Documentation

Mathematica

The Mathematica Book

The Mathematica Book, version 5.0

Browsable Index

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C

D

E

F

G

H

I

J

K

L

M

N

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P

Q

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T

U

V

W

X

Y

Z

\L (TeX), \[CapitalLSlash] (), 998

\l (TeX), \[LSlash] (), 998

L-series, LerchPhi, 774, 1193

L'Hospital's rule, 893

Label, for window, WindowTitle, 620, 1322

Label, 354, 1190

Labeling, of three-dimensional graphics, 548

         of two-dimensional graphics, 511

Labels, for cells, CellLabel, 607, 1099

         formats for, StyleForm, 558, 1295

         in graphics, 560

         in notebooks, 38

         in tables, TableHeadings, 443, 1300

         on axes, AxesLabel, 134, 512, 1087

         on plots, PlotLabel, 134, 511, 1243

Ladder form, of matrices, RowReduce, 907, 1268

Lagarias-Miller-Odlyzko algorithm, Prime, 1067, 1250

Lagrangian density, \[ScriptCapitalL] (), 992

Laguerre functions, LaguerreL, 778, 1191

LaguerreL, 766, 778, 1191

\[Lambda] (), 175, 990, 1374

Lambda expressions, Function (&), 249, 1159

Lambda function, Carmichael, CarmichaelLambda, 752, 1096

Lambert W function, ProductLog, 781, 1252

Lambert's law, 547

Lamina, Polygon, 520, 1245

\land (TeX), \[And] (), 1001, 1079

Landscape mode, ImageRotated, 569, 1174

\langle (TeX), \[LeftAngleBracket] (), 1002

Language, 592

$Language, 483, 706, 1331

Language options, for front end, 622

Language specification, 232, 467, 1018, 1023

LanguageCategory, 613, 1191

Languages, character sets for various, $CharacterEncoding, 421, 1327

         for messages, 483, 706

         traditional computer, 36

LAPACK, 1069

         Eigensystem, 910, 1130

Laplace transform, discrete, ZTransform, 879, 1325

LaplaceTransform, 96, 875, 1191

Laplacian, \[Del] (), 1000

Laptop computers, styles for, ScreenStyleEnvironment, 197, 1272

Larger, Greater (>), 86, 1166

Largest, Max, 31, 129, 745, 1208

         position of, Ordering, 129, 1233

Las Vegas integration, NIntegrate, 957, 1219

Laserprinter, copy of notebook, NotebookPrint, 591, 1224

Last, 122, 1191

Last result, 38

Lattice bottom, \[UpTee] (), 1007

LatticeReduce, 752, 754, 1067, 1191

         implementation of, 1067

$LaunchDirectory, 637

Launching programs, in MathLink, LinkLaunch, 683, 1197

Laurent series, Series, 883, 1276

Laws of form, Nand, 87, 1215

Layout, of output, 444

         of palettes, 452

         of plots, GraphicsArray, 139, 1165

Lazy evaluation (delayed assignment), 311

Lazy S, \[Tilde] (), 1003

\lbrace (TeX), \[RawLeftBrace] ({), 1010

\lceil (TeX), \[LeftCeiling] (), 1002

LCM, 749, 1192

\ldots (TeX), \[Ellipsis] (), 996

\le (TeX), \[LessEqual] (), 1004, 1193

Leading, between cells, CellMargins, 605, 1099

         LineSpacing, 611, 1196

Leading digits, in output of numbers, 437

LeafCount, 714, 1192

Learning Mathematica , suggestions about, xiii

Least common multiple, LCM, 749, 1192

Least fixed point, FixedPoint, 241, 1149

Least integer function, Ceiling, 745, 1096

Least universal exponent, CarmichaelLambda, 752, 1096

Least-squares fits, FindFit, 108, 1146

         Fit, 926, 929, 1149

Leaves, in expression trees, 237, 239

         of parse tree, 467

Lebesgue integration, DiracDelta, 879, 1124

Left, 442, 450

\left (TeX), 456

Left aligned, TextAlignment, 610, 1303

Left justification, TextJustification, 610, 1303

Left shift, RotateLeft, 127, 291, 1266

\[LeftAngleBracket] (), 191, 1002, 1374

\[LeftArrow] (), 1006, 1374

\Leftarrow (TeX), \[DoubleLeftArrow] (), 1006

\leftarrow (TeX), \[LeftArrow] (), 1006

\[LeftArrowBar] (), 1006, 1374

\[LeftArrowRightArrow] (), 1006, 1374

\[LeftBracketingBar] (), 987, 1002, 1374

\[LeftCeiling] (), 1002, 1374

\[LeftDoubleBracket] (), 184, 1002, 1374

\[LeftDoubleBracketingBar] (), 1002, 1375

\[LeftDownTeeVector] (), 1007, 1375

\[LeftDownVector] (), 1007, 1375

\[LeftDownVectorBar] (), 1007, 1375

\[LeftFloor] (), 1002, 1375

\[LeftGuillemet] (), 996, 1375

\leftharpoonup (TeX), \[LeftVector] (), 1007

\[LeftModified] (), 1009, 1375

\[LeftRightArrow] (), 191, 1006, 1375

\Leftrightarrow (TeX), \[DoubleLeftRightArrow] (), 1006

\leftrightarrow (TeX), \[LeftRightArrow] (), 1006

\[LeftRightVector] (), 1007, 1375

\[LeftSkeleton] (), 1009, 1375

\[LeftTee] (), 1001, 1007, 1376

\[LeftTeeArrow] (), 1006, 1376

\[LeftTeeVector] (), 1007, 1376

\[LeftTriangle] (), 1005, 1376

\[LeftTriangleBar] (), 1005, 1376

\[LeftTriangleEqual] (), 1005, 1376

\[LeftUpDownVector] (), 1007, 1376

\[LeftUpTeeVector] (), 1007, 1376

\[LeftUpVector] (), 1007, 1376

\[LeftUpVectorBar] (), 1007, 1376

\[LeftVector] (), 1007, 1376

\[LeftVectorBar] (), 1007, 1376

Legendre functions, LegendreP, 777, 1192

Legendre polynomials, associated, LegendreP, 766, 1192

         LegendreP, 766, 1192

Legendre symbol, JacobiSymbol, 752, 1189

Legendre-Jacobi elliptic integrals, 783

LegendreP, 766, 777, 778, 1192

LegendreQ, 777, 1192

Legends on plots, 560

         PlotLabel, 134, 511, 1243

Length, of a vector, Norm, 119, 1221

         of files, FileByteCount, 641, 1145

         of numbers, Precision, 727, 1249

         of strings, StringLength, 407, 1291

Length, 75, 119, 236, 1192

Lengths, of pages, 609

Lenstra-Lenstra-Lovasz algorithm, LatticeReduce, 754, 1067, 1191

\leq (TeX), \[LessEqual] (), 1004, 1193

Lerch transcendent, LerchPhi, 773, 1193

LerchPhi, 772, 773, 774, 1193

Less (<), 86, 1027, 1193

LessEqual (<=), 86, 1027, 1193

\[LessEqual] (), 182, 1004, 1377

\[LessEqualGreater] (), 1004, 1377

\[LessFullEqual] (), 1004, 1377

\[LessGreater] (), 1004, 1377

\[LessLess] (), 1004, 1377

\lesssim (TeX), \[LessTilde] (), 1004

\[LessSlantEqual] (), 1004, 1377

\[LessTilde] (), 1004, 1377

Letter-like forms, 984, 1351

LetterQ, 413, 1193

Letters, capital, 31

         Greek, 174

         of alphabet, CharacterRange, 413, 417, 1102

         operations on, 413

Level, 239, 1193

Levels, 237, 1041

         for cell options, 600

         in contour plots, Contours, 519, 1113

         in expressions, 1014

         in Inner, 920

         in lists, 129

         in Map, 245

         in Outer, 920

         in Position, 238

         negative, 239, 1041

         permuting, Transpose, 290, 1313

Levenberg-Marquardt method, FindMinimum, 1068, 1148

Levi-Civita symbol, Signature, 760, 1282

Lexical analysis, in box input, 462, 1036

Lexical scoping, Module, 391, 1213

\lfloor (TeX), \[LeftFloor] (), 1002

Library, MathLink, 658, 1340

Library (packages), 59

Library directory, $BaseDirectory, 637, 1325

$LicenseExpirationDate, 718

$LicenseID, 718

$LicenseProcesses, 718

Licenses, network, 1058

$LicenseServer, 718

Lie derivative, \[Sterling] (), 994

Life, programs for Game of, 18

Light sources, coordinate system for, 546

         default arrangement of, 545

\[LightBulb] (), 995, 1377

Lighting, 151, 155, 526, 544, 1194

LightSources, 545, 1194

Limit, on iteration, $IterationLimit, 369, 1330

         on process number, $MaxLicenseProcesses, 718

         on recursion, $RecursionLimit, 369, 1337

Limit, 95, 893, 1194

Limitations, on patterns, Conditions, 265

Limiting factors, in calculations, 76

Limiting functions, DiracDelta, 879, 1124

Limits, directional, 894

         for sums, 184

         formatting of, 458

         formatting of, UnderoverscriptBox, 445, 1314

         functions with definite, 894

         in integrals, 866

         infinite, 743

         of unknown functions, 895

LimitsPositioning, 458, 1194

LimitsPositioningTokens, 459

Line, 492, 520, 1195

         in three dimensions, 525

$Line, 702, 703, 1056, 1331

         in dialogs, 708

Line breaking, in expressions, 459

         \[NonBreakingSpace] (), 1008

Line breaks, 431

         in strings, 415

Line continuation, 1038

Line feed, 415, 1037

Line length, output, PageWidth, 634, 1237

Line number, $Line, 1056, 1331

Line numbers, 38

         in cells, CellLabel, 607, 1099

         in notebooks, 50

         preserving, CellLabelAutoDelete, 607, 1099

Linear algebra, 896

         speed of, 77

Linear congruences, CarmichaelLambda, 752, 1096

Linear differential equations, DSolve, 871, 1129

Linear equations, 90, 820

         matrices from, CoefficientArrays, 922, 1105

         over integers, 842

Linear expressions, patterns for, 280

Linear fits, Fit, 926, 1149

Linear programming, 975

         exact, Minimize, 92, 851, 1212

         NMinimize, 106, 974, 1220

Linear syntax, for boxes, 1036

Linear systems, repeated solution of, LUDecomposition, 914, 1203

         solution of, LinearSolve, 907, 1195

Linearity, property of functions, 255

LinearProgramming, 975, 1068, 1195

         implementation of, 1068

LinearSolve, 907, 1069, 1195

         implementation of, 1069

LinearSolveFunction, 252, 1196

\linebreak (TeX), \[NewLine] (), 460

LineIndent, 1196

LineIndentMaxFraction, 1196

Lines, colored, PlotStyle, 138, 1244

         colors of in three dimensions, 528

         continuation, 48

         dashed, PlotStyle, 138, 1244

         dashing of, Dashing, 501, 1117

         grid in plots, GridLines, 515, 1167

         in contour plots, ContourLines, 519, 1113

         in tables, RowLines, 446, 1268

         input, In, 702, 1177

         length of, PageWidth, 634, 1237

         multiple, 48

         numbering of in dialogs, 708

         output, Out (%), 702, 1234

         previous output, Out (%), 38, 1234

         styles for, 501

         styles of, PlotStyle, 138, 503, 1244

         thickness of, Thickness, 501, 1304

         through points, PlotJoined, 159, 1243

Lines of text, exporting, Export, 643, 1141

         importing, Import, 643, 1176

LineSpacing, 611, 1196

LinkClose, 680, 1196

LinkConnect, 680, 691, 1197

LinkCreate, 680, 1197

$Linked, 1331

Linked lists, Reap, 284, 355, 1259

Linking, Mathematica sessions, 680

LinkInterrupt, 686, 1197

LinkLaunch, 683, 1197

LinkObject, 659, 687, 1198

LinkPatterns, 662, 1198

LinkProtocol, 677, 1198

LinkRead, 680, 1198

LinkReadyQ, 680, 681, 1198

Links, in notebooks, 56

         via MathLink, 657

Links, 662, 1198

LinkWrite, 680, 1199

LINPACK, Inverse, 903, 1185

         LinearSolve, 907, 1195

         LUDecomposition, 914, 1203

LISP, bigfloats, 731

         bignums, 33

         dynamic scoping in, 391

         gensym in, Unique, 382, 1316

         in MathLink, 658

         pure functions in, 249

         quote in, Hold, 338, 1169

Lissajous figures, ParametricPlot, 162, 1237

List, 40, 42, 115, 118, 232, 1199

List brackets, 1022

Listability, implementing, Thread, 256, 1304

Listable, 329, 332, 900, 1043, 1199

ListContourPlot, 159, 487, 1199

ListConvolve, 937, 1200

         implementation of, 1069

ListCorrelate, 937, 1201

         implementation of, 1069

ListDensityPlot, 159, 487, 1201

Listen on link, LinkCreate, 680, 1197

Listener, Mathematica, 702, 1056

Listing, of symbol names, Names, 403, 1215

ListInterpolation, 934, 1201

ListPlay, 172, 565, 1201

ListPlot, 158, 159, 487, 1202

ListPlot3D, 159, 487, 537, 542, 1202

ListPlotVectorField, 168

Lists, adding elements to, 125, 288

         alphabetizing, Sort, 127, 1286

         appending elements to, Append, 125, 288, 1080

         applying functions to, 115

         applying functions to specific elements of, MapAt, 246, 1205

         arbitrary length in MathLink, 670

         arithmetic on, 40

         as arrays, 307

         as collections of objects, 115

         as matrices, 118, 899

         as sets, 126

         as tensors, 915

         as vectors, 118

         assignments to, Set (=), 305, 1277

         automatic threading over, Listable, 329, 1199

         blocks in, Partition, 292, 1240

         building up iteratively, 306

         combining, Union, 126, 1315

         common elements in, Intersection, 127, 1184

         concatenating, Join, 126, 1190

         creating, 283

         creating nested, 116

         deleting elements from, Delete, 125, 288, 1119

         deleting elements from, Drop, 123, 287, 1128

         difference between, Complement, 127, 1109

         distinct elements in, Union, 127, 1315

         elements of, 41

         exporting, Export, 643, 1141

         extracting elements from, 41, 117

         extracting ranges of elements in, 123, 287

         finding structure of, 124

         flattening of, Flatten, 130, 1150

         formatting of, 439

         generation from functions, 250

         generation of, Table, 115, 1299

         grouping elements in, Partition, 128, 292, 1240

         growing, Sow, 355, 1286

         importing, Import, 643, 1176

         in MathLink, 665

         indices in, 118

         inserting elements in, Insert, 125, 288, 1180

         intersection of, Intersection, 127, 1184

         joining, Join, 126, 1190

         last element of, Last, 122, 1191

         levels in, 129

         manipulating, 283

         manipulation by name, 306

         maximum in, Max, 129, 1208

         minimum in, Min, 129, 1212

         multidimensional, 116

         nested, 289

         nesting depth, ArrayDepth, 916, 1083

         of graphics elements, 499

         of lists, 116

         of parts in expressions, Part, 235, 1238

         of random numbers, 116

         of rules, 299

         operations on, 115

         ordering, Sort, 127, 129, 1286

         ordering in, Ordering, 129, 1233

         pairing of elements in, Partition, 128, 292, 1240

         partitioning in, Partition, 292, 1240

         parts of, Part, 285, 1238

         patterns for, 260, 278, 280

         picking out sequences of elements, Take, 123, 287, 1301

         pieces of, 122

         plotting, ListPlot, 158, 1202

         prepending elements to, Prepend, 125, 288, 1250

         rearranging, 127

         rearranging nested, 129

         removing elements from, Drop, 123, 287, 1128

         replacing parts of, ReplacePart, 125, 288, 1263

         resetting parts of, 42, 125

         reversal of, Reverse, 127, 1265

         rotation of, RotateLeft, 127, 291, 1266

         searching for sublists in, ReplaceList, 263, 302, 1263

         segments of, Take, 123, 287, 1301

         selecting parts based on criteria, Select, 251, 1273

         sorting of, Sort, 127, 129, 1286

         sparse, SparseArray, 295, 1287

         splitting elements in, Split, 128, 292, 1288

         testing for as matrices, MatrixQ, 267, 1208

         testing for as vectors, VectorQ, 267, 1318

         tests for elements in, MemberQ, 124, 1210

         threading over, Thread, 256, 1304

         transposition of, Transpose, 130, 290, 1313

         with specified dimensions, Array, 250, 1083

         wrapping functions around elements of, Map (/@), 245, 1205

         zero length, 1022

Lists of functions, plotting, 132

Literal patterns, Verbatim, 278, 1318

Lithography, exporting for, Export, 569, 1141

Lithography format, importing from, Import, 570, 1176

\ll (TeX), \[LessLess] (), 1004

LLL algorithm, LatticeReduce, 1067, 1191

\lnot (TeX), \[Not] (), 1001, 1221

Loadable files, directories for, 1063

Loaded packages, list of, $Packages, 397, 1335

Loading files, Get (<<), 623, 1162

Loading of packages, automatic, 401

Loading packages, 59, 640

         Get (<<), 400, 1162

Local constants, With, 380, 1323

Local functions, 378

Local links, 692

Local maxima, 106

Local minima, 106

Local minimization, FindMinimum, 973, 1148

Local values, Block, 389, 1091

Local variables, 112, 378

         in dialogs, DialogSymbols, 708, 1123

         tracing, 364

Localization, of pseudorandom sequences, $RandomState, 748, 1336

Location, in notebooks, NotebookLocate, 585, 1223

         of data, Mean, 924, 1209

Locked, 329, 331, 1044, 1202

Locking, position of window, WindowMovable, 620, 1322

Locking cells, Editable, 607, 1130

Locking notebooks, Editable, 619, 1130

Log, 31, 761, 1202

Log file, for network licenses, 1059

Logarithm, discrete, MultiplicativeOrder, 752, 1214

         generalization of, ProductLog, 781, 1252

Logarithmic integral, LogIntegral, 774, 1203

Logarithms, base of natural, E, 32, 765, 1130

         bases of, 761

         branch cuts in, 763

         exact, 33

         expansion of, PowerExpand, 798, 1248

         Log, 31, 761, 1202

LogGamma, 770, 1202

Logging, of network license manager, 1060

Logging off from Mathematica, Quit, 28, 1057, 1254

Logic expressions, input of, 183, 1001

Logic programming, 847

Logical and, \[Wedge] (), 1002

Logical connectives, 87

Logical operations, 86

         argument evaluation in, 1046

         evaluation in, 347

Logical or, \[Vee] (), 1002

LogicalExpand, 87, 819, 829, 889, 1203

Login name, $UserName, 716, 1339

LogIntegral, 774, 1203

LogListPlot, 168

LogLogListPlot, 168

LogLogPlot, 168

LogNormalDistribution, 794

LogPlot, 168

long C type, 678

Long characters, 998

Long input, 48

Long numbers, 33

\[LongDash] (), 996, 1377

\[LongEqual] (), 183, 985, 1003, 1377

\[LongLeftArrow] (), 1006, 1377

\Longleftarrow (TeX), \[DoubleLongLeftArrow] (), 1006

\longleftarrow (TeX), \[LongLeftArrow] (), 1006

\[LongLeftRightArrow] (), 1006, 1377

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

\longleftrightarrow (TeX), \[LongLeftRightArrow] (), 1006

\[LongRightArrow] (), 191, 1006, 1377

\Longrightarrow (TeX), \[DoubleLongRightArrow] (), 1006

\longrightarrow (TeX), \[LongRightArrow] (), 1006

Lookahead, inhibiting, HoldAllComplete, 340, 1169

Lookalike characters, 984

Loopback links, 692

Loops, 348

         avoiding, xiv

         exiting, Break, 353, 1092

         infinite, 369

         nested, 348

Looseness, of lines, LineSpacing, 611, 1196

Loosening formatting, 454

\lor (TeX), \[Or] (), 1001, 1233

Lorenz equations, 968

Lotus 1-2-3 format, exporting, Export, 208, 642, 1141

         importing, Import, 208, 642, 1176

Low-precision numbers, 728

Lower-case letters, 40, 1014

LowerCaseQ, 413, 1203

\[LowerLeftArrow] (), 1006, 1378

\[LowerRightArrow] (), 1006, 1378

Lowest, Min, 31, 745, 1212

Lowest terms, cancellation to, GCD, 750, 1161

Lozenge, \[Diamond] (), 1002

LP (linear programming), 975

         Minimize, 851, 1212

lpr, 215

\lq (TeX), \[RawBackquote] (`), 1010

ls, FileNames, 206, 638, 1145

ls -l Unix command, FileByteCount, 641, 1145

\[LSlash] (), 998, 1378

LSODA, NDSolve, 1068, 1216

Lucas test, PrimeQ, 1067, 1250

LUDecomposition, 914, 1203

         implementation of, 1069

Lyapunov exponent, 979