This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
[an error occurred while processing this directive]

The Mathematica Book, version 4.0

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] (), 955, 1331

\[ABar] (), 955, 1331

Abel equations, DSolve, 850, 1119

Abel's Theorem, 812

Abends, 60, 464

Abort, Throw, 336, 1283

Abort, 356, 1037, 1067

$Aborted, 356, 1037, 1303

Aborting calculations, 61

AbortProtect, 356, 357, 1067

Aborts, 356

Above, overscript, 184

         OverscriptBox, 430, 1217

\above (TeX), FractionBox, 430, 1142

Above parenthesis, \[OverParenthesis] (), 954

Abs, 31, 34, 736, 737, 805, 1067

Abscissa, Axes, 138, 498, 1077

Absent from expression, FreeQ, 270, 1143

Absent from list, Complement, 126, 1098

         FreeQ, 123, 1143

Absolute coordinates, 491, 517

Absolute size, for points, AbsolutePointSize, 486, 1068

Absolute value, Abs, 31, 34, 736, 737, 1067

         notation for, \[LeftBracketingBar] (), 959

AbsoluteDashing, 487, 1067

         in three dimensions, 511

AbsoluteOptions, 149, 476, 567, 1067

AbsolutePointSize, 486, 1068

         in three dimensions, 511

AbsoluteThickness, 487, 1068

         in three dimensions, 511

AbsoluteTime, 700, 1068

Abut boxes, RowBox, 430, 1247

\accent (TeX), OverscriptBox, 430, 1217

Accent grave (`), as context mark, 377, 1001

         in package names, 630

Accented characters, 194, 955

Accents, 955

Account, of user, $UserName, 706, 1316

AccountingForm, 420, 1068

Accumulate, FoldList, 245, 1137

Accumulate (Version 1 function), see FoldList, 1378

Accuracy, in examples, xvii

         in timings, $TimeUnit, 701, 1315

         increasing, SetAccuracy, 728, 1257

         numerical, 33, 720, 910

         of solutions to differential equations, 927

Accuracy, 720, 1068

AccuracyGoal, 914, 917, 922, 927, 1069

Acknowledgments, v

Action, in notebooks, 49

Activating 2D forms, 415

Activating textual input, 181

Active, 433, 581, 595, 1069

Active cells, 54

Active element, ButtonBox, 433, 581, 1083

Active elements in notebooks, 54

Active links, Links, 652, 1183

Active text, in notebooks, 56

\[ACup] (), 955, 1331

Adamchik techniques, Sum, 1063, 1274

Adams method, NDSolve, 1061, 1199

Adaptive integration procedure, 911

Adaptive procedure, in NDSolve, 928

Adaptive sampling, in plots, 141

Add, without carry, BitXor, 747, 1081

Add-in programs, 647

Add-on products, v

Add-ons, location of files for, 1056

Addition, of elements to lists, Append, 124, 1072

         patterns involving, 272

         Plus (+), 29, 1226

Addresses, v

AddTo (+=), 291, 1017, 1069

Adjoint, Conjugate, 737, 1100

AdjustmentBox, 440, 1069

Adjustments, to formatting, 434

Adobe character encoding, 406

Adobe Illustrator format, exporting, Export, 554, 1129

         importing, Import, 555, 1162

\[ADoubleDot] (), 194, 955, 1331

Advanced topic sections, xvii

\[AE] (), 955, 1331

\ae (TeX), \[AE] (), 955

\AE (TeX), \[CapitalAE] (), 955

Agemo, \[Mho] (), 951

Aggregating brace, \[OverBrace] (), 954

\[AGrave] (), 194, 955, 1331

\[AHat] (), 955, 1331

AI88 format, exporting, Export, 554, 1129

         importing, Import, 555, 1162

AIFF format, exporting, Export, 555, 1129

         importing, Import, 555, 1162

Airy functions, AiryAi, 767, 1070

         derivatives of, AiryAiPrime, 767, 1070

Airy's differential equation, DSolve, 849, 1119

AiryAi, 767, 1070

AiryAiPrime, 767, 1070

AiryBi, 767, 1070

AiryBiPrime, 767, 1070

Alarm, Pause, 700, 1223

Albedo, 533

\[Aleph] (), 196, 950, 1331

Algebraic algorithms, GroebnerBasis, 798, 1154

Algebraic computation, 62

Algebraic constraints in equations, 825

Algebraic curves, 814

Algebraic equations, 87

         Solve, 812, 1264

Algebraic expressions, internal representation of, 236, 281

         parts in, 236

         patterns for, 263, 281

         pieces of, 73

Algebraic extensions, 742

Algebraic numbers, 802, 816

Algebraic operations on polynomials, 795

Algebraic rules, 826

Algebraic simplification, 62

         Simplify, 67, 806, 1262

Algebraic transformations, 66

Algebraic variables, 65

Algebraic varieties, GroebnerBasis, 798, 1154

Algebraics, 809, 1070

Algorithms, algebraic, 225

         algebraic, GroebnerBasis, 798, 1154

         complexity of, 75

         in Mathematica, 221, 1059

         precision in numerical, 725

Alias (Version 1 function), see $PreRead, 1378

Aliases, conventions for, 1330

         HTML, 1330

         SGML, 1330

         TeX, 1330

         user defined, 944

         user defined, InputAliases, 602, 1164

\[AliasIndicator] (), 966, 1331

Aliasing, of sound, SampleRate, 176, 1250

Aligning lists, on left, PadRight, 125, 1218

         on right, PadLeft, 125, 1218

Alignment, in numerical output, 422

         in tables, TableAlignments, 427, 1277

         of buttons, 437

         of columns, ColumnAlignments, 434, 1095

         of expressions, ShowContents, 440

         of GridBox, GridBaseline, 434, 1152

         of inline cells, CellBaseline, 592, 1088

         of numbers in tables, PaddedForm, 425, 1217

         of rows, RowAlignments, 434, 1247

         of subscripts, ScriptBaselineShifts, 442, 1252

\[AlignmentMarker] (), 436, 965, 1331

Aliquant, Mod, 740, 1196

All, 140, 1070

All expressions, pattern for, Blank (_), 261, 1081

All parts of expressions, 240, 1029

         applying functions to, MapAll (//@), 247, 1189

Allocating memory, in MathLink, 657

\[Alpha] (), 179, 947, 1331

Alphabet, generating, CharacterRange, 398, 403, 1091

Alphabetic characters, test for, LetterQ, 398, 1178

Alphabetizing, of strings, Sort, 396, 1265

Alternation, Or (||), 86, 1215

         patterns involving, 271

Alternatives, patterns involving, 271

Alternatives (|), 271, 1016, 1070

AmbientLight, 531, 1071

Ambiguities, in special characters, 942, 1019

         in TraditionalForm, 198

Ampersand, double (&&), And, 86, 1071

Ampersand (&), Function, 251, 1145

Amplitude, in elliptic functions, JacobiAmplitude, 774, 1174

         of sound, 176, 552

Analog input, 51

Analysis of variance, 786

Analytic continuation, 760

AnchoredSearch, 641, 1071

And, bitwise, BitAnd, 747, 1080

And (&&), 86, 333, 822, 1016, 1071

         argument evaluation in, 1035

         evaluation in, 333

\[And] (), 188, 942, 958, 1331

\[Angle] (), 196, 953, 1331

Angle bracket, \[LeftAngleBracket] (), 196, 959

Angle of view, ViewPoint, 156, 157, 518, 1297

Angles, 32

\[Angstrom] (), 196, 941, 951, 1332

Angular momentum, in quantum mechanics, 751

Animate, ShowAnimation, 136

Animate, 174

Animate Selected Graphics menu item, 605

Animate selection, SelectionAnimate, 574, 1253

Animation, 51, 174, 606

         examples of, 996

         of three-dimensional rotation, 174, 522

AnimationDirection, 606, 1071

AnimationDisplayTime, 606, 1071

Animations, exporting, Export, 553, 1129

Annotated names, 946

Annotated operator, 461

Annotation, of input, ShowAutoStyles, 602, 1260

Annotations, in graphics, 546

Anonymous functions, Function (&), 250, 1145

ANOVA (analysis of variance), 786

ANSI prototypes, 667

Anti-derivative, Integrate, 836, 1167

Antilogarithm, Exp, 31, 1127

Antique fonts, 949

Antisymmetry, Signature, 132, 751, 1262

Any expression, pattern for, Blank (_), 261, 1081

Apart, spacing characters, 965

Apart, 69, 794, 1062, 1072

API, for Mathematica, 647

APL, catenate in, Join, 126, 1175

         compress in, Select, 253, 1253

         grade in, Sort, 127, 1265

         iota operator in, Range, 117, 1236

         ravel in, Flatten, 131, 1137

         reduce in, Apply (@@), 245, 1072

         reshape in, Partition, 128, 1222

         shape in, Dimensions, 117, 888, 1113

Appell hypergeometric function, AppellF1, 772, 1072

AppellF1, 771, 772, 1072

Append, 124, 238, 1072

Appending, to files, PutAppend (>>>), 614, 1235

         to lists, Append, 124, 1072

         to notebooks, CellPrint, 561, 1091

         to strings, StringInsert, 393, 1269

AppendTo, 292, 1072

Apple events, 648

Apple key, \[CloverLeaf] (), 966

AppleTalk, 648

Applicability, regions of, Assumptions, 845, 1075

Applicability of transformation rules, Condition (/;), 267, 1100

Application, precedence of function, 1011

Application directory, $TopDirectory, 627, 1316

Application packages, 58, 94, 106

Apply (@@), 130, 245, 1013, 1072

         levels in, 1029

Applying functions, by name, Apply (@@), 245, 1072

         to all parts of expressions, Map (/@), 246, 1189

         to lists, Apply (@@), 245, 1072

         to specific parts of expressions, MapAt, 248, 1190

         with side effects, Scan, 249, 1251

\approx (TeX), \[TildeTilde] (), 960

Approximate differentiation, 783

Approximate formulas, derivation of from data, Fit, 895, 1136

         Series, 91, 861, 1256

Approximate functions, InterpolatingFunction, 897, 1167

Approximate numbers, Real, 714, 1239

Approximately equal, \[TildeEqual] (), 960

Approximation, rational, ContinuedFraction, 745, 1101

Approximation of functions, Fit, 105, 895, 1136

         Interpolation, 897, 1168

         on grids, ListInterpolation, 900, 1186

         Series, 91, 860, 1256

Approximations, algebraic, Series, 91, 860, 1256

         numerical, N, 30, 721, 1198

Arbitrary length, lists in MathLink, 660

Arbitrary-precision functions, 724

Arbitrary-precision numbers, 33, 724

         in MathLink, 665

         in plots, 142

Arc trigonometric functions, 31, 752

ArcCos, 31, 752, 1073

ArcCosh, 752, 1073

ArcCot, 752, 1073

ArcCoth, 752, 1073

ArcCsc, 752, 1073

ArcCsch, 752, 1073

Archimedean spiral, 983

Architecture, of Mathematica system, 44

         processor, $ProcessorType, 707, 1313

Archives, Mathematica, v

Arcs, of circles, Circle, 482, 1092

ArcSec, 752, 1073

ArcSech, 752, 1073

ArcSin, 31, 752, 1074

ArcSinh, 752, 1074

ArcTan, 31, 752, 1074

ArcTanh, 752, 1074

Area, Integrate, 80, 1167

Arg, 34, 737, 805, 1074

Argand diagrams, ParametricPlot, 166, 1220

argc, argv, $CommandLine, 706, 1304

argc, in MathLink, 669

Argument of complex number, Arg, 34, 737, 1074

Arguments, 232

         constraining types of, 266

         conventions for, 1027

         default values for, 276, 1039

         dropping for printing, Shallow, 417, 1259

         evaluation of, 318, 1034

         evaluation of in assignments, 328

         function names as, 242

         functions with variable numbers of, 275

         in pure functions, 251

         named, 278

         non-standard evaluation of, 1034

         on Mathematica command line, $CommandLine, 706, 1304

         optional, 1039

         options as, 137, 1027

         overriding non-standard evaluation of, Evaluate, 1036, 1126

         positional, 278

         preventing evaluation of, 322

         preventing evaluation of, Unevaluated, 325, 1294

         scoping of names for, 372

         sequences of, 275

         to external functions, 652

         transformation rules as, 278

         unevaluated, 322

         warning about number of, 60

argv array, 688

argx message, 466

\[ARing] (), 194, 955, 1332

Arithmetic, 29

         in finite fields, 31, 740, 828

         interval, Interval, 731, 1169

         machine, 721, 729

         speed of, 76

Arithmetic geometry, 829

Arithmetical functions, higher, 740

ArithmeticGeometricMean, 780, 1074

Arity, of functions, 275

Arrange, Sort, 127, 1265

Arrangement, of output, 429

Array, 117, 252, 871, 888, 1075

Array origins, 656

\arraycolsep (TeX), ColumnSpacings, 434, 1096

Arrays, 42

         as lists, 293

         as matrices, 873

         as tensors, 887

         color, RasterArray, 484, 1237

         creation of, Table, 113, 1277

         exporting, Export, 633, 1129

         extensible, 293

         extracting elements from, 115

         formatting of, 424, 428

         formatting of, GridBox, 430, 1153

         importing, Import, 633, 1162

         in C, 658

         in MathLink, 655

         input of, 191

         interpolation of, ListInterpolation, 900, 1186

         List, 40, 1183

         multidimensional, 114

         origin of, Mod, 740, 1196

         plotting, 163, 503

         reading from data files, ReadList, 634, 1239

         sparse, 293

         with continuous indices as functions, 295

Arrow (->), Rule, 63, 285, 1249

Arrow characters, 963

Arrow keys, 184

Arrows, control, 440

Art, computer, 11, 990

Artificial intelligence, in simplification, Simplify, 68, 1262

\[AscendingEllipsis] (), 954, 1332

ASCII, xvii, 404, 406

         in MathLink, 669

Aspect ratios, of geometrical figures, 481

         of parametric plots, 167

AspectRatio, 138, 154, 167, 481, 495, 1075

         for three-dimensional plots, 521

AspectRatioFixed, 605, 1075

Assertions, 270

         simplification with, Simplify, 72, 807, 1262

Assignments, 289, 1040

         associated with particular objects, 302, 1040

         chains of, 299

         compared with equality tests, 83

         compared with replacements, 64

         delayed, SetDelayed (:=), 297, 1258

         evaluation in, 297, 322, 326, 1036

         immediate, Set (=), 297, 1257

         local, 363

         local variables in, 364

         of downvalues directly, DownValues, 308, 1118

         of upvalues directly, UpValues, 308, 1296

         of values for symbols, Set (=), 39, 1257

         ordering of, 296

         preventing evaluation in, 329

         testing for, ValueQ, 270, 1296

         tracing, Trace, 342, 1289

Assistance, 57

         in notebook front end, 56

Associated packages, 209

Associative functions, 312

         in patterns, 273

Associativities, of operators, 1019

         table of, 1012

Associativity, 257

         in pattern matching, 263

         of operators, 455

Assume real variables, 805

Assumptions, about complex variables, ComplexExpand, 804, 1098

         in simplification, Simplify, 72, 807, 1262

Assumptions, 845, 1075

Asterisk, Times (*), 29, 1285

Asterisk (*), as string metacharacter, 58, 396

Astronomy, example from, 11

\asymp (TeX), \[CupCap] (), 960

Asymptotes, limits near, 870

Asymptotic, \[TildeTilde] (), 960

Asymptotic expansions, Series, 861, 1256

Asymptotically equal, \[TildeEqual] (), 960

Asynchronous interrupts, 61

At sign (@), 235

         as string metacharacter, 397

\[ATilde] (), 955, 1332

Atomic subexpressions, in simplification, ExcludedForms, 806, 1126

AtomQ, 270, 1075

Atoms, 1002

         as leaves in trees, 241

         lexical, 452

         number in expression, LeafCount, 704, 1177

Atop, overscript, 184

         OverscriptBox, 430, 1217

\atop (TeX), GridBox, 430, 1153

Attractors, strange, 937

Attributes, 313

         for pure functions, 318

         functions for testing, 269

         in pattern matching, 273

         of built-in functions, 315

         of cells, CellTags, 594, 1091

         used in matching patterns, 1039

Attributes, 273, 314, 1041, 1076

AU format, exporting, Export, 555, 1129

         importing, Import, 555, 1162

Audio, exporting, Export, 555, 1129

         importing, Import, 555, 1162

Audio output, 175

         representation of, 551

Auditory system, human, 176

Aut, Xor, 86, 1302

Author's address, vii

Authorization, of network licenses, 1048

AutoIndent, 602, 1076

AutoItalicWords, 602, 1077

Autoload directory, 1057

Autoloading, of packages, 59, 386

Automatic, 140, 1077

Automatic evaluation, of cells, InitializationCell, 595, 1163

Automatic grouping, CellGrouping, 607, 1090

Automatic numbering, 206

Automatic options, finding values of, AbsoluteOptions, 149, 476, 1067

Automatic styles, ShowAutoStyles, 602, 1260

Automatic variables, 363

Autoplectic sequences, 937

Autoscaling, in plots, PlotRange, 494, 1226

AutoSpacing, 439, 1077

Average, Mean, 107

Avoiding evaluation, 322

Axes, in contour plots, 506

         in density plots, 506

         in three-dimensional graphics, 535

         in two-dimensional graphics, 498

         labeling of three-dimensional, AxesLabel, 538, 1077

         options for, 498

         positions of three-dimensional, AxesEdge, 537, 1077

         tick marks on, Ticks, 138, 498, 1284

Axes, 138, 154, 497, 498, 535, 1077

AxesEdge, 537, 1077

AxesLabel, 138, 154, 498, 538, 1077

AxesOrigin, 138, 498, 1078

AxesStyle, 498, 536, 1078

Axis, 436

Azimuth, Arg, 737, 1074