Maple V Library Reference Manual

722 Pages·1991·13.807 MB·English

by  Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton Leong, Michael B. Monagan, Stephen M. Watt (auth.)

Maple V
Library Reference Manual
Brucc W. Char Keith O. Geddes Gaston H. Gonnet
Benton 1. Leong Michael B. Monagan Stephen M. Watt
Maple V
Library Reference Manual
Springer Science+Business Media, LLC
BruceW.Char Keith O.Geddes GastonH. Gonnet
DepartmentofMathematics DepartmentofComputerScience Department Informatik
and ComputerScience UniversityofWaterloo ETH Zentrum
DrexelUniversity Waterloo, ON 8092 Zürich
Philadelphia, PA 19104 CanadaN2L3G1 Switzerland
U.S.A.
BentonLeong Michael B. Monagan Stephen M.Watt
SymbolicComputationGroup Department Informatik IBM ThomasJ.Watson
UniversityofWaterloo ETH Zentrum ResearchCenter
Waterloo, ON 8092 Zürich P.O. Box 128
CanadaN2L3G1 Switzerland Yorktown Heights, NY 10598
U.S.A.
Mapleisa registeredtrademarkofWaterlooMapleSoftware.
LibraryofCongressCataloging-in-PublicationData
MapleV Libraryreferencemanual /
BruceChar...[etal.] 1st 00.
p. cm.
Includesbibliographicalreferencesandindex.
1.Maple(Computerprogram) 1. Char, BruceW.
QA155.7E4M36 1991
51O.'285'5369dc20 91-20181
Printedon acid-freepaper.
ISBN978-0-387-94160-8 ISBN978-1-4757-2133-1 (eBook)
DOI 10.1007/978-1-4757-2133-1
©1991 by Springer Science+BusinessMediaNewYork
Originallypublished byWaterlooMaplePublishingin 1991.
Softcoverreprint ofthehardcover 1stedition 1991
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeor inpartwithoutthewrittenpermissionofthecopyright
holderexceptfor briefexcerptsin connectionwithreviewsor scholarlyanalysis.Use in connectionwithanyform ofinformation
storageandretrieval,electronicadaptation,computersoftware,or by similaror dissimilarmethodologynow knownor hereafter
developedisforbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially
identified,isnotto betakenasasignthatsuchnames,as understoodbytheTradeMarksandMerchandiseAct,mayaccordingly
beused freely by anyone.
Photocomposedcopypreparedfrom theauthors' TEXfiles.
987654321
Preface
The design and implementation of the Maple system is an on-going project of the Symbolic Com
putation Group at the University of Waterloo in Ontario, Canada. This manual corresponds with
version V (roman numeral five) of the Maple system. The on-line help subsystem can be invoked
from within a Maple session to view documentation on specific topics. In particular, the command
?updates points the user to documentation updates for each new version of Maple.
The Maple project was first conceived in the autumn of 1980, growing out of discussions on the
state of symbolic computation at the University of Waterloo. The authors wish to acknowledge
many fruitful discussions with colleagues at the University of Waterloo, particularly Morven Gen
tleman,Michael Malcolm, and FrankTompa.It wasrecognized in thesediscussions that none ofthe
locaIly-available systems for symbolic computation provided the facilities that should be expected
for symbolic computation in modern computing environments. We concluded that since the basic
design decisions for the then-current symbolic systems such as ALTRAN, CAMAL, REDUCE, and
MACSYMA were based on 1960's computing technology, it would be wise to design a new system
"from scratch". Thus we could take advantage of the software engineering technology which had
become available in recent years, as well as drawing from the lessons ofexperience.
Maple's basic features (elementary data structures, Input/output, arithmetic with numbers, and
elementary simplification) are coded in a systems programming language for efficiency. For users,
there is a high-level language with a modern syntax more suitable for describing algebraic algo
rithms. An important property of Maple is that most of the algebraic facilities in the system are
implemented using the high-level user language. The basic system,or kernel, issufficiently compact
and efficientto be practical for use in a shared environment or on personal computers that have as
little as two megabytes of main memory. Library functions are loaded into the system as required,
adding to the system such facilities as polynomial factorization, equation solving, indefinite inte
gration, and matrix manipulation functions. The modularity ofthis design allows users to consume
computer resources proportional to the algebraic facilities actually being used.
The system kernel is written in macros which can be translated by a locaIly-developed macro
processor (called Margay) into versions ofthe kernel in the C programminglanguageforvarious dif
ferent operating systems. Operating systems currently supporting a Maple implementation include
UNIX and various UNIX-like systems, 386 DOS, Macintosh Finder, DEC VMS, IBM VM/CMS
and Amiga DOS.
vi Preface
Acknowledgments
This manual has benefited from comments given to us by students, faculty, and staff at the Uni
versity of Waterloo, and by users at sites throughout the world. These "friends of Maple" are too
numerous to list here. Wehope they willfeelthat theirassistance has been acknowledgedwhen they
find their suggestions incorporated into the present edition. For their assistance in the production
ofthis manual wewould liketo thank Kate Atherley, Greg Fee,Krishna Gopinathan, Blair Madore,
Liyuan Qiao, Mare Rybowicz, Katy Simonsen, and Hans Ziemann.
The Maple project has received support from various sources, including the Academic Develop
ment Fund of the University of Waterloo, the Natural Seiences and Engineering Research Council
ofCanada, Digital Equipment Corporation, the Sloan Foundation,and the Information Technology
Research Centre of Ontario.
Contents
1 The Maple Library 1
1.1 Introduction . 1
1.2 Description of the Maple Library . ' ,' . . 1
1.3 Format of Library Function Descriptions . 4
2 Main Routines 5
2.1 Standard Library Functions 5
2.1.1 abs . . 5
2.1.2 Ai, Bi .. 5
2.1.3 alias .. . 6
2.1.4 allvalues . 7
2.1.5 anames . 8
2.1.6 arc-trigonometrie functions 8
2.1.7 arc-hyperbolic functions . . 9
2.1.8 array . 9
2.1.9 assemble, disassemble, pointto, addressof ... .. .. 10
2.1.10 assign . 12
2.1.11 assigned . 13
2.1.12 asympt . 14
2.1.13 bernoulli . 15
2.1.14 BesselI, BesselK 15
2.1.15 BesselJ, BesselY 16
2.1.16 Beta(x,y) 16
2.1.17 binomial. 16
2.1.18 cat .... 17
2.1.19 chebyshev 17
2.1.20 chrem 18
2.1.21 Ci . . 19
2.1.22 coeff . 19
2.1.23 coeffs 20
2.1.24 collect 21
2.1.25 combine 22
2.1.31 compoly . 27
viii Contents
2.1.32 Content, Primpart 27
2.1.33 content, primpart . 28
2.1.34 convert .. 29
2.1.81 copy . 56
2.1.82 D . 56
2.1.83 define . 57
2.1.88 degree, Idegree . . . . . . . . . . . . .. .. . 61
2.1.89 Det .. .. 62
2.1.90 diff or Diff . 63
2.1.91 dilog(x) 64
2.1.92 discrim 64
2.1.93 DistDeg 65
2.1.94 Divide . 66
2.1.95 divide 66
2.1.96 dsolve . 67
2.1.98 Ei ... 71
2.1.99 Eigenvals . 71
2.1.100 eqn . 72
2.1.101 erf . 73
2.1.102 erfc . 73
2.1.103 ERROR. 73
2.1.104 euler . 74
2.1.105 Eval . 75
2.1.106 eval . 75
2.1.107 evala . 76
2.1.108 evalb . 77
2.1.109 evalc . 78
2.1.111 evalf . 79
2.1.112 evalhf 80
2.1.120 evalm 86
2.1.121 evaln . 87
2.1.122 example 88
2.1.123 exp . .. 89
2.1.124 Expand 89
2.1.125 expand 89
2.1.126 Factor . 91
2.1.127 factor . 91
2.1.128 Factors 92
2.1.129 FresnelC . 93
2.1.130 FresnelS . 94
2.1.131 Fresnelf 94
2.1.132 Fresnelg . 94
Contents ix
2.1.133 fnormal 94
2.1.134 fortran . . 95
2.1.135 frontend . 96
2.1.136 fsolve . . 97
2.1.137 galois .. 98
2.1.138 GAMMA 99
2.1.139 gc . 99
2.1.140 Gcd . · 100
2.1.141 gcd, lern . · 100
2.1.142 Gcdex . · 101
2.1.143 gcdex .. · 102
2.1.144 genpoly · 102
2.1.145 harmonie · 103
2.1.146 has ... · 103
2.1.147 hastype · 104
2.1.148 help .. . · 104
2.1.149 Hermite, Smith . · 105
2.1.150 icontent · 106
2.1.151 ifactor .. · 107
2.1.152 igcd, ilem · 108
2.1.153 igcdex .. · 108
2.1.154 indets . . · 109
2.1.155 indices, entries · 110
2.1.156 int or Int · 110
2.1.157 interface. · 113
2.1.158 Interp .. · 116
2.1.159 interp . . · 117
2.1.160 irem, iquo . · 117
2.1.161 Irreduc · 118
2.1.162 irreduc . · 119
2.1.163 isolve · 120
2.1.164 isprime · 120
2.1.165 isqrt, iroot · 120
2.1.166 ithprime . · 121
2.1.167 laplace . · 121
2.1.168 latex . · 123
2.1.171 leoeff, tcoeff . · 125
2.1.172 length · 126
2.1.173 lexorder .. · 126
2.1.174 lhs, rhs . . · 127
2.1.175 limit, Limit · 127
2.1.179 In, log, loglO · 131
x Contents
2.1.180 lprint 131
2.1.181 macro 132
2.1.182 map 133
2.1.183 match 133
2.1.184 max, min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
2.1.185 maxnorm. . . . . . . . . . . . . . . . 135
2.1.186 MeijerG . . 135
2.1.187 mellin . . . . 136
2.1.188 member 137
2.1.189 mod, modp, mods 138
2.1.190 modp1 140
2.1.191 msolve 141
2.1.192 nextprime, prevprime 142
2.1.193 norm 143
2.1.194 Normal 143
2.1.195 normal 144
2.1.196 Nullspace . . . . . . . . . . . . . '. . . . . . . . . . . . . . . . . . . . . . 145
2.1.197 numer, denom 146
2.1.198 O . . . . . . . . . . . . . . . . . . . 146
2.1.199 op, nops . . . . . . . . . 147
2.1.200 order. . . . . . . . . . . 147
2.1.201 plot . 148
2.1.202 plot[plotdevice] . . . . . . . . . . . . . . . . . . 149
2.1.203 plot[function] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
2.1.204 plot[infinity] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
2.1.205 plot[line] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. 153
2.1.206 plot[multiple] . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. 153
2.1.207 plot[options] . 154
2.1.208 plot[parametric] .. 155
2.1.209 plot[point] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 156
2.1.210 plot[polar] 156
2.1.211 plot[range]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
2.1.212 plotjsetup] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
2.1.213 plot[spline] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
2.1.214 plot[structure] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
2.1.215 plot3d 160
2.1.216 plot3d[option] 161
2.1.217 plot3d[structure] 162
2.1.218 plotsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
2.1.219 Power 164
2.1.220 Powmod 165
2.1.221 Prem, Sprem 165