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

E, 32, 765, 1130

         implementation of, 1067

e format, 29

\[EAcute] (), 190, 998, 1367

\[EBar] (), 998, 1367

EBCDIC, preprocessing, $PreRead, 703, 1336

Echelon form, of matrices, 914

         of matrices, RowReduce, 907, 1268

$Echo, 705, 1328

echo Unix command, 628

\[ECup] (), 998, 1367

EdgeForm, 528, 1130

Edges, of cells, CellMargins, 605, 1099

Edges of plot, labeling, 514

Edit Button menu item, 595

Edit Style Sheet menu item, 574, 602

Editable, 448, 574, 607, 619, 1130

EditBar toolbar element, 622

Editing, in TraditionalForm, 195

         of strings, StringReplace, 410, 1292

         of two-dimensional expressions, 180

         output in notebooks, 50

Editing operations, DragAndDrop, 615, 1128

Edition, changes since earlier, 1402

\[EDoubleDot] (), 998, 1367

ee, \[ExponentialE] (), 988

Efficiency, compilation for increasing, 372

         Compile, 213, 1109

         in forcing evaluation in iteration functions, 344

         in tracing, 362

         measurements of, Timing, 711, 1306

         of applying rules, Dispatch, 303, 1125

         of building up lists, 306

         of plots, 138

         of Simplify, 69, 814

         of using upvalues, 317

Efficiency of algorithms, 220

\[EGrave] (), 190, 998, 1367

\[EHat] (), 998, 1367

Eigensystem, 910, 1130

Eigenvalues, difficulty of finding explicit forms for, 911

         for non-symmetric matrices, 911

         number of, 911

         numerical, Eigenvalues, 122, 910, 1131

Eigenvalues, 121, 122, 910, 912, 913, 1069, 1131

         implementation of, 1069

Eigenvectors, independence of, 911

         number of, 911

         numerical, Eigenvectors, 910, 1131

Eigenvectors, 121, 910, 1131

         implementation of, 1069

Einstein summation convention, 388

EISPACK, Eigensystem, 910, 1130

Elapsed time, SessionTime, 710, 1277

Electrical engineering, 776, 936

Electron wave functions, MathieuS, 789, 1207

Electronic documents, 44

Element, 73, 816, 1132

\[Element] (), 182, 191, 984, 1001, 1004, 1367

Element spacings, for cells, CellElementSpacings, 605

Elementary cellular automata, CellularAutomaton, 942, 1101

Elementary functions, 761

Elements, in power series, SeriesCoefficient, 889, 1276

         in window, WindowElements, 620, 1321

         of expressions, 236, 1014

         of expressions, Part, 234, 1238

         of lists, Part, 117, 1238

         satisfying criterion, Select, 251, 1273

         specifications of sequences of, 1040

Elided arguments, 273

Eliminate, 90, 832, 1132

Eliminating variables, Eliminate, 90, 832, 1132

Elimination, Gaussian, LUDecomposition, 914, 1203

         Gaussian, RowReduce, 907, 1268

Elimination basis, GroebnerBasis, 803, 1168

\ell (TeX), \[ScriptL] (), 992

Ellipse, Circle, 496, 1103

\[Ellipsis] (), 996, 997, 1367

Elliptic curve equations, 842

Elliptic functions, 785

         double periodicity of, 786

         solving equations with, 827

Elliptic integral of first kind, EllipticF, 783, 1132

Elliptic integral of second kind, EllipticE, 783, 1132

Elliptic integral of third kind, EllipticPi, 784, 1133

Elliptic integrals, 783

Elliptic modular functions, 787

Elliptical blob, during input, ShowCursorTracker, 613, 1072, 1281

Elliptical geometries, MathieuS, 789, 1207

EllipticE, 783, 1132

EllipticExp, 788, 1132

EllipticF, 783, 1132

EllipticK, 783, 1132

EllipticLog, 788, 1133

EllipticNomeQ, 782, 1133

EllipticPi, 783, 784, 1133

EllipticTheta, 785, 786, 1133

EllipticThetaPrime, 785, 1133

Elongation, of plots, AspectRatio, 509, 1084

Else, If, 345, 1173

em, 453

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

Embedded formulas, 196

Embedded information, in formatted expressions, 431

Embedded Mathematica kernels, 46

Embedding, of boxes in strings, 461

emf, \[ScriptCapitalE] (), 992

Emphasis, FontWeight, 444, 612, 1152

Empirical distribution, Quantile, 925, 1253

Empty boxes, \[Placeholder] (), 1008

Empty bracket, \[LeftDoubleBracket] (), 1002

Empty list, 1022

Empty notebook, NotebookCreate, 592, 1222

\[EmptyCircle] (), 995, 1367

\[EmptyDiamond] (), 995, 1368

\[EmptyDownTriangle] (), 995, 1368

\[EmptyRectangle] (), 995, 1368

\[EmptySet] (), 192, 984, 994, 1368

\emptyset (TeX), \[EmptySet] (), 994

\[EmptySmallCircle] (), 995, 1368

\[EmptySmallSquare] (), 995, 1368

\[EmptySquare] (), 995, 1368

\[EmptyUpTriangle] (), 995, 996, 1368

en, 453

Encapsulated PostScript, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Enclosures, around cells, CellFrame, 604, 1098

Encode, FromDigits, 725, 1158

Encode, 626, 1133

Encoding, character, $CharacterEncoding, 420, 1327

         of characters, 417

         run length, Split, 128, 292, 1288

Encryption, of files, 626

End, 398, 400, 1134

End conditions, in rules, 310

End of proof, \[FilledRectangle] (), 995

End-of-file character, 706, 1057

Endian, big and little, 678

         big and little, $ByteOrdering, 717, 1326

Ending, dialogs, 707

Ending input, 48

Ending Mathematica, Quit, 28, 1057, 1254

Endless loops, 369

EndOfFile, 649, 1134

EndPackage, 398, 1134

Engine, Mathematica, 44

EngineeringForm, 435, 1134

English keyboard, xv

Enhancements, in current version, x

Enter, 48, 49

EnterExpressionPacket, 684

Entering input, 26, 27, 48

         in notebooks, 49

\[EnterKey] (), 1009, 1368

EnterTextPacket, 683

Entier, Floor, 745, 1150

Entry, of numbers, 729

Enumerating sublists, ReplaceList, 274, 1263

Environment, parameters of, 715

Environment, 716, 1134

Environment variables, 1055

Environments, in blocks, 389

         setting up with delayed assignments, 313

EOF, 1057

         EndOfFile, 649, 1134

Epilog, 504, 1134

$Epilog, 706, 709, 1328

EPS, exporting, Export, 568, 1141

         importing, Import, 570, 1176

EPSF, exporting, Export, 568, 1141

         importing, Import, 570, 1176

EPSI, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Epsilon, machine number, $MachineEpsilon, 739, 1331

\[Epsilon] (), 175, 984, 990, 1368

Epsilon symbol, Signature, 760, 1282

EPSTIFF, exporting, Export, 568, 1141

         importing, Import, 570, 1176

\eqalign (TeX), \[AlignmentMarker] (), 451

Equal (==), 84, 85, 86, 347, 411, 819, 1027, 1135

\[Equal] (), 183, 1003, 1368

Equal column widths, ColumnsEqual, 449, 1108

Equality testing, compared with assignment, 84

         Equal (==), 84, 1135

         for numbers, 732

         for strings, Equal (==), 411, 1135

         from canonical forms, 326

         general problem of, 327

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

         random numbers for, 747

Equals sign (=), Set, 39, 303, 1277

\[EqualTilde] (), 1003, 1368

Equations, algebraic, 88, 820

         as logical statements, 84, 819

         consistency of, 90, 830

         cubic, 820

         difference, RSolve, 891, 1269

         differential, 93, 105, 869, 961

         Diophantine, 753

         Diophantine, Reduce, 841, 1261

         eliminating variables in, Eliminate, 90, 832, 1132

         Equal (==), 84, 1135

         existence of solutions, 90, 830

         getting full solutions to, Reduce, 90, 830, 1261

         in text, 196

         integer, Reduce, 841, 1261

         involving power series, 889

         linear, 90, 820

         manipulation of, 819

         matrix, 829

         matrix, LinearSolve, 907, 1195

         naming of, 85

         non-generic solutions of, Reduce, 90, 830, 1261

         numbering of, 202

         numerical solution of, 87

         numerical solution of polynomial, NSolve, 959, 1226

         numerical solution of transcendental, FindRoot, 960, 1149

         polynomial, 88, 90, 820

         quadratic, 820

         quartic, 820

         quintic, 88, 821

         recurrence, RSolve, 891, 1269

         representation of, 85

         simultaneous, 89, 828

         solution of, Solve, 87, 819, 1285

         solving logical combinations of, 833

         subsidiary, 90

         symbolic, 84, 819

         symbolic representation of roots, Root, 88, 821, 1265

         systems of, 828

         that are always satisfied, SolveAlways, 833, 1285

         threading operations over, Thread, 257, 1304

         transcendental, 89, 823, 824

         transcendental, ProductLog, 781, 1252

         trigonometric, 89

         unwinding lists of, LogicalExpand, 829, 1203

         using solutions of, 819

         variables in, 829

\[Equilibrium] (), 191, 1007, 1368

Equinox, 991

\equiv (TeX), \[Congruent] (), 1003

Equivalence, mathematical, Equal (==), 347, 1135

         patterns and expression, 260

         testing for, SameQ (===), 268, 347, 1270

         \[Tilde] (), 1003

Erasing files, DeleteFile, 641, 1120

Erasing objects, 1052

Erasing values, Unset (=.), 39, 1052, 1316

Erf, 775, 1135

Erfc, 775, 1135

Erfi, 775, 1135

Error, of data, StandardDeviation, 109, 924, 1289

         syntax in string, SyntaxLength, 466, 1298

Error analysis, 740

Error function, complementary, Erfc, 775, 1135

         Erf, 775, 1135

Error handling, in MathLink, 696

Error messages, 61, 479

         multiple, 480

ErrorBox, 447, 1135

\[ErrorIndicator] (), 1009, 1369

ErrorListPlot, 168

Errors, 66

         common, 34, 39

         handling of, Check, 481, 1102

         handling of, Throw, 354, 1304

         handling syntax, $SyntaxHandler, 704, 1337

         in files, 623

         in Mathematica, 226

         in numerical operations, 732, 952

         in reproducing examples, xv

         infinite recursion, 369

         name conflict, 59

         numerical overflow, 742

         rounding off numerical, Chop, 730, 1103

         syntax, 51

         trapping, Check, 481, 1102

Escape indicator, \[AliasIndicator] (), 1009

Escape key, 36, 174, 982

Escape sequences, user-defined, InputAliases, 613, 1178

\[EscapeKey] (), 1009, 1369

Escapes, in box input, 463

Ess-zed, \[SZ] (), 190, 998

Essential singularities, in integrals, 868

         in limits, 894

         in plots, 137

         in series, 884

Estimation, of statistical parameters, 795

\[Eta] (), 175, 990, 1369

\[Eth] (), 998, 1369

Ethernet address, $MachineID, 718, 1331

EUC, 421

Euclid's algorithm, GCD, 1067, 1161

Euler beta function, Beta, 770, 1089

Euler gamma, \[DoubledGamma] (), 994

Euler gamma function, Gamma, 770, 1160

Euler methods, NDSolve, 1216

Euler numbers, EulerE, 758, 1135

Euler polynomials, EulerE, 758, 1135

Euler-Maclaurin method, 958

Euler-Maclaurin summation, Zeta, 1068, 1324

Euler-Maclaurin summation formula, 758

Euler-Mascheroni constant, EulerGamma, 765, 1136

Euler's constant, EulerGamma, 765, 771, 1136

         generalization of, StieltjesGamma, 772, 1290

Euler's formula, TrigToExp, 71, 812, 1314

Euler's pentagonal formula, PartitionsP, 1067, 1240

EulerE, 757, 758, 1135

EulerGamma, 765, 771, 1067, 1136

         implementation of, 1067

EulerPhi, 752, 1136

\[Euro] (), 994, 1369

European characters, 190, 421, 998

European currency, \[Euro] (), 994

European languages, characters in, 418

eval, 1045

Evaluatable, 608, 1136

Evaluate, 132, 337, 344, 1047, 1136

Evaluate button action, 200, 596

Evaluate selection, SelectionEvaluate, 588, 1274

EvaluateCell button action, 200, 596

EvaluatePacket, 685, 689

Evaluating Mathematica expressions, in external programs, 663

Evaluation, automatic save after, NotebookAutoSave, 618, 1222

         deferred, 336

         full story on, 1045

         global control of, 1048

         holding in, 336

         immediate of arguments, 1047

         in assignments, 311, 340, 1047

         in definitions, 340

         in iteration functions, 343

         in logical expressions, 347

         in notebooks, 49

         in palettes, 199

         in patterns, 340

         in place, 181

         in plots, 132

         in plotting, 338

         in rules, 340

         method for requesting, 48

         non-standard, 336, 1045

         numerical, 102, 728

         of held arguments, Evaluate, 337, 1136

         of two-dimensional expressions, 181

         preventing for printing, HoldForm, 338, 1170

         principles of, 324

         repeated, Do, 348, 1127

         standard procedure for, 332, 1045

         tracing of, 356

         using buttons, 55

         with assumptions, Refine, 816, 1261

         with memory constraints, MemoryConstrained, 713, 1210

         with time constraints, TimeConstrained, 712, 1305

Evaluation at a point, ReplaceAll (/.), 65, 1263

Evaluation chain, 358

         maximum length of, $IterationLimit, 369, 1330

EvaluationCell, 582

EvaluationMonitor, 977, 1136

EvaluationNotebook, 579, 1136

Evaluator, for button, ButtonEvaluator, 597, 1093

Evaluator, 577, 608, 1136

Even numbers, testing for, EvenQ, 267, 1137

EvenQ, 267, 723, 1137

Exact computation, 30

Exact differential, Dt, 854, 1129

Exact numbers, conversion to, Rationalize, 746, 1256

Examples, of Mathematica, 3

         reproducing from book, xv

         timing of, xv

Excel format, exporting, Export, 208, 642, 1141

         importing, Import, 208, 642, 1176

Exception handling, Catch, 350, 1096

Exceptions, floating point, 742

         handling of, 481

Exchange values, Set (=), 305, 1277

Exchanging, notebooks with kernel, NotebookGet, 580, 1223

         text, 425

Exclamation point, Factorial (!), 31, 757, 1143

Exclamation point (!), as pipe prefix, 628

         for shell escapes, 629

         Not, 87, 1221

ExcludedForms, 814, 1137

Exclusive or, Xor, 87, 1324

.exe files, 659

Executables, naming of, 676

Execute external command, Run, 629, 1269

Execute shell command, 629

Executing Mathematica, 26

Execution, as interpretation of evaluation, 324

         tracing of, 356

Execution time, Timing, 711, 1306

Existence, Exists, 847, 1137

Existence of solutions, 830

Existential quantifier, Exists, 847, 1137

Exists, 847, 1137

\[Exists] (), 1001, 1369

Exit, emergency, 62

Exit, 706, 1057, 1137

Exit code, in Run, 629

Exit notebook, NotebookClose, 591, 1222

Exiting, from dialogs, 707

Exiting Mathematica, Quit, 28, 1057, 1254

Exp, 31, 761, 1137

Expand, 67, 69, 797, 801, 1137

Expand selection, 180

ExpandAll, 69, 801, 1138

ExpandDenominator, 801, 1138

Expanding, of polynomials over finite fields, 809

         special functions, FunctionExpand, 792, 1159

Expanding polynomials, speed of, 77

ExpandNumerator, 801, 1138

Expansion, continued fraction, ContinuedFraction, 754, 1112

         control of, 798

         in series, Series, 883, 1276

         of Boolean expressions, LogicalExpand, 87, 1203

         of complex expressions, ComplexExpand, 812, 1110

         of complex powers, ExpToTrig, 812, 1141

         of functions, Series, 94, 883, 1276

         of polynomials, Expand, 67, 797, 1137

         of powers, PowerExpand, 798, 1248

         trigonometric, TrigExpand, 71, 811, 1313

         with arbitrary operators, Distribute, 256, 1126

Expected value, \[LeftAngleBracket] (), 1002

Experimental data, plotting, ErrorListPlot, 168

Experimental` context, 1074

ExpIntegralE, 774, 1138

ExpIntegralEi, 774, 1138

Explanation, of messages, 61

Explanations of functions, 58

Explode, Characters, 412, 1102

         IntegerDigits, 725, 1181

Exponent, integer, IntegerExponent, 725, 749, 1181

         least universal, CarmichaelLambda, 752, 1096

Exponent, 73, 799, 1138

Exponent law, PowerExpand, 72, 798, 1248

ExponentFunction, 436, 1139

Exponential constant, E, 32, 765, 1130

Exponential equations, 825

Exponential function, Exp, 31, 761, 1137

         generalized inverse of, ProductLog, 781, 1252

Exponential integrals, ExpIntegralE, 774, 1138

Exponential notation, 29, 1021

         ScientificForm, 435, 1272

Exponential time, 76

\[ExponentialE] (), 988, 994, 1369

Exponentials, conversion of complex, ExpToTrig, 71, 812, 1141

         of matrices, MatrixExp, 906, 1207

Exponents, distributing, PowerExpand, 798, 1248

         in output of numbers, 436

         input of, 176

         of numbers, MantissaExponent, 726, 1204

Export, 207, 208, 210, 212, 567, 568, 569, 570, 642, 643, 1141

Export options, for front end, 622

$ExportFormats, 208, 1328

Exporting, from notebooks, 47

         of textual forms, 424

         of two-dimensional notation, 177

         three-dimensional graphics, 556

         two-dimensional forms, 430

Exporting graphics, Export, 208, 567, 1141

Exporting numbers, 729

Exporting sounds, Export, 567, 1141

Exporting symbols from packages, 397

ExportString, 567, 1141

Exposition, in notebooks, 202

Expression, converting to, ToExpression, 428, 464, 1307

Expression, 582, 646, 1141

Expression form, of a cell, 572

ExpressionML, exporting, Export, 212, 1141

         importing, Import, 212, 1176

Expressions, 230, 1014

         alternative input forms for, 233

         as structural objects, 232

         as trees, 237, 1014

         conversion to boxes, ToBoxes, 428, 464, 1307

         conversion to string, ToString, 428, 464, 1309

         corresponding to cells, 572

         creating from strings, ToExpression, 428, 464, 1307

         depth of, 239, 1041

         display of large, 74

         elements of, Part, 234, 1238

         evaluation of, 324, 1045

         exchanging with external programs, 628

         for notebooks, 578

         in MathLink, 669

         indices in, 1040

         input, In, 702, 1177

         input of, 48, 1021

         internal storage of, 221

         interpretations of, 231

         lambda, Function (&), 249, 1159

         levels in, 237, 1041

         manipulation like lists, 236

         nested, 234

         ordering in, Ordering, 255, 1233

         output, Out (%), 702, 1234

         output of, 425

         parts in algebraic, 234

         parts of, Part, 234, 1040, 1238

         patterns as classes of, 259

         patterns for common types of, 278

         pieces of algebraic, 73

         rational, 69

         reading without evaluation, 649

         reduction to standard form of, 325

         replacing parts in, ReplacePart, 235, 1263

         resetting parts of, 235

         selecting parts based on criteria, Select, 251, 1273

         sharing common parts of, Share, 714, 1279

         simplification of, Simplify, 68, 813, 1282

         size of, ByteCount, 714, 1095

         special input forms for, 232, 1023

         storing in external programs, 692

         structural operations on, 254

         structure of, 237

         symbols in, 1041

         testing properties of, 267

         transforming, 69

         traversal of, 1041

         trigonometric, 811

         types of, 232

         writing to streams, Write, 632, 1324

ExpToTrig, 71, 812, 1141

Extend selection, 180

         SelectionMove, 582, 1275

Extended character sets, 421

Extended Unix code, 421

ExtendedGCD, 752, 753, 1141

Extensible characters, 456

Extension, 809, 1142

Extensions, field, 809

         file name, 1053

Extensions (packages), 59

Exterior faces of three-dimensional objects, 529

Exterior product, \[Wedge] (), 1002

Exterior products, Outer, 902, 1234

External commands, available, $OperatingSystem, 717, 1334

External conversions, for cells, ConversionRules, 607, 1114

External data, exporting, Export, 208, 642, 1141

         importing, Import, 208, 642, 1176

         reading, Import, 207, 1176

         writing, Export, 207, 1141

External files (packages), 59

External functions, calling, 216, 657

External interface, 204

External programs, 213

         creating compiled code for, 376

         on remote computers, 690

         output for, 425

         processing of graphics by, 554

         reading data from, ReadList, 649, 1257

         running, 215, 628

         sound output by, 566

External symbols, in packages, 397

ExternalCall, 662, 687

Extract, 286, 339, 1142

Extracting, bracketed data in files, RecordSeparators, 648, 1259

Extrapolation, Interpolation, 932, 1183

Extrema, D, 80, 853, 1117

ExtremeValueDistribution, 794

Extremization, Minimize, 850, 1212

         NMinimize, 974, 1220

         numerical, NMinimize, 974, 1220

Eye motion, ShowCursorTracker, 613, 1072, 1281

Eye position, ViewPoint, 152, 532, 1319