Documentation

Mathematica

The Mathematica Book

The Mathematica Book, version 5.0

Browsable Index

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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

\P (TeX), \[Paragraph] (), 996

Packages, 59, 396

         and notebooks, 205

         automatic loading of, 60, 401

         compared to notebooks, 61

         contexts in, 392, 1016

         files for, $BaseDirectory, 637, 1325

         for symbolic mathematics, 97

         interdependence between, 399

         list of loaded, $Packages, 397, 1335

         location of files for, 1063

         names of, 396, 640

         reading in, 59, 400

         searching for, 640

         setting up, 397

$Packages, 397, 1335

Packed arrays, 1066

Packets, in MathLink, 633, 683

         names for, 700

PaddedForm, 437, 440, 1235

Padding, of cellular automata, CellularAutomaton, 949, 1101

         of digits, IntegerDigits, 725, 1181

         of lists, PadLeft, 128, 294, 1236

Pade technique, Apart, 1069, 1080

PadLeft, 128, 291, 294, 941, 1236

PadRight, 128, 291, 294, 1236

Page breaks, 609

         ShowPageBreaks, 618, 1281

Page layout, 569

PageBreakAbove, 609, 1236

PageBreakBelow, 609, 1236

PageBreakWithin, 609, 1237

PageWidth, 609, 619, 634, 635, 1054, 1237

         resetting for standard output, SetOptions, 635, 1278

Paint programs, input for, Import, 570, 1176

         output for, Export, 568, 1141

Palette, basic, 176

Palette buttons, ButtonBox, 595, 1092

Palette element, ButtonBox, 448, 1092

Palette notebook, ButtonNotebook, 579, 1094

Palette window frame option, 621

Palette windows, WindowFloating, 620, 1321

Palettes, 35, 54

         creating your own, 198

         for Greek letters, 174

         for special characters, 174, 982

         formatting of, 452

Palindromes, 9

Paper copy, of notebook, NotebookPrint, 591, 1224

Paper output, of notebooks, 51

PaperWidth, 610

Parabolic cylinder functions, 768

         Hypergeometric1F1, 779, 1171

\[Paragraph] (), 996, 1385

Paragraph skip, ParagraphSpacing, 611, 1237

ParagraphIndent, 609, 611, 1237

ParagraphSpacing, 611, 1237

Parallel, \[DoubleVerticalBar] (), 1005

Parallel form of Map, MapThread, 247, 1206

Parallel Mathematica sessions, 657, 680

Parallel operations, 256

Parameters, 232

         assumptions about, Assumptions, 867, 1084

         defining, Set (=), 39, 1277

         external, Environment, 716, 1134

         in elliptic functions, InverseEllipticNomeQ, 782, 1185

         in pure functions, 249

         scoping of in pure functions, 385

         special values of in equations, 830

Parametric amplifiers, MathieuS, 789, 1207

Parametric surfaces, 164

ParametricPlot, 161, 162, 487, 1237

ParametricPlot3D, 163, 487, 969, 1238

Parametrized zeros, 735

Parent subexpression, selecting, 180

ParentDirectory, 637, 1238

Parentheses, 29, 42, 233, 1022, 1031

         colored, ShowAutoStyles, 613, 1280

         in function input, TraditionalForm, 194, 1313

         in output, 474

         unmatched, 1037

Parenthesis, horizontal, \[UnderParenthesis] (), 997

Parenthesization, in Mathematica input, 468

$ParentLink, 686, 716, 1335

$ParentProcessID, 716, 1335

Parse trees, 237

Parser, input, 1021

         redefining the, 476

Parser construction, ReplaceList, 302, 1263

Parsing, 468

         errors in, 51

         of data files, 647

         of input, ToExpression, 428, 464, 1307

         of strings, 654

         processing before, $PreRead, 703, 1336

\parskip (TeX), ParagraphSpacing, 611, 1237

Part, 41, 42, 73, 117, 118, 120, 122, 234, 235, 285, 898, 1014, 1024, 1040, 1238

\partial (TeX), \[PartialD] (), 994, 1000

Partial derivatives, D, 80, 853, 1117

         input of, 186

Partial difference equations, RSolve, 893, 1269

Partial differential equations, 962

         DSolve, 874, 1129

         NDSolve, 970, 1216

         numerical, NDSolve, 106, 1216

Partial fractions, Apart, 70, 802, 1080

Partial quotients, ContinuedFraction, 754, 1112

Partial recurrence equations, RSolve, 893, 1269

\[PartialD] (), 184, 185, 994, 1000, 1385

Partition, 128, 130, 291, 292, 293, 938, 1240

Partitions, number of, Multinomial, 758, 1214

         number of, PartitionsP, 759, 1240

         number of, PartitionsQ, 759, 1240

         number of, StirlingS2, 759, 1290

PartitionsP, 757, 759, 1067, 1240

         implementation of, 1067

PartitionsQ, 757, 759, 1240

Parts, extracting without evaluation, Extract, 339, 1142

         finding positions of, Position, 124, 261, 1247

         input of, 184

         numbering of, 1040

         of algebraic expressions, 73

         of expressions, Part, 234, 1014, 1040, 1238

         of lists, 41, 122

         of strings, StringTake, 407, 1293

         picking out ranges of, 235

         replacing, 285

         replacing, ReplacePart, 125, 288, 1263

         replacing without evaluation, ReplacePart, 339, 1263

         specifications of sequences of, 1040

Parts of expressions, applying functions to, 244

         applying functions to numbered, MapIndexed, 246, 1205

         applying functions to specific, MapAt, 246, 1205

Pascal, in MathLink, 658

Passing of arguments, mechanism for, 387

$PasswordFile, 718

Passwords, for encoded files, 626

Paste button action, 200, 596

Pasting, in notebooks, NotebookWrite, 585, 1225

Pasting of boxes, 461

Path, context search, $ContextPath, 394, 1327

         for external programs, 659

         for files, $Path, 207, 1335

Path, 637, 1240

$Path, 206, 207, 637, 659, 1335

Path integral, \[CapitalDifferentialD] (), 994

Pattern (:), 263, 1028, 1030, 1240

Pattern variables, Blank (_), 259, 1090

         names of, 263

         scope of, 263, 386

Patterns, 113, 259, 1049

         alternatives in, 269

         an example of defining an integration function, 281

         associative functions in, 271

         conditions on, Condition (/;), 265, 1111

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

         deleting elements that match, DeleteCases, 262, 1120

         equality testing and, 260

         evaluation in, 340

         examples of, 259

         finding elements that match, Cases, 261, 1096

         flat functions in, 270

         for algebraic expressions, 261, 279

         for common types of expressions, 278

         for files, FileNames, 638, 1145

         for linear expressions, 280

         for numbers, 279

         for quadratic expressions, 280

         for strings, 406, 411

         implementation of, 1066

         in controlling expansion, 798

         in rearranging polynomials, Collect, 799, 1106

         multiple cases in, 270

         naming of, 263

         non-unique matches in, 270

         number types in, 724

         optional arguments in, 274

         ordering of testing cases for, 1050

         orderless functions in, 270

         repeated, 277

         scoping of, 386

         testing for matching of, MatchQ, 268, 347, 1206

         types of expressions in, 264

         unevaluated objects in, HoldPattern, 340, 1170

PatternTest (?), 269, 1024, 1241

Pause, 710, 1241

Pay-off functions, Minimize, 850, 1212

         NMinimize, 974, 1220

PBM graphics format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

pd, \[PartialD] (), 185

PDEs, DSolve, 874, 1129

         NDSolve, 970, 1216

         numerical, NDSolve, 106, 1216

PDF, 794

Pell equations, 842

         Reduce, 1070, 1261

Pending evaluations, Stack, 367, 1289

Pendulum, 783

Penning traps, MathieuS, 789, 1207

Pentagon, 495

Percent, in notebooks, 38

Percent (%), Out, 38, 1234

Percentiles, Quantile, 795, 925, 1253

Performance analysis, 220

         Timing, 711, 1306

Periodic potentials, MathieuS, 789, 1207

Periodic signals, Fourier transforms of, 936

Permutations, enumeration of, StirlingS1, 759, 1290

         finding, Ordering, 129, 255, 1233

Permutations, 129, 1241

Permute values, Set (=), 305, 1277

\perp (TeX), \[UpTee] (), 1007

Perpendicular, \[UpTee] (), 1007

Persistent objects, 383

Perspective effects, 153, 533

PGM graphics format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

\phantom (TeX), ShowContents, 455

Phase, Arg, 34, 746, 1083

Phase plots, NDSolve, 105, 133, 1216

Phi, GoldenRatio, 765, 1162

\[Phi] (), 175, 990, 1385

Phonetic spelling correction, 1072

Phong lighting model, 547

Pi, 32, 765, 1067, 1241

         implementation of, 1067

         input of, 175

\[Pi] (), 175, 182, 988, 990, 1385

Piano, 172

Picking elements of lists, Select, 251, 1273

PICT, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Picture size, ImageSize, 569, 616, 1174

Pictures, 486

         exporting, Export, 208, 567, 1141

PID, $ProcessID, 716, 1336

Pie slices, Disk, 496, 1125

Piecewise continuous functions, UnitStep, 879, 1316

Piecewise functions, If, 87, 1173

         Which, 346, 1320

Piecewise linear functions, Interpolation, 933, 1183

PieChart, 168

Pilcrow sign, \[Paragraph] (), 996

Pipes, 215, 628

         as streams, 631

         named, 658

         reading data from, ReadList, 649, 1257

         reading from, Get (<<), 215, 1162

         running Mathematica through, 1057

         writing to, Put (>>), 215, 1253

Pipes protocol, LinkProtocol, 677, 1198

Pixel array, Raster, 492, 497, 1255

Pixel motion, in formatting, 455

Pixel size, 453

Pixmap graphics format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

\[Placeholder] (), 199, 587, 1008, 1385

Placeholders, in buttons, 55

Planar polygons, 524

Planck's constant, \[HBar] (), 994

Platform, computer, $System, 717, 1338

Platform dependence, of MathLink programs, 676

Play, 171, 565, 1241

PlayRange, 172, 1242

Plot, 131, 487, 1242

         evaluation in, 336, 343

         options for, 134

         styles of curves in, PlotStyle, 503, 1244

Plot3D, 149, 156, 487, 537, 542, 1242

         evaluation in, 343

         options for, 151

Plot3Matrix (Version 1 option), see ViewCenter, 1402

PlotDivision, 138, 1243

PlotJoined, 159, 1243

PlotLabel, 134, 511, 549, 558, 1243

PlotPoints, 137, 138, 147, 148, 151, 1243

PlotRange, 134, 137, 147, 151, 507, 508, 540, 1243

         finding setting for, AbsoluteOptions, 145, 490, 1075

         in three-dimensional graphics, 530

PlotRegion, 507, 509, 1244

         for three-dimensional plots, 535

Plots, 131

         arbitrary-precision numbers in, 138

         arrays of, GraphicsArray, 139, 487, 1165

         aspect ratio of, AspectRatio, 134, 1084

         automatic choice of range in, 136

         axes in, 134, 512, 549

         axis labels, AxesLabel, 134, 512, 1087

         axis position, AxesOrigin, 512, 1087

         boundary of, PlotRange, 134, 1243

         color of curves in, PlotStyle, 500, 1244

         combining, Show, 139, 1280

         compilation of functions in, 138

         contour, ContourPlot, 146, 517, 1113

         converting between types of, 157

         density, DensityPlot, 146, 517, 1121

         efficiency of, 138

         evaluation in, 338

         evaluation of functions in, 132

         false color, ColorFunction, 147, 517, 1106

         frames in, Frame, 134, 511, 514, 1155

         from tables of functions, 132

         full story on, 486

         generating without displaying, 491

         generating without rendering, 170

         glitches in, 137

         grid lines in, GridLines, 134, 511, 1167

         internal representation of, 143

         labeling three-dimensional, 548

         labeling two-dimensional, 511

         labels on, PlotLabel, 134, 511, 1243

         limits of, PlotRange, 134, 1243

         log, 168

         of lists, ListPlot, 158, 1202

         of lists of functions, 132

         of surfaces, Plot3D, 149, 1242

         overlaying, Show, 139, 1280

         packages for, 167

         parametric, ParametricPlot, 161, 1237

         points to sample in, PlotPoints, 138, 1243

         polar, 168

         range of, PlotRange, 134, 1243

         redrawing, Show, 139, 1280

         region in, PlotRange, 134, 1243

         semilog, LogPlot, 168

         shaded, 146

         shading functions in three-dimensional, 156

         shape of, AspectRatio, 134, 509, 1084

         smoothness of, 137

         styles of curves in, PlotStyle, 138, 1244

         subdivision level in, PlotDivision, 138, 1243

         superimposing, Show, 139, 1280

         text in, 556

         three-dimensional, Plot3D, 149, 1242

         tick marks in, Ticks, 134, 552, 1305

         view point for, ViewPoint, 152, 532, 1319

         within plots, 516

PlotStyle, 138, 500, 503, 1244

Plotting symbols, drawing, Offset, 507, 1230

         TextListPlot, 168

PlotVectorField, 168

Plug-in programs, 657

Plug-ins, 1065

Plus (+), 29, 1027, 1244

         optional arguments in patterns involving, 275

         patterns involving, 270

Plus function markers, 1073

\[PlusMinus] (), 191, 1000, 1385

\pm (TeX), \[PlusMinus] (), 1000

PNG, exporting, Export, 568, 1141

         importing, Import, 570, 1176

PNM graphics format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Pochhammer, 770, 1244

Pochhammer symbol, Pochhammer, 770, 1244

Point, 492, 520, 1244

         in three dimensions, 525

Point location, IntervalMemberQ, 741, 1184

Point of view, ViewPoint, 152, 532, 1319

Pointers, in internal representation, 221

Points, colors of in three dimensions, 528

         printer's, 453, 507

         size of, PointSize, 500, 1245

PointSize, 500, 1245

         in three dimensions, 525

Poisson series, 811

Poisson-Charlier polynomials, Hypergeometric1F1, 779, 1171

Polar angles, ExpToTrig, 71, 812, 1141

Polar form, 813

PolarPlot, 168

Poles, residues at, 895

Pollard algorithm, FactorInteger, 1067, 1143

Polling, in MathLink, 701

PolyGamma, 770, 771, 890, 1245

         implementation of, 1068

Polygon, 488, 492, 520, 521, 1245

PolygonIntersections, 556, 1245

Polygons, colors of in three dimensions, 526, 546

         edges of in three dimensions, EdgeForm, 528, 1130

         self-intersection of, 495

         three-dimensional, Polygon, 521, 1245

Polyhedra, package on, 522

         seeing inside, 529

Polyline, Line, 492, 1195

PolyLog, 772, 773, 1246

         implementation of, 1068

Polylogarithm functions, PolyLog, 773, 1246

Polynomial, minimal, 826

Polynomial degree, Exponent, 73, 1138

Polynomial equations, 88, 820

         numerical solution of, NSolve, 959, 1226

         solution of, Solve, 87, 820, 1285

Polynomial factorization, Factor, 797, 1143

Polynomial fit, FindFit, 929, 1146

Polynomial root finding, NSolve, 104, 959, 1226

Polynomial time, 76

PolynomialGCD, 803, 804, 1069, 1246

PolynomialLCM, 803, 811, 1246

PolynomialMod, 803, 804, 1246

PolynomialQ, 267, 799, 1246

PolynomialQuotient, 803, 1247

PolynomialReduce, 803, 805, 1247

PolynomialRemainder, 803, 1247

Polynomials, 797

         algebraic operations on, 803

         Bernoulli, BernoulliB, 758, 1088

         canonical forms, 326

         coefficients in, Coefficient, 799, 1105

         construction from power series of, 888

         cyclotomic, Cyclotomic, 807, 1116

         decomposition of, Decompose, 807, 1118

         degree of, Exponent, 799, 1138

         division of, PolynomialQuotient, 803, 1247

         Euler, EulerE, 758, 1135

         expansion of, Expand, 797, 1137

         exponential, 825

         factoring of, Factor, 797, 1143

         Fibonacci, Fibonacci, 758, 1144

         finding structure of, 799

         GCD of, PolynomialGCD, 804, 1246

         Gegenbauer, GegenbauerC, 766, 1161

         Hermite, HermiteH, 766, 1169

         inequalities involving, 835

         JacobiP, JacobiP, 766, 1189

         Laguerre, LaguerreL, 766, 1191

         Legendre, LegendreP, 766, 1192

         making lists of factors in, FactorList, 806, 1143

         modulo primes, 809

         nested, Decompose, 807, 1118

         number of roots of, 823

         orthogonal, 766

         over algebraic number fields, 809

         patterns for, 279

         pieces of, 73, 74

         rearranging, Collect, 797, 1106

         restrictions on, 803

         resultants of, Resultant, 805, 1264

         structural operations on, 797

         testing for, PolynomialQ, 267, 1246

         variables in, Variables, 799, 1318

         with complex coefficients, 807

Polytopes, three-dimensional, 524

Pomeron, \[DoubleStruckCapitalP] (), 992

Population count, DigitCount, 755, 1123

Portability, of character encodings, 421

         of file names, 639

         of Mathematica, 46

         of MathLink programs, 676

Portable anymap format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Portable bitmap format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Portable computers, styles for, ScreenStyleEnvironment, 197, 1272

Portable graymap format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Portable pixmap format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

Portrait mode, ImageRotated, 569, 1174

Ports, 682

Position, of observer, ViewPoint, 152, 532, 1319

         of substring, StringPosition, 409, 1292

Position, 124, 238, 246, 261, 1247

         level specification in, 262

         levels in, 238, 1041

Position-value pairs, SparseArray, 295, 1287

Positioning, in expression formatting, 455

         of cells, CellMargins, 605, 1099

         of limits, LimitsPositioning, 458, 1194

         of textual output, 444

         of windows, WindowMargins, 620, 1322

Positions, in MathLink, 693

         of elements in expressions, Ordering, 255, 1233

         of elements in lists, Ordering, 129, 1233

Positive, 1247

$Post, 703, 1335

Post-decrement, Decrement (--), 305, 1118

Post-increment, Increment (++), 305, 1177

Postfix, 474, 1248

Postfix notation, 233

Postfix operators, 468

Postprocessor, $Post, 703, 1335

PostScript, 554

         color in, 563

         exporting Encapsulated, Export, 568, 1141

         exporting formulas as, 210

         exporting of, 556

         importing Encapsulated, Import, 570, 1176

         reducing amount of, RenderAll, 556, 1262

         sound extensions to, 566

PostScript, 554, 1248

Pound sterling, \[Sterling] (), 994

Pounds sign, on keyboard, xv

Pounds sign (#), Slot, 249, 1284

Power, maximum in integer, IntegerExponent, 749, 1181

         of variable, Exponent, 73, 1138

Power (^), 29, 1025, 1248

         optional arguments in patterns involving, 275

Power series, about infinity, Series, 884, 1276

         absorbing normal expressions into, 886

         as approximate formulas, 884

         cancellations in, 884

         composition of, ComposeSeries, 887, 1110

         constants in, 884

         conversion to normal expressions of, 888

         differentiation of, 886

         for inverse functions, 888

         integration of, 886

         inversion of, InverseSeries, 887, 1188

         involving fractional powers, 883

         involving logarithms, 884

         nested, 885

         of unknown functions, 883, 887

         operations on, 94, 886

         output form of, 885

         precision of, 884

         representation of, 885

         reversion of, InverseSeries, 887, 1188

         Series, 94, 883, 1276

         solving equations involving, 889

         summation of, Sum, 890, 1296

         truncation of, 888

         truncation of, Normal, 94, 1221

         variables in, 884

         ZTransform, 879, 1325

Power spectrum, Fourier, 108, 935, 1154

         FourierTransform, 876, 1155

PowerExpand, 71, 72, 798, 1248

PowerMod, 752, 1248

Powers, branch cuts in, 763

         expansion of, PowerExpand, 798, 1248

         in expression, Exponent, 73, 1138

         in logarithms, PowerExpand, 798, 1248

         input of, 176

         of \(-1\), ExpToTrig, 812, 1141

         of matrices, MatrixPower, 906, 1208

         patterns for, 261

         simplification of, PowerExpand, 72, 1248

PPC protocol, LinkProtocol, 677, 1198

PPID, $ParentProcessID, 716, 1335

PPM graphics format, exporting, Export, 568, 1141

         importing, Import, 570, 1176

$Pre, 703, 1335

\prec (TeX), \[Precedes] (), 1005

Precedence, of @, 234

         of &, 249

         of ->, 249

         of ;, 233

         of //, 234

         of operators, 29, 233, 468, 1031

         outline table of, 469

         table of for all operators, 1024

Precedence levels, 474

PrecedenceForm, 474, 1249

\[Precedes] (), 1005, 1385

\[PrecedesEqual] (), 1005, 1385

\[PrecedesSlantEqual] (), 1005, 1386

\[PrecedesTilde] (), 1005, 1386

\preceq (TeX), \[PrecedesEqual] (), 1005

Precision, global parameters of, 736

         in examples, xv

         in input, 1021

         increasing, SetPrecision, 736, 1278

         numerical, 33, 727

         of numerical output, 435

         propagation of, 732

Precision, 727, 1249

PrecisionGoal, 956, 958, 976, 1249

\precsim (TeX), \[PrecedesTilde] (), 1005

PreDecrement (--), 305, 1025, 1249

Predicate logic, 847

Predicates, as assumptions, Simplify, 72, 815, 1282

         for testing expressions, 267

         in Select, 251

Predictor-corrector methods, NDSolve, 1216

Preferences directory, 1064

         $BaseDirectory, 637, 1325

Preferences file, 622

Prefix, 474, 1249

Prefix notation, 233

Prefix operation, FoldList, 243, 1151

Prefix operators, 468

PreIncrement (++), 305, 1025, 1249

Preliminary features, 1074

Prepend, 125, 288, 1250

Prepending, to strings, StringInsert, 408, 1291

PrependTo, 306, 1250

$PrePrint, 703, 1336

Preprocess MathLink programs, 661

Preprocessor, $Pre, 703, 1335

$PreRead, 703, 1336

Present, in expression, MemberQ, 268, 1210

         in list, MemberQ, 124, 1210

Presentation style environment, 197, 603

Preventing evaluation, 336

         in printing, HoldForm, 338, 1170

Previous results, 38

Primality testing, PrimeQ, 267, 750, 1250

Primary colors, 563

Primary decomposition, GroebnerBasis, 805, 1168

Prime, 750, 1067, 1250

         implementation of, 1067

\[Prime] (), 996, 999, 1386

\prime (TeX), \[Prime] (), 996, 1250

Prime character, Derivative ('), 855, 1122

Prime factors, FactorInteger, 31, 750, 1143

Prime moduli, 809

PrimePi, 750, 1250

         implementation of, 1067

PrimeQ, 267, 723, 750, 1067, 1250

         implementation of, 1067

Primes, density of, LogIntegral, 774, 1203

         distribution of, PrimePi, 750, 1250

         examples of fits to sequence of, 926

         Gaussian, 751

Primes, 73, 817, 1250

Primitive root, MultiplicativeOrder, 752, 1214

Primitives, graphics, 486

Principal roots, 763

Principal subresultant coefficients, Subresultants, 805, 1295

PrincipalValue, 866, 1251

Print, notebook, NotebookPrint, 591, 1224

Print, 113, 477, 1251

         channel for, 633

Print trace of evaluation, TracePrint, 365, 1312

Printer resolution, ImageResolution, 569, 1174

Printer's points, 453, 500, 507

Printing, in notebooks, StylePrint, 477, 575, 1295

         of contexts for symbols, 395, 401

         of expressions, 425

         of messages, Message, 482, 1211

         of notebooks, 197

         of numbers, 729

         page breaks in, 609

         suppression of, 43

         without evaluation, HoldForm, 338, 1170

Printing expressions, Put (>>), 215, 1253

Printing files, 204, 623

PrintingStyleEnvironment, 197, 602, 618, 1251

Printout style environment, 197, 603

Private contexts, in packages, 398

Probabilistic calculations, 748

Procedural programming, avoiding, xiv

Procedure, Module, 378, 1213

Procedures, 43, 111

         compilation of, Compile, 376, 1109

         exiting, Return, 354, 1265

         local variables in, 378

Process size, 713

Processes, multiple Mathematica, 680

$ProcessID, 716, 1336

Processing images, Import, 570, 1176

$ProcessorType, 717, 1336

Product, cap, \[Cap] (), 1002

         cup, \[Cup] (), 1002

         dot, Dot (.), 118, 1127

         inverted, \[Coproduct] (), 1002

         of vectors, Dot (.), 119, 1127

         wedge, \[Wedge] (), 1002

         wreath, \[VerticalTilde] (), 1002

Product, 83, 951, 1251

         implementation of, 1071

\[Product] (), 184, 185, 984, 994, 1000, 1386

$ProductInformation, 717, 1336

Production rules, in strings, StringReplace, 410, 1292

         ReplaceList, 302, 1263

Production rules (transformation rules), 299

ProductLog, 781, 1252

Products, formatting of, 459

         input of, 184

         multiple, Product, 83, 1251

         numerical, NProduct, 103, 957, 1226

         patterns involving, 270

Profiling, Timing, 711, 1306

Program equals data, 384

Program flow, 348

Program fragments, in text, 196

Program-program communication, 657

Programmability, 222

Programming, graphics, 486

Programming interface to Mathematica, 657

Programming languages, variables in traditional, 66

Programs, 111

         active, Links, 662, 1198

         C, CForm, 213, 1101

         communicating with external, 657

         constants in, With, 380, 1323

         debugging of, 356

         external, 213

         external, Splice, 214, 1288

         Fortran, FortranForm, 213, 1153

         local variables in, 378

         naming of external, 676

         reading data from, ReadList, 649, 1257

         scoping in, 391

         symbolic manipulation of, 338

Projection point, ViewPoint, 532, 1319

Prolog, 504, 1252

Prompts, input, 27, 48, 702

         suppressing, $BatchOutput, 715, 1326

Proof, end of, \[FilledRectangle] (), 995

Proofs, 816

         errors in, 226

Properties, functions for testing, 267

         of functions, 327

\[Proportion] (), 1003, 1386

\[Proportional] (), 191, 1003, 1386

Propositional calculus, operations in, 87

Proprietary files (encoding), 626

\propto (TeX), \[Proportional] (), 1003

Protect, 321, 330, 1044, 1252

Protected, 329, 1052, 1252

Protecting against evaluation, 336

Protection, of cells, Editable, 607, 1130

         of definitions, ReadProtected, 330, 1258

         of notebooks, Editable, 619, 1130

         with encoded files, 626

Protocol, for interprocess communication, 657

         for MathLink , LinkProtocol, 677, 1198

         MathLink, 657

Prototypes, C, 677

Proves, \[RightTee] (), 1001

Provided that, Condition (/;), 265, 1111

Pseudocode, in compiled code, 377

PseudoInverse, 914, 1252

Pseudoprime test, PrimeQ, 1067, 1250

Pseudorandom numbers, Random, 31, 747, 1254

         with special distributions, 795

Pseudotensors, Signature, 760, 1282

\[Psi] (), 175, 990, 1386

Psi function, PolyGamma, 771, 1245

Publish link, LinkCreate, 680, 1197

Publishing, with notebooks, 44

Punctuation, WordSeparators, 646, 1323

Pure functions, 248, 856

         as examples of heads, 252

         attributes for, 332

         in differential equations, 869

         nested, 385

         scoping of, 385

         variables in, 385

         with several arguments, 250

Purging directories, DeleteDirectory, 641, 1120

Purple brackets, ShowAutoStyles, 613, 1280

Put, notebook, NotebookPut, 578, 1224

Put (>>), 204, 215, 624, 1029, 1253

PutAppend (>>>), 204, 624, 1029, 1253

Putting data in MathLink, 667

Putzer's method, MatrixExp, 1069, 1207

pwd, Directory, 206, 636, 1124

Python, and MathLink, 217

         in MathLink, 658