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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

i, dotless, \[DotlessI] (), 992

I, 32, 34, 765, 1173

\i (TeX), \[DotlessI] (), 992

i/o primitives, 630

\[IAcute] (), 190, 998, 1372

Icon, Mathematica, 26

Iconic characters, 1009

Icons, in graphics, Offset, 507, 1230

Icosahedron, 527

\[ICup] (), 998, 1372

ID, of computer, $MachineID, 718, 1331

         of Mathematica process, $ProcessID, 716, 1336

         of session, $SessionID, 384, 716, 1337

Ideals, polynomial, GroebnerBasis, 805, 1168

Idempotence, OneIdentity, 272, 1231

Identical, SameQ (===), 268, 347, 1270

Identical expressions, testing for, Equal (==), 85, 1135

Identifiers, 40, 1014

Identities, special function, FunctionExpand, 792, 1159

Identity, 253, 1173

Identity matrix, sparse array for, 296

IdentityMatrix, 120, 896, 1173

\[IDoubleDot] (), 998, 1372

IEEE Floating Point Standard, 742

If, 87, 345, 1173

         evaluation in, 336

\iff (TeX), \[DoubleLongLeftRightArrow] (), 1006

Ignore data, in files not between separators, RecordSeparators, 648, 1259

         Skip, 650, 1284

IgnoreCase, 410, 412, 651, 1173

$IgnoreEOF, 706, 707, 1057, 1329

\[IGrave] (), 998, 1372

\[IHat] (), 998, 1372

ii, \[ImaginaryI] (), 988

Illegal syntax, 51

Illumination, 544

         Lighting, 526, 1194

Im, 34, 746, 813, 1173

\Im (TeX), \[GothicCapitalI] (), 992

Image, of session, DumpSave, 627, 1129

Image array, Raster, 492, 497, 1255

Image capture, Import, 570, 1176

Image of, \[DotEqual] (), 1003

Image processing, 9

         Import, 570, 1176

         ListConvolve, 937, 1200

Image transform, two-dimensional, Fourier, 937, 1154

ImageMargins, 616, 1174

ImageResolution, 569, 1174

ImageRotated, 569, 1174

Images, exporting, Export, 208, 567, 1141

ImageSize, 569, 616, 1174

Imaginary part, finding symbolic, 813

         Im, 34, 746, 1173

Imaginary quantities, expressions involving, 812

Imaginary unit, I, 34, 1173

\[ImaginaryI] (), 984, 988, 994, 1372

\[ImaginaryJ] (), 988, 994, 1372

\imath (TeX), \[DotlessI] (), 992

Immediate definitions, Set (=), 311, 1277

Immediate evaluation, of cells, 205

         of cells, InitializationCell, 608, 1178

Implementation, of Mathematica, 218, 1066

Implicit curves, algebraic, 822

Implicit function application, \[InvisibleApplication] (), 1008

Implicit multiplication, \[InvisibleSpace] (), 1008

Implicit space, \[InvisibleSpace] (), 454

Implies, \[RightTee] (), 1001

Implies, 834, 1174

\[Implies] (), 183, 985, 1001, 1006, 1373

Implode, FromDigits, 725, 1158

         StringJoin (<>), 407, 412, 1291

Import, 207, 208, 212, 568, 570, 571, 642, 643, 923, 1176

$ImportFormats, 208, 1329

Importing, numbers, 729

         to notebooks, 47

         two-dimensional forms, 430

ImportString, 570, 1176

Impossibility, of solution in radicals, 820

Improper functions, DiracDelta, 879, 1124

Impulse function, DiracDelta, 879, 1124

In, 38, 48, 50, 702, 1177

         deleting, 703

\in (TeX), \[Element] (), 1004, 1132

In-place evaluation, 181

In-text formulas, 461

Inactivity, caused by name conflicts, 59

Inches, \[DoublePrime] (), 996

         sizes in, 500

Include files, for MathLink, 677

Incompatibilities, between Versions 1 and 2, 1402

         between Versions 2 and 3, 1402

         between Versions 3 and 4, 1404

         between Versions 4 and 5, 1404

Incomplete beta function, Beta, 770, 1089

Incomplete elliptic integrals, 783

Incomplete gamma function, Gamma, 770, 1160

Inconsistent linear systems, 909

Increment (++), 305, 1025, 1177

Indentation, automatic, AutoIndent, 613, 1086

         \[IndentingNewLine] (), 460, 1008

         of paragraphs, ParagraphIndent, 611, 1237

\[IndentingNewLine] (), 460, 1008, 1373

Independence, testing for, FreeQ, 124, 268, 1156

Indeterminate, 742, 1177

Indeterminate results, 742

Index, of numbers, MantissaExponent, 726, 1204

         of substring, StringPosition, 409, 1292

         online, 57

Index files (names files), 402

Index function, MultiplicativeOrder, 752, 1214

Index law, PowerExpand, 72, 798, 1248

Indexed functions, 251

         applying to expressions, MapIndexed, 246, 1205

Indexed variables, 41, 307

Indicator, for unmatched brackets, ShowAutoStyles, 613, 1280

Indicator characters, 1009

Indicator function, UnitStep, 879, 1316

Indices, applying functions to parts with specific, MapAt, 246, 1205

         commas between, 1008

         dummy, 387

         finding, Position, 124, 261, 1247

         in expressions, 234

         manipulating lists by, 285

         of expression parts, 1014

         of list elements, 41

         part subscript, 184

         parts with given number of (levels), 238

         permutation of, Transpose, 917, 1313

Inequalities, 835

         linear, 975

         linear, Minimize, 851, 1212

         on parameters, Assumptions, 867, 1084

         reducing, Reduce, 92, 1261

Inequality, Unequal (!=), 86, 1315

Inequality, 1033

Inequivalence, logical, Xor, 87, 1324

Inert forms, Hold, 336, 1169

         of symbols, 402

Inert functions, Remove, 59, 1261

Infeasible constraints, Minimize, 852, 1212

Inferences, 268

         about parameters, Assumptions, 867, 1084

Infimum, Min, 31, 745, 1212

Infinite evaluation, 324

Infinite recursion, 369

Infinite results, 742

Infinity, complex, 743

         complex direction of, 743

Infinity, 32, 238, 743, 765, 1177

\[Infinity] (), 182, 988, 994, 1373

Infix, 474, 1177

Infix notation, 233

Infix operators, 468

Information, about user-defined functions, 110

         on functions, 484

         on symbols, 484

         product, $ProductInformation, 717, 1336

Information, 58, 1038, 1178

\infty (TeX), \[Infinity] (), 994, 1177

Inheritance, of cell options, 600

Inhibiting, evaluation, 336

         line breaks, \[NoBreak] (), 459

         output, 43

         page breaks, 609

Inhomogeneous differential equations, DSolve, 871, 1129

init.m files, 640, 1056, 1065

Initial conditions, for NDSolve, 962

Initial values, in modules, 379

$InitialDirectory, 637, 1330

Initialization, 1056

         of front end, 1038

         of kernel, 1063

         of random number generator, SeedRandom, 747, 1273

Initialization cells, 205

Initialization files, 1065

         for packages, 640, 1065

InitializationCell, 608, 1178

Inks, printing, 564

Inline cells, positioning of, CellBaseline, 605, 1097

Inline code, 138, 196

Inline formulas, 196, 461

Inline text, 196

Inner, 257, 917, 919, 920, 1178

Inner loops, via MathLink, 657

Inner products, Dot (.), 118, 902, 1127

         generalized, Inner, 919, 1178

         of tensors, Dot (.), 917, 1127

Input, as string, InString, 702, 1180

         basic rules for, 475

         current, $Input, 639, 1330

         entering, 26, 27, 48

         file, Get (<<), 59, 1162

         from data file, ReadList, 644, 1257

         full story on, 623

         in notebooks, 174

         low-level, 630

         multiline, 48

         of delimiters, ShowAutoStyles, 613, 1280

         of numbers, 729

         re-executing, 48

         special forms, 232, 1018, 1023

         termination of, 48, 1037

         textual, 424

         two-dimensional, 176

         with notebook interface, 26

Input, 478, 1178

$Input, 639, 705, 1330

Input cell, Evaluatable, 608, 1136

Input errors, 51

Input forms, 1024

         for boxes, 462

         for expressions, 233

         for numbers, 1021

         hierarchy of, 429

Input lines, In, 38, 1177

Input of operators, 230, 1023

Input streams, opening, OpenRead, 649, 1231

Input style, 573

InputAliases, 613, 1178

InputAutoReplacements, 613, 1179

InputForm, 139, 192, 424, 488, 1179

         number marks in, 730

InputNamePacket, 683, 700

InputNotebook, 579, 1179

InputPacket, 700

InputStream, 631, 1054, 1179

InputString, 478, 1179

Insert, 125, 288, 1180

Inserting cells, CellPrint, 575, 1100

Insertion, into external files, Splice, 214, 1288

         of substrings, StringInsert, 408, 1291

Insertion bar, in notebooks, 581

Insertion box, \[Placeholder] (), 1009

Insides of three-dimensional objects, 529

Inspector, 62, 366, 707

         option, 574, 601

$Inspector, 1330

Inspiration, \[LightBulb] (), 995

Install, 216, 659, 676, 687, 1180

         path in, 659

Installation, xii, 1061

$InstallationDate, 717, 1330

$InstallationDirectory, 637, 1061, 1330

Installing Mathematica, 26

InString, 48, 702, 703, 1180

\int (TeX), \[Integral] (), 1000

int C type, 678

Integer, 722, 1017, 1180

Integer equations, Reduce, 841, 1261

Integer factoring, FactorInteger, 750, 1143

Integer sequence equations, RSolve, 891, 1269

IntegerDigits, 725, 749, 1181

         implementation of, 1067

IntegerExponent, 725, 749, 1181

IntegerList MathLink type, 665

IntegerPart, 745, 1181

IntegerQ, 267, 723, 1181

Integers, bases of, 439

         big, 30

         complex, 750

         conversion to, 746

         exact, 30

         factoring of, FactorInteger, 31, 750, 1143

         Gaussian, 750, 751

         in C, 678

         in various bases, 725

         output form for, 436

         partitions of, 759

         random, Random, 747, 1254

         set of, \[DoubleStruckCapitalZ] (), 992

         testing for, IntegerQ, 267, 1181

         testing for even, EvenQ, 267, 1137

         testing for odd, OddQ, 267, 1230

         testing for prime, PrimeQ, 267, 1250

Integers, 73, 817, 839, 1181

\[Integral] (), 184, 185, 1000, 1373

Integral representations, 769

Integral transforms, 96, 875

Integrals, elliptic, 783

         in mathematical tables, 864

         input of, 184

         manipulation of in symbolic form, 869

         multiple, 865

         standard forms for, 864

         syntax of, 470

         that cannot be done, 81, 861

Integrate, 68, 81, 82, 859, 862, 864, 865, 951, 1070, 1182

         implementation of, 1070

Integration, as inverse of differentiation, 859

         constants in, 860

         constants of, 859

         defining your own, 281

         definite, 82, 865

         errors in numerical, 952

         genericity assumptions in, 860

         indefinite, Integrate, 81, 859, 1182

         Integrate, 81, 859, 1182

         making definitions for, 864

         numerical, NIntegrate, 103, 954, 1219

         of derivatives, 869

         of power series, 886

         of rational functions, 862

         symbolic, Integrate, 81, 859, 1182

         variables in, 387, 860

Integration operators, syntax of, 1031

Intensity, GrayLevel, 499, 1165

         of sound, 566

Interactive input, dialogs, 707

Interchange format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Interchange values, Set (=), 305, 1277

Interface, command-line, 27, 48

         for Mathematica, 44

         graphical, 26, 49

         notebook, 26, 49

         test for type of, $Notebooks, 715, 1334

         text-based, 27, 48

Interfaces, creating, 598

Interfacing with Mathematica, 204

Interior faces of three-dimensional objects, 529

Interior point methods, LinearProgramming, 1068, 1195

Interline spacing, LineSpacing, 611, 1196

Intermediate expression swell, 76

Intermediate expressions, tracing, 356

Intermediate files, in MathLink, 667

Intermediate results, monitoring, StepMonitor, 977, 1290

         saving, Sow, 355, 1286

Intermediate variables, 378

Internal arithmetic, 734

Internal code of Mathematica, 76

Internal form, of expressions, 234

         of graphics, 486

         output of, FullForm, 230, 1158

Internal state, of pseudorandom generator, $RandomState, 748, 1336

Internals, of Mathematica, 218, 1066

International characters, 189, 421

         in streams, 635

         in symbol names, 1014

International keyboard, xv

International keys, superscripts on, 177

Internet address, $MachineDomain, 718, 1331

Internet ports, 682

Interparagraph spacing, ParagraphSpacing, 611, 1237

InterpolatingFunction, 105, 252, 930, 962, 1182

         implementation of, 1069

InterpolatingPolynomial, 808, 1183

Interpolation, derivatives in, 932

         multidimensional, 934

         of quantiles, Quantile, 925, 1253

Interpolation, 930, 931, 932, 933, 1183

InterpolationOrder, 933

Interpretation, setting up your own rules for, 476

Interpretation of input, ToExpression, 428, 464, 1307

InterpretationBox, 447, 1183

Interpreter, Mathematica as, 222

Interpreting input, 468

Interprocess communication, 215, 628, 657

Interquartile range, Quantile, 925, 1253

Interrupt, 371, 1184

Interrupts, 62, 370

         in MathLink, 696

         in MathLink, LinkInterrupt, 686, 1197

         inspecting state during, 707

Intersecting surfaces, 537

Intersection, 127, 1184

\[Intersection] (), 183, 1002, 1373

Interval, 740, 894, 1184

Interval arithmetic, 740

IntervalIntersection, 741, 1184

IntervalMemberQ, 741, 1184

IntervalUnion, 741, 1184

\intop (TeX), \[Integral] (), 1000

Invariance, of Mathematica, 46

Invariant subspaces, JordanDecomposition, 915, 1190

Invariants, in elliptic functions, WeierstrassInvariants, 782, 1319

Inverse, 121, 903, 905, 1185

         implementation of, 1069

Inverse CDF, Quantile, 925, 1253

Inverse functions, 89

         power series for, 888

Inverse hyperbolic functions, 761

Inverse of a matrix, Inverse, 121, 903, 1185

Inverse trigonometric functions, 761

         branch cuts in, 764

Inverse video, 504

InverseBetaRegularized, 770, 1185

InverseEllipticNomeQ, 782, 1185

InverseErf, 775, 1185

InverseErfc, 775, 1185

InverseFourier, 108, 935, 1186

InverseFourierCosTransform, 878, 1186

InverseFourierSinTransform, 878, 1186

InverseFourierTransform, 96, 876, 1187

InverseFunction, 89, 240, 253, 825, 1187

InverseFunctions, 824, 1187

InverseGammaRegularized, 770, 1188

InverseJacobiSN, 786

InverseJacobiSN, InverseJacobiCN, ..., 785, 1188

InverseLaplaceTransform, 96, 875, 1188

Inverses in finite fields, PowerMod, 752, 1248

InverseSeries, 887, 1188

InverseWeierstrassP, 785, 1188

InverseZTransform, 879, 1189

Inversion, Not (!), 87, 1221

Invisible, ReadProtected, 330, 1258

Invisible characters, 1008

Invisible contents, ShowContents, 455

Invisible notebooks, 592

Invisible selection, ShowSelection, 619, 1281

Invisible tags, in TraditionalForm, 195

Invisible windows, Visible, 620, 1319

\[InvisibleApplication] (), 183, 1008, 1373

\[InvisibleComma] (), 183, 1008, 1373

\[InvisibleSpace] (), 454, 1008, 1373

\[Iota] (), 990, 1373

Iota in APL, Range, 119, 1255

IPC, 215, 628, 657

IPX, 658

Irreducibility, of polynomials, Factor, 797, 1143

ISO Latin-1, 419, 421

ISO Latin-2, 421

ISO Latin/Cyrillic, 421

ISO standard C, 677

\it (TeX), FontSlant, 444, 612, 1151

Italian characters, 190, 998

Italic fonts, 444, 558, 612

Italicization, automatic, AutoItalicWords, 613, 1086

Italics, FontSlant, 444, 612, 1151

         single letter, SingleLetterItalics, 613, 1283

Iterated functions, Nest, 241, 349, 1217

Iterated maps, 979

Iteration, 241

         Do, 348, 1127

Iteration constructs, 112

         variables in, 390

Iteration functions, 83, 1042

         evaluation in, 343, 1046

         forcing evaluation in, 344

$IterationLimit, 369, 1048, 1330

Iterative arrays, CellularAutomaton, 942, 1101

Iterators, 83, 116, 1042

         evaluation of, 343, 1046

         locality of variables in, 1042

IVPs, NDSolve, 962, 1216



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