfiveyearsold. Well,she’snowalittleolder,andshestillwantstohelp;now,shedoes. Myparents(bothsets),towhomthisbookisdedicated,providedmewithan invaluablefoundationfromwhichtowork. Fortechnicalhelp,thanksgotoKeithGeddesforgettingmeinterestedincom- puter algebra with the first Maple course offered at the University of Waterloo. ThecoursebeganwithALTRANandfinishedwithMaple(thiswasbackbefore versionnumbers).Ihavesinceusedcomputeralgebrainnearlyallmywork,both researchandteaching.Theothermajorinfluenceonmycomputeralgebracareer is David Jeffrey, who taught me what it means to do research in applied mathe- maticsandhascontinuedasagoodfriendandcollaborator.Themembersofthe watmaple mailing group, past and present, from Gaston Gonnet and Michael Monaganthroughtothemostrecentstudentresearchassistant,haveparticipated inmanyextremelyinterestingdiscussionsandhavetaughtmealotaboutMaple. George Labahn gave some interesting examples of Maple plots and consulted on several aspects. George Corliss, Dave Hare, Henning Rasmussen, and Kelly Roachprovidedparticularlydetailedcriticismsofearlydraftsofthefirstedition ofthisbook. Bill Bauldryand an anonymousrevieweralso provided helpfulre- marks.NiklausMannharthelpedwithsomefinalLaTeXwork,aswellasreading overthemanuscript.