Documentation

Mathematica

The Mathematica Book

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

.m files, 205, 1053

.ma files, 1053

Machine arithmetic, 728, 737

Machine dependence, of file names, 639

Machine independence, 46

Machine-precision arithmetic, intervals in, 741

Machine-precision numbers, 728, 737

Machine-size numbers, in compilation, 375

$MachineDomain, 718, 1331

$MachineEpsilon, 739, 1331

MachineID, 626

$MachineID, 718, 1331

$MachineName, 718, 1331

MachineNumberQ, 728, 1203

MachinePrecision, 728, 1203

$MachinePrecision, 728, 739, 1332

$MachineType, 717, 1332

Macintosh, character encoding, 421

         file names on, 639, 1053

Macintosh (notebook interface), 26, 49

Macintosh command key, \[CloverLeaf] (), 1009

Macintosh PICT, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Maclaurin series, Series, 883, 1276

Macron mark, 998

Macros, 110

         text, $PreRead, 703, 1336

         user-defined, InputAutoReplacements, 613, 1179

         With, 380, 1323

Magenta, 500

Magic numbers, for executables, 676

Magnification, 604, 619, 1204

MagnificationPopup window element, 621

Magnitude, Abs, 745, 1075

         notation for, \[LeftBracketingBar] (), 1002

Magnitude of complex number, Abs, 746, 1075

Main directory, $InstallationDirectory, 637, 1330

Main loop, in MathLink, 685

         of Mathematica, 702, 1056

         subsidiary, 708

main(), 664, 679

         arguments to, 698

Maintain unevaluated (hold), 336

Make 2D menu item, 176, 177, 430, 461

MakeBoxes, 475, 1204

MakeExpression, 475, 1204

Manipulation, of algebraic expressions, 69, 797

         of strings, 407

         of trigonometric expressions, 811

Mantissa, 437, 1021

MantissaExponent, 726, 1204

Manual MathLink type, 665

Manufacturer, $MachineType, 717, 1332

Map (/@), 244, 245, 284, 1025, 1205

         levels in, 1041

MapAll (//@), 245, 254, 1025, 1205

MapAt, 245, 246, 1205

MapIndexed, 246, 284, 1205

         levels in, 1041

Mapping, of characters, 417

Mappings, functions as, 309

\mapsto (TeX), \[RightTeeArrow] (), 1006

MapThread, 247, 1206

Margins, around windows, WindowMargins, 620, 1322

         for cells, CellMargins, 605, 1099

         for plots, PlotRegion, 509, 1244

         of box, BoxMargins, 455

Marichev-Adamchik methods, Integrate, 1070, 1182

Marker, alignment, \[AlignmentMarker] (), 451

         cell, ShowCellBracket, 604, 1280

Markers, in data files, TokenWords, 648, 1308

Markings, on axes, Ticks, 512, 552, 1305

Markowitz products, Solve, 1068, 1285

Marks, in MathLink, 693

         in numbers, NumberMarks, 730, 1228

Markup, for web, MathMLForm, 211, 1207

Marsaglia-Zaman generator, Random, 1067, 1254

Mask, BitAnd, 756, 1089

Masking, of images, ListConvolve, 937, 1200

Master files, for packages, 640, 1065

Master index, online, 57

MAT format, exporting, Export, 208, 1141

         importing, Import, 208, 1176

Matches, non-unique, 270, 274, 1050

Matchfix operators, 468, 1021

Matching, implementation of, 1066

         of brackets, DelimiterFlashTime, 613, 1120

         of fonts, 613, 1010

         of patterns, 259, 1049

         of strings, StringMatchQ, 411, 1292

         putting constraints on, Condition (/;), 265, 1111

Matching characters, 1003

MatchLocalNames, 365, 1206

MatchQ, 268, 346, 347, 1206

Material implication, Implies, 834, 1174

Materials, reflection properties of, 547

$MATHEMATICA_BASE environment variable, 1055

$MATHEMATICA_USERBASE environment variable, 1055

\[MathematicaIcon] (), 995, 1378

Mathematical constants, 32, 765

Mathematical equivalence, Equal (==), 347, 1135

Mathematical facts, 817

Mathematical functions, general conventions for, 1043

         naming conventions for, 745

Mathematical notation, for derivatives, 856

         in notebooks, 35

         traditional, 37

         TraditionalForm, 193, 1313

Mathematical operations, 79

Mathematical physics, special functions of, 769

Mathematical relations, 281

Mathematical tables, integrals in, 864

Mathematics of computation, 327

MathieuC, 789, 1206

MathieuCharacteristicA, 789, 1206

MathieuCharacteristicB, 789, 1206

MathieuCharacteristicExponent, 789, 1207

MathieuCPrime, 789, 1207

MathieuS, 789, 1068, 1207

MathieuSPrime, 789, 1207

$MATHINIT environment variable, 1055

$MATHKERNELINIT environment variable, 1055

MathLink, 44, 216, 657

         intermediate files in, 667

MathLink files, 1053

MathLink library, listing of functions in, 1340

MathLink templates, 659

mathlink.h, 677

MathLive, 20

mathlm, 1058

MathMLForm, 211, 425, 1207

MathReader, 53

Matrices, 118, 896

         applying functions to, 244, 245

         band diagonal, 897

         columns of, 898

         columns of, Part, 120, 1238

         components of, Part, 118, 1238

         condition number of, SingularValueList, 913, 1283

         construction of, 896

         determinants of, Det, 121, 905, 1122

         diagonal, DiagonalMatrix, 120, 896, 1122

         division of, LinearSolve, 907, 1195

         eigenvalues of, Eigenvalues, 121, 910, 1131

         eigenvectors of, Eigenvectors, 121, 910, 1131

         elements of, Part, 118, 1238

         exponentials of, MatrixExp, 906, 1207

         exporting, Export, 208, 1141

         extracting columns of, 898

         extracting pieces of, 898

         extracting submatrices of, 898

         formatting of, 439

         formatting of, GridBox, 445, 1167

         formatting of, MatrixForm, 120, 1207

         from linear equations, CoefficientArrays, 922, 1105

         functions of, JordanDecomposition, 915, 1190

         generalized inverses of, PseudoInverse, 914, 1252

         generating, Array, 250, 1083

         generation of, 120, 896

         Hilbert, 121

         identity, IdentityMatrix, 120, 896, 1173

         ill-conditioned, 904

         importing, Import, 208, 1176

         input of, 186

         inversion of, Inverse, 121, 903, 1185

         Jordan decomposition of, JordanDecomposition, 915, 1190

         kernel of, NullSpace, 908, 1227

         left multiplication, Dot (.), 902, 1127

         linear programming, 975

         lower triangular, 897

         minors of, Minors, 905, 1212

         Moore-Penrose inverse of, PseudoInverse, 914, 1252

         multiplication by scalar of, 901

         multiplication by vectors of, Dot (.), 901, 1127

         multiplication of, Dot (.), 119, 901, 1127

         null spaces of, NullSpace, 907, 1227

         operations on, 900, 905

         outer products of, Outer, 901, 1234

         patterns for, 280

         powers of, MatrixPower, 906, 1208

         pseudoinverses of, PseudoInverse, 914, 1252

         QR decomposition of, QRDecomposition, 914, 1253

         random, 897

         rank of, MatrixRank, 910, 1208

         reading from data files, ReadList, 644, 1257

         rectangular, 909

         resetting parts of, 126, 285, 899

         right multiplication, Dot (.), 902, 1127

         row reduction of, RowReduce, 907, 1268

         rows of, Part, 118, 1238

         Schur decomposition of, SchurDecomposition, 915, 1271

         singular, 904

         singular value decomposition of, SingularValueDecomposition, 914, 1283

         sparse, SparseArray, 295, 920, 1287

         special types of, 897

         symbolic representation of, 902

         testing for, MatrixQ, 267, 900, 1208

         trace of, Tr, 905, 1310

         transpose of, Transpose, 121, 905, 1313

         tridiagonal, 897

         upper triangular, 897

         zero, 897

Matrix equations, 829

         existence and uniqueness of solutions, 908

         LinearSolve, 907, 1195

Matrix indices, commas between, 1008

Matrix inversion, approximate numerical, 904

         assumption of non-zero determinant in, 903

         high-precision numbers in, 904

         numerical errors in, 904

         speed of, 77

Matrix Market format, exporting, Export, 208, 1141

         Import, 923, 1176

         importing, Import, 208, 1176

Matrix pencils, Eigenvalues, 913, 1131

MatrixExp, 906, 1069, 1207

         implementation of, 1069

MatrixForm, 120, 439, 1207

MatrixPower, 906, 1208

MatrixQ, 267, 900, 1208

MatrixRank, 907, 910, 1208

         implementation of, 1069

Matte surfaces, 546

Max, 31, 129, 745, 1208

MaxBend, 138, 1208

$MaxExtraPrecision, 733, 1332

Maximal element, of list, Max, 129, 1208

Maximization, numerical, NMaximize, 106, 974, 1219

Maximize, 92, 850, 951, 1209

         implementation of, 1070

Maximum, Max, 31, 745, 1208

$MaxLicenseProcesses, 718

$MaxMachineNumber, 739, 1017, 1332

MaxMemoryUsed, 712, 713, 1209

$MaxNumber, 739, 1332

$MaxPrecision, 736, 1332

MaxRecursion, 956

MaxSteps, 966, 968

MaxStepSize, 966

mcc, 661, 677

mdefs.h, 213

Mean, 109, 794, 924, 1209

Measure of complexity, ComplexityFunction, 815, 1110

\[MeasuredAngle] (), 996, 1378

Measures (units), 78

Media (streams), 630

Median, Quantile, 795, 1253

Median, 109, 924, 1209

Medical imaging, exporting, Export, 568, 1141

         importing, Import, 570, 1176

\[MediumSpace] (), 454, 1008, 1378

Megabytes, of memory used, 713

MeijerG, 780, 872, 1209

Mellin transform, program for, 18

Mellin transform methods, DSolve, 1071, 1129

         Integrate, 1070, 1182

MemberQ, 124, 268, 1210

Membership test, MemberQ, 124, 1210

Memo functions, 314

Memory, allocation by Mathematica, 712

         arrangement of expressions in, 221

         disowning in MathLink, 674

         in infinite loops, 370

         limitations imposed by size of, 75

         optimizing use of, 714

         saving, 703

         used by expressions, ByteCount, 714, 1095

Memory allocation, in MathLink, 667

Memory management, 221, 712, 1066

MemoryConstrained, 713, 1210

MemoryInUse, 712, 1210

Menu, interrupt, 62

         palettes, 35

Menu item, for creating arrays, 186

Menu settings, for front end, 622

Menus, executing from kernel, FrontEndTokenExecute, 593

Merging lists, Union, 126, 1315

Mesh, 148, 151, 517, 539, 540, 1210

MeshRange, 539, 1210

MeshStyle, 503, 517, 539, 1210

Message, 482, 1211

         channel for, 633

Message options, for front end, 622

MessageList, 481, 702, 1211

$MessageList, 481, 709, 1333

MessageName (::), 479, 1024, 1211

MessageOptions, 592

MessagePacket, 684, 700

$MessagePrePrint, 480, 706, 1333

Messages, 61, 479

         about new symbols, 404

         checking for, Check, 481, 1102

         full form of, $MessagePrePrint, 706, 1333

         in object-oriented programming, 319

         international, 483, 706

         languages for, $Language, 706, 1331

         preprocessing of, $MessagePrePrint, 706, 1333

         suppressing, 61, 479

         switching off, 61, 479

         switching on, 61, 479

         symbol creation, 1015

         tracing of, Trace, 358, 1310

         usage, 484

Messages, 479, 1052, 1211

$Messages, 705, 1333

Messaging mechanisms, 657

Metacharacters, 58, 411

         in file names, 637, 1053

Metafile format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Metallic surfaces, 547

Method, 978

Method of lines, NDSolve, 1068, 1216

Method of undetermined coefficients, SolveAlways, 833, 1285

Methods, in object-oriented programming, 319

Metric, Norm, 119, 1221

Metric tensors, 915

MGF graphics format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

\[Mho] (), 994, 1378

\[Micro] (), 192, 984, 994, 1378

Microsoft metafile format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Microsoft wave format, exporting, Export, 569, 1141

         importing, Import, 570, 1176

Microsoft Windows, character encoding, 421

         files in, DOSTextFormat, 1054

Microsoft Windows (notebook interface), 26, 49

Microsoft Word, 20

\mid (TeX), \[VerticalBar] (), 1005

Miller-Rabin test, PrimeQ, 1067, 1250

Min, 31, 129, 745, 1212

Minimal element, of list, Min, 129, 1212

Minimal polynomial, 826

Minimax approximations, 1068

Minimization, errors in numerical, 953

         exact, Minimize, 850, 1212

         numerical, FindMinimum, 973, 1148

         numerical, NMinimize, 106, 974, 1220

Minimize, 92, 850, 851, 852, 1070, 1212

         implementation of, 1070

Minimum, Min, 31, 745, 1212

$MinMachineNumber, 739, 1017, 1333

$MinNumber, 739, 1333

Minors, 905, 1212

$MinPrecision, 736, 1333

MinRecursion, 956

Minus (-), 29, 1027, 1212

\[MinusPlus] (), 1000, 1378

Minute, Date, 709, 1117

Minutes, \[Prime] (), 996, 1250

Mirrors, 547

Mistakes, common, 34, 39

         syntax, 51

Mixing text and formulas, 196

mkdir command, CreateDirectory, 641, 1116

.ml files, 1053

MLAbort, 697, 1341

MLActivate(), 698, 1341

MLCheckFunction(), 672, 1341

MLClearError(), 696, 1341

MLClose(), 692, 698, 1341

MLCreateMark(), 693, 1341

MLDeinitialize(), 698, 1341

MLDestroyMark(), 693, 1342

MLDisownByteString(), 679, 1342

MLDisownIntegerArray(), 675, 1342

MLDisownIntegerList(), 674, 1342

MLDisownRealArray(), 675, 1342

MLDisownRealList(), 674, 1342

MLDisownString(), 675, 1342

MLDisownSymbol(), 675, 676, 1342

MLDisownUnicodeString(), 679, 1343

MLEndPacket(), 689, 699, 1343

MLENV, 1340

MLError(), 696, 1343

MLErrorMessage(), 696, 1343

MLEvaluateString(), 664, 689, 1343

MLFlush(), 700, 1343

MLGetArgCount(), 694, 1343

MLGetByteString(), 679, 1344

MLGetDouble(), 678, 1344

MLGetFloat(), 678, 1344

MLGetFunction(), 676, 1344

MLGetInteger(), 671, 694, 1344

MLGetIntegerArray(), 675, 1345

MLGetIntegerList(), 674, 1345

MLGetLongInteger(), 678, 1345

MLGetNext(), 694, 1345

MLGetReal(), 671, 694, 1345

MLGetRealArray(), 675, 1346

MLGetRealList(), 674, 1346

MLGetShortInteger(), 678, 1346

MLGetString(), 675, 679, 694, 1346

MLGetSymbol(), 675, 694, 1346

MLGetUnicodeString(), 679, 1346

MLInitialize(), 698, 1347

MLINK, 1340

MLLoopbackOpen(), 692, 1347

MLMain(), 664, 679, 1347

MLMARK, 1340

MLNewPacket(), 697, 699, 1347

MLNextPacket(), 699, 1347

MLOpenArgv(), 698, 1347

MLOpenString(), 698, 1348

MLPROTOTYPES, 677

MLPutArgCount(), 696, 1348

MLPutByteString(), 679, 1348

MLPutDouble(), 678, 1348

MLPutFloat(), 678, 1348

MLPutFunction(), 667, 1348

MLPutInteger(), 667, 696, 1348

MLPutIntegerArray(), 667, 1349

MLPutIntegerList(), 667, 1349

MLPutLongInteger(), 678, 1349

MLPutNext(), 696, 1349

MLPutReal(), 667, 696, 1349

MLPutRealArray(), 667, 1349

MLPutRealList(), 667, 1349

MLPutShortInteger(), 678, 1350

MLPutString(), 667, 679, 696, 1350

MLPutSymbol(), 667, 696, 1350

MLPutUnicodeString(), 679, 1350

MLReady(), 700, 1350

MLSeekMark(), 693, 1350

MLTK constants, 695

MLTransferExpression(), 692, 1350

Mnemonic, ButtonNote, 597, 1094

Mobius function, MoebiusMu, 752, 1214

Mobius inversion formula, 753

Mod, 31, 749, 809, 1213

ModalDialog window frame option, 621

ModelessDialog window frame option, 621

Modeling lights, AmbientLight, 545, 1079

Models, determination of parameters in, Fit, 929, 1149

         discrete, CellularAutomaton, 942, 1101

         \[DoubleRightTee] (), 1007

\models (TeX), \[DoubleRightTee] (), 1007

Modem, 27

Modification date, for files, FileDate, 641, 1145

Modified names, 989

Modifier keys, 1009

Modifiers, input of, 188

Modifying built-in functions, 321

Modular angle, in elliptic functions, 782

Modular equations, Reduce, 843, 1261

Modular functions, elliptic, 787

Modular inverses, PowerMod, 752, 1248

Modular powers, PowerMod, 752, 1248

Modular root, of unity, MultiplicativeOrder, 752, 1214

ModularLambda, 787, 1213

Module, 112, 378, 386, 389, 391, 1213

         evaluation of, 384

$ModuleNumber, 381, 1333

Modules, compared with blocks, 391

         full story on, 381

Moduli, polynomial, PolynomialMod, 804, 1246

Modulo, Mod, 31, 749, 1213

Modulus, 31

         Abs, 34, 745, 746, 1075

         in elliptic functions, 782

Modulus, 809, 1213

MoebiusMu, 752, 1214

Monitor escapes, 629

Monitoring, algorithms, 977

         of program execution, 356

Monitoring evaluation, in real time, TracePrint, 365, 1312

monitorlm, 1060

Monochrome display, ColorOutput, 564, 1106

         graphics on, 563

Monte Carlo integration, NIntegrate, 957, 1219

Monte Carlo methods, 31, 748

MonteCarlo, 1068

Month, Date, 709, 1117

Moore-Penrose inverse, PseudoInverse, 914, 1252

Most, 123, 1214

Motion keys, 176, 180

Mouse input, 51

Mouse selection, in two-dimensional expressions, 180

MovableModalDialog window frame option, 621

Move selection, SelectionMove, 582, 1275

Movies, 51, 170, 617

Moving, of windows, WindowMovable, 620, 1322

Moving around, on screen, 176

Moving averages, ListCorrelate, 937, 1201

Moving directories, RenameDirectory, 641, 1262

Moving files, RenameFile, 641, 1262

Moving graphics object, Offset, 507, 1230

\mp (TeX), \[MinusPlus] (), 1000

mprep, 661

MPS, importing, Import, 570, 1176

MS-DOS, files in, DOSTextFormat, 1054

MS-DOS (text-based interface), 27, 48

MTX format, exporting, Export, 208, 1141

         Import, 923, 1176

         importing, Import, 208, 1176

\[Mu] (), 175, 984, 990, 1378

Mu law format, exporting, Export, 569, 1141

         importing, Import, 570, 1176

Mu operator, FixedPoint, 241, 1149

         Select, 251, 1273

MultiDimensional, 1068

Multifrontal methods, LinearSolve, 1069, 1195

Multiline expressions, 1037

MultilineFunction, 459

Multinomial, 757, 758, 1214

Multinormal distribution, 109

Multiple angle formulas, TrigReduce, 71, 811, 1314

Multiple arguments, applying functions with, MapIndexed, 246, 1205

         matching of, 272

Multiple curves, styles of, PlotStyle, 503, 1244

Multiple derivatives, input of, 186

Multiple functions, plots of, 132

Multiple integrals, Integrate, 82, 1182

Multiple invocations, of external programs, 687

Multiple matches for patterns, ReplaceList, 302, 1263

Multiple parts, picking out, Part, 235, 1238

         replacing, ReplacePart, 235, 1263

Multiple-valued functions, 764

Multiplication, notation for, 35

         of matrices, Dot (.), 119, 1127

         patterns involving, 270

         represented by spaces, 1032

Multiplicative properties, 818

MultiplicativeOrder, 752, 1214

Multiplicity, Count, 124, 261, 1115

         of eigenvalues, 911

         of roots, 823

Multiply, Times (*), 29, 1306

Multivalued functions, 762

Multivariate differential equations, DSolve, 874, 1129

Multivariate hypergeometric function, AppellF1, 781, 1080

Multivariate normal distribution, 109

Music, 171

Musical notation, 996

mv Unix command, RenameFile, 641, 1262

.mx files, 205, 627, 640, 1053