The Mathematica Book, version 5.0

Browsable Index

 !@# 0 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

\[AAcute] (), 998, 1354

\[ABar] (), 998, 1354

Abel equations, DSolve, 873, 1129

Abel's Theorem, 820

Abends, 61, 479

Abort, Throw, 350, 1304

Abort, 371, 1048, 1075

\$Aborted, 371, 1048, 1325

Aborting calculations, 62

AbortProtect, 371, 1075

Aborts, 370

Above, overscript, 180

OverscriptBox, 445, 1235

\above (TeX), FractionBox, 445, 1155

Above parenthesis, \[OverParenthesis] (), 997

Abramov algorithm, DSolve, 1071, 1129

RSolve, 1071, 1269

Abs, 31, 34, 745, 746, 813, 1075

Abscissa, Axes, 134, 512, 1086

Absent from expression, FreeQ, 268, 1156

Absent from list, Complement, 127, 1109

FreeQ, 124, 1156

Absolute coordinates, 505, 531

Absolute error, Accuracy, 727, 1077

Absolute invariant, KleinInvariantJ, 787, 1190

Absolute size, for points, AbsolutePointSize, 500, 1076

Absolute value, Abs, 31, 34, 745, 746, 1075

notation for, \[LeftBracketingBar] (), 1002

AbsoluteDashing, 501, 1075

in three dimensions, 525

AbsoluteOptions, 145, 490, 581, 1075

AbsolutePointSize, 500, 1076

in three dimensions, 525

AbsoluteThickness, 501, 1076

in three dimensions, 525

AbsoluteTime, 710, 1076

AbsoluteTiming, 711, 1076

Abut boxes, RowBox, 445, 1267

\accent (TeX), OverscriptBox, 445, 1235

Accent grave (`), as context mark, 392, 1015

in package names, 640

Accented characters, 190, 998

Accents, 998

Account, of user, \$UserName, 716, 1339

AccountingForm, 435, 1076

Accumulate, FoldList, 243, 1151

Accumulate (Version 1 function), see FoldList, 1402

Accumulating expressions, Reap, 355, 1259

Accuracy, in examples, xv

in timings, \$TimeUnit, 711, 1338

increasing, SetAccuracy, 736, 1277

numerical, 33, 727, 952

Accuracy, 727, 1077

AccuracyGoal, 958, 976, 1077

Action, in notebooks, 49

Activating 2D forms, 430

Activating textual input, 177

Active, 448, 595, 607, 1077

Active cells, 54

Active element, ButtonBox, 448, 595, 1092

Active elements in notebooks, 54

Active text, in notebooks, 56

\[ACup] (), 998, 1354

Adams methods, NDSolve, 979, 1068, 1216

Adaptive procedure, in NDSolve, 966, 1216

Add, without carry, BitXor, 756, 1090

Add-ons, location of files for, 1063

Addition, of elements to lists, Append, 125, 288, 1080

patterns involving, 270

Plus (+), 29, 1244

Additive cellular automata, CellularAutomaton, 946, 1101

\[AE] (), 998, 1354

\ae (TeX), \[AE] (), 998

\AE (TeX), \[CapitalAE] (), 998

Agemo, \[Mho] (), 994

Aggregating brace, \[OverBrace] (), 997

\[AGrave] (), 190, 998, 1354

\[AHat] (), 998, 1354

AIFF format, exporting, Export, 569, 1141

importing, Import, 570, 1176

Airy functions, AiryAi, 776, 1078

derivatives of, AiryAiPrime, 776, 1078

Airy's differential equation, DSolve, 872, 1129

AiryAi, 775, 776, 1078

AiryAiPrime, 775, 776, 1078

AiryBi, 775, 776, 1078

AiryBiPrime, 775, 1078

Alarm, Pause, 710, 1241

Albedo, 547

\[Aleph] (), 192, 993, 1354

Algebraic algorithms, GroebnerBasis, 805, 1168

Algebraic computation, 63

Algebraic curves, 822

Algebraic equations, 88

Solve, 820, 1285

Algebraic expressions, internal representation of, 234, 279

parts in, 234

patterns for, 261, 279

pieces of, 73

Algebraic extensions, 751

Algebraic geometry, 845

Algebraic numbers, 809, 826

Algebraic operations on polynomials, 803

Algebraic simplification, 63

Simplify, 68, 813, 1282

Algebraic transformations, 67

Algebraic variables, 66

Algebraic varieties, GroebnerBasis, 805, 1168

Algebraics, 817, 1079

Algorithms, algebraic, 223

algebraic, GroebnerBasis, 805, 1168

complexity of, 76

in Mathematica, 219, 1066

monitoring, 977

precision in numerical, 733

time complexity of, 76

Alias (Version 1 function), see \$PreRead, 1402

Aliases, conventions for, 1353

HTML, 1353

SGML, 1353

TeX, 1353

user defined, 987

user defined, InputAliases, 613, 1178

\[AliasIndicator] (), 1009, 1354

Aliasing, of sound, SampleRate, 172, 1270

Alignment, in numerical output, 437

in tables, TableAlignments, 442, 1299

of buttons, 452

of columns, ColumnAlignments, 449, 1107

of expressions, ShowContents, 455

of GridBox, GridBaseline, 449, 1166

of inline cells, CellBaseline, 605, 1097

of numbers in tables, PaddedForm, 440, 1235

of rows, RowAlignments, 449, 1267

of subscripts, ScriptBaselineShifts, 457, 1272

\[AlignmentMarker] (), 451, 1008, 1354

Aliquant, Mod, 749, 1213

All, ForAll, 847, 1152

All, 125, 136, 1040, 1079

All expressions, pattern for, Blank (_), 259, 1090

All parts of expressions, 238, 1041

applying functions to, MapAll (//@), 245, 1205

\[Alpha] (), 175, 990, 1354

Alphabet, generating, CharacterRange, 413, 417, 1102

Alphabetic characters, test for, LetterQ, 413, 1193

Alphabetizing, of strings, Sort, 411, 1286

Alternation, Or (||), 87, 1233

patterns involving, 269

Alternatives, patterns involving, 269

Alternatives (|), 269, 1028, 1079

Always, ForAll, 847, 1152

AmbientLight, 545, 1079

Ambiguities, in special characters, 985, 1031

Ampersand, double (&&), And, 87, 1079

Ampersand (&), Function, 249, 1159

Amplitude, in elliptic functions, JacobiAmplitude, 782, 1189

of sound, 172, 566

Analysis of variance, 794

Analytic continuation, 769

AnchoredSearch, 651, 1079

And, bitwise, BitAnd, 756, 1089

And (&&), 87, 347, 1028, 1079

argument evaluation in, 1046

evaluation in, 347

\[And] (), 183, 985, 1001, 1354

And bar, \[Nand] (), 1001, 1215

\[Angle] (), 192, 996, 1354

Angle bracket, \[LeftAngleBracket] (), 191, 1002

Angle of view, ViewPoint, 152, 153, 532, 1319

Angles, 32

\[Angstrom] (), 192, 984, 994, 1355

Angular momentum, in quantum mechanics, 760

Animate, 170

Animate Selected Graphics menu item, 617

Animate selection, SelectionAnimate, 588, 1274

Animation, 51, 170, 617

of three-dimensional rotation, 170, 536

AnimationDirection, 617, 1080

AnimationDisplayTime, 617, 1080

Animations, exporting, Export, 567, 1141

Annotated names, 989

Annotated operator, 476

Annotation, of input, ShowAutoStyles, 613, 1280

Annotations, in graphics, 560

Anonymous functions, Function (&), 248, 1159

ANOVA (analysis of variance), 794

ANSI prototypes, 677

Anti-derivative, Integrate, 859, 1182

Antilogarithm, Exp, 31, 1137

Antique fonts, 992

Antisymmetry, Signature, 760, 1282

Any expression, pattern for, Blank (_), 259, 1090

Apart, spacing characters, 1008

Apart, 69, 70, 802, 1069, 1080

API, for Mathematica, 657

APL, catenate in, Join, 126, 1190

compress in, Select, 251, 1273

grade in, Ordering, 129, 255, 1233

iota operator in, Range, 119, 1255

ravel in, Flatten, 130, 1150

reduce in, Apply (@@), 243, 1081

reshape in, Partition, 128, 292, 1240

shape in, Dimensions, 120, 916, 1124

Appell hypergeometric function, AppellF1, 781, 1080

AppellF1, 780, 781, 1080

Append, 125, 236, 288, 1080

Appending, to files, PutAppend (>>>), 624, 1253

to lists, Append, 125, 288, 1080

to lists, Sow, 355, 1286

to notebooks, CellPrint, 575, 1100

to strings, StringInsert, 408, 1291

AppendTo, 306, 1081

Apple events, 658

Apple key, \[CloverLeaf] (), 1009

AppleTalk, 658

Applicability, regions of, Assumptions, 867, 1084

Applicability of transformation rules, Condition (/;), 265, 1111

Application, precedence of function, 1023

Application directory, \$InstallationDirectory, 637, 1330

Application packages, 59, 97, 109

Apply (@@), 243, 1025, 1081

levels in, 1041

Applying functions, by name, Apply (@@), 243, 1081

to all parts of expressions, Map (/@), 244, 1205

to lists, Apply (@@), 243, 1081

to specific parts of expressions, MapAt, 246, 1205

with side effects, Scan, 247, 1271

\approx (TeX), \[TildeTilde] (), 1003

Approximate differentiation, 791

Approximate formulas, derivation of from data, Fit, 926, 1149

Series, 94, 884, 1276

Approximate functions, InterpolatingFunction, 930, 1182

Approximate numbers, Real, 722, 1258

Approximately equal, \[TildeEqual] (), 1003

Approximation, rational, ContinuedFraction, 754, 1112

Approximation of functions, FindFit, 108, 1146

Fit, 926, 1149

Interpolation, 930, 1183

on grids, ListInterpolation, 934, 1201

Series, 94, 883, 1276

Approximations, algebraic, Series, 94, 883, 1276

numerical, N, 30, 728, 1214

Arbitrary length, lists in MathLink, 670

Arbitrary-precision functions, 731

Arbitrary-precision numbers, 33, 731

in plots, 138

input of, 729

Arc trigonometric functions, 31, 761

ArcCos, 31, 761, 1081

ArcCosh, 761, 1081

ArcCot, 761, 1081

ArcCoth, 761, 1081

ArcCsc, 761, 1081

ArcCsch, 761, 1082

Architecture, of Mathematica system, 44

processor, \$ProcessorType, 717, 1336

Arcs, of circles, Circle, 496, 1103

ArcSec, 761, 1082

ArcSech, 761, 1082

ArcSin, 31, 761, 1082

ArcSinh, 761, 1082

ArcTan, 31, 761, 1082

ArcTanh, 761, 1082

Area, Integrate, 81, 1182

Arg, 34, 746, 813, 1083

Argand diagrams, ParametricPlot, 161, 1237

argc, argv, \$CommandLine, 716, 1327

Argument of complex number, Arg, 34, 746, 1083

Arguments, 230

constraining types of, 264

conventions for, 1039

default values for, 274, 1050

dropping for printing, Shallow, 432, 1279

evaluation of, 332, 1045

evaluation of in assignments, 342

function names as, 240

functions with variable numbers of, 273

in pure functions, 249

named, 276

non-standard evaluation of, 1045

on Mathematica command line, \$CommandLine, 716, 1327

optional, 1050

options as, 133, 1039

overriding non-standard evaluation of, Evaluate, 1047, 1136

positional, 276

preventing evaluation of, 336

preventing evaluation of, Unevaluated, 339, 1315

scoping of names for, 387

sequences of, 273

to external functions, 662

transformation rules as, 276

unevaluated, 336

argv array, 698

argx message, 480

\[ARing] (), 190, 998, 1355

Arithmetic, 29

in finite fields, 31, 749

interval, Interval, 740, 1184

machine, 728, 737

speed of, 77

Arithmetic difference equations, RSolve, 96, 891, 1269

Arithmetical functions, higher, 749

ArithmeticGeometricMean, 788, 1083

Arity, of functions, 273

Arnoldi methods, Eigenvalues, 1069, 1131

ARPACK, Eigenvalues, 1069, 1131

Arrange, Sort, 127, 1286

Arrangement, of output, 444

Array, 119, 250, 283, 289, 896, 916, 1083

Array automata, CellularAutomaton, 942, 1101

Array origins, 666

\arraycolsep (TeX), ColumnSpacings, 449, 1108

ArrayDepth, 290, 916, 1083

ArrayQ, 267, 290, 916, 1083

ArrayRules, 898, 922, 1084

Arrays, 42

as lists, 307

as matrices, 899

as tensors, 915

color, RasterArray, 498, 1255

creation of, 283

creation of, Table, 115, 1299

exporting, Export, 643, 1141

extensible, 307

extracting elements from, 117

formatting of, 439, 443

formatting of, GridBox, 445, 1167

importing, Import, 643, 1176

in C, 668

input of, 186

interpolation of, ListInterpolation, 934, 1201

List, 40, 1199

multidimensional, 116

origin of, Mod, 749, 1213

plotting, 159, 517

sparse, 307

sparse, SparseArray, 295, 1287

testing for, ArrayQ, 267, 1083

with continuous indices as functions, 309

Arrow (->), Rule, 64, 299, 1269

Arrow characters, 1006

Arrow keys, 180

Arrows, control, 455

Art, computer, 11

Artificial intelligence, in simplification, Simplify, 69, 1282

\[AscendingEllipsis] (), 997, 1355

ASCII, xv, 419, 421

Aspect ratios, of geometrical figures, 495

of parametric plots, 163

AspectRatio, 134, 151, 163, 495, 509, 1084

for three-dimensional plots, 535

AspectRatioFixed, 616, 1084

Assertions, 268

simplification with, Simplify, 72, 815, 1282

Assignments, 303, 1051

associated with particular objects, 316, 1051

chains of, 313

compared with equality tests, 84

compared with replacements, 65

delayed, SetDelayed (:=), 311, 1278

evaluation in, 311, 336, 340, 1047

immediate, Set (=), 311, 1277

local, 378

local variables in, 379

of downvalues directly, DownValues, 322, 1128

of upvalues directly, UpValues, 322, 1317

of values for symbols, Set (=), 39, 1277

ordering of, 310

preventing evaluation in, 343

testing for, ValueQ, 268, 1317

tracing, Trace, 357, 1310

Assistance, 58

in notebook front end, 57

Associated packages, 205

Associative functions, 326

in patterns, 271

Associativities, of operators, 1031

table of, 1024

Associativity, 255

in pattern matching, 261

of operators, 470

Assume real variables, 813

Assuming, 818, 1084

Assumptions, about complex variables, ComplexExpand, 812, 1110

in simplification, Simplify, 72, 815, 1282

Assumptions, 867, 1084

\$Assumptions, 818, 1325

Asterisk, Times (*), 29, 1306

Asterisk (*), as string metacharacter, 58, 411

Astronomical data, importing, Import, 208, 1176

Astronomy, example from, 11

\asymp (TeX), \[CupCap] (), 1003

Asymptotes, limits near, 895

Asymptotic, \[TildeTilde] (), 1003

Asymptotic expansions, Series, 884, 1276

Asymptotically equal, \[TildeEqual] (), 1003

Asynchronous interrupts, 62

At sign (@), 233

as string metacharacter, 412

\[ATilde] (), 998, 1355

Atomic subexpressions, in simplification, ExcludedForms, 814, 1137

AtomQ, 268, 1085

Atoms, 1016

as leaves in trees, 239

lexical, 467

number in expression, LeafCount, 714, 1192

Atop, overscript, 180

OverscriptBox, 445, 1235

\atop (TeX), GridBox, 445, 1167

Attractors, strange, 981

Attributes, 327

for pure functions, 332

functions for testing, 267

in pattern matching, 271

of built-in functions, 329

of cells, CellTags, 607, 1100

used in matching patterns, 1050

Attributes, 271, 328, 1052, 1085

AU format, exporting, Export, 569, 1141

importing, Import, 570, 1176

Audio, exporting, Export, 569, 1141

importing, Import, 570, 1176

Audio output, 171

representation of, 565

Auditory system, human, 172

Aut, Xor, 87, 1324

AutoCAD format, exporting, Export, 569, 1141

importing, Import, 570, 1176

AutoIndent, 613, 1086

AutoItalicWords, 613, 1086

Automata, cellular, CellularAutomaton, 942, 1101

Automatic, 136, 1086

Automatic evaluation, of cells, InitializationCell, 608, 1178

Automatic grouping, CellGrouping, 618, 1099

Automatic numbering, 202

Automatic options, finding values of, AbsoluteOptions, 145, 490, 1075

Automatic styles, ShowAutoStyles, 613, 1280

Automatic variables, 378

Autoplectic sequences, 980

Autoscaling, in plots, PlotRange, 508, 1243

AutoSpacing, 454, 1086

Average, Mean, 109, 924, 1209

Avoiding evaluation, 336

Axes, in contour plots, 520

in density plots, 520

in three-dimensional graphics, 549

in two-dimensional graphics, 512

labeling of three-dimensional, AxesLabel, 552, 1087

options for, 512

positions of three-dimensional, AxesEdge, 551, 1087

tick marks on, Ticks, 134, 512, 1305

Axes, 134, 151, 511, 512, 549, 1086

AxesEdge, 551, 1087

AxesLabel, 134, 151, 512, 552, 1087

AxesOrigin, 134, 512, 1087

AxesStyle, 512, 550, 1087

Axis, 451

Azimuth, Arg, 746, 1083

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