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

N, 30, 33, 102, 103, 320, 728, 735, 1214

         implementation of, 1067

         precision in, 728

Nabla, \[Del] (), 1000

         Grad, 97

\nabla (TeX), \[Del] (), 994, 1000

Name, of user, $UserName, 716, 1339

Named pipes, 658

NameQ, 403, 1215

Names, 40

         ending with Q, 1039

         for symbols, 392

         full, 1015

         functions without, Function (&), 248, 1159

         general treatment of, 378

         generating unique, Unique, 382, 1316

         in packages, 59

         in tables, TableHeadings, 443, 1300

         listing of all built-in, 1073

         of characters, 985, 1352

         of files, ToFileName, 639, 1308

         of functions, 111

         of packages, 400

         of patterns, 263

         of streams, 631

         of symbols, 1014

         of symbols, SymbolName, 402, 1298

         on plots, PlotLabel, 134, 511, 1243

         removing, Remove, 395, 403, 1261

         scope of, 378

         searching for, 58

         shadowing of, 395

         short, 1015

         special characters in, 1014

         uniqueness of, 392

Names, 403, 1215

Names files, 402

Naming, of fonts, FontSubstitutions, 612, 1152

Naming conventions, 35, 1039

         for mathematical functions, 745, 1039

         for symbols, 1014

NaN, 742

Nand, 87, 1215

\[Nand] (), 1001, 1378

Native character sets, $CharacterEncoding, 421, 1327

\[Natural] (), 192, 996, 1378

Natural logarithm, Log, 31, 1202

Natural numbers, set of, \[DoubleStruckCapitalN] (), 992

.nb files, 205, 1053

nb2tex, 210

NDSolve, 105, 106, 133, 951, 961, 962, 969, 970, 979, 1068, 1216

         implementation of, 1068

         initial conditions for, 962

         InterpolatingFunction in, 930

         multiple solutions in, 963

         plotting solutions from, 963

\ne (TeX), \[NotEqual] (), 1003

Nearest integer function, Floor, 745, 1150

\nearrow (TeX), \[UpperRightArrow] (), 1006

Needs, 400, 1217

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

Negation, Not (!), 87, 1221

         \[Not] (), 1001, 1221

Negative, 1217

NegativeBinomialDistribution, 796

\[NegativeMediumSpace] (), 454, 1008, 1379

\[NegativeThickSpace] (), 454, 1008, 1379

\[NegativeThinSpace] (), 454, 1008, 1379

\[NegativeVeryThinSpace] (), 454, 1008, 1379

Neighborhoods, in arrays, Partition, 130, 1240

\neq (TeX), \[NotEqual] (), 1003

Nest, 241, 349, 1217

Nested cells, 51

Nested expressions, printing, 432

Nested lists, 289

         rearrangement of, 129

Nested loops, 348

\[NestedGreaterGreater] (), 1004, 1379

\[NestedLessLess] (), 1004, 1379

Nesting, indenting to represent, \[IndentingNewLine] (), 460

Nesting level, Depth, 239, 1122

NestList, 241, 242, 250, 1217

         and Throw, 351

NestWhile, 242, 349, 1218

NestWhileList, 242, 1218

Network diagrams, 11

Network licenses, 1058

Networked computing, 47

$NetworkLicense, 718

Networks, and MathLink, 690

         computer, 27

Neumann function, BesselY, 776, 1089

\[NeutralSmiley] (), 995, 1379

Neville theta functions, 787

New features in Mathematica Version 5, x

New notebook, NotebookCreate, 591, 1222

New symbols, reporting, 404, 1015

New York Times, ix

\[NewLine] (), 460, 1008, 1010, 1379

Newlines, 48, 415, 1037

         in MS-DOS, DOSTextFormat, 1054

         in strings, 415

         RecordSeparators, 646, 1259

$NewMessage, 482, 1334

newsym, 404, 1015

$NewSymbol, 405, 1015, 1334

Newton interpolation, InterpolatingPolynomial, 808, 1183

Newton's approximation, as example of FixedPoint, 242

Newton's method, FindRoot, 104, 1149

\nexists (TeX), \[NotExists] (), 1001

NEXTSTEP (notebook interface), 49

\ngeq (TeX), \[NotGreaterEqual] (), 1004

\ngtr (TeX), \[NotGreater] (), 1004

NHoldAll, 329, 1218

NHoldFirst, 329, 1218

NHoldRest, 329, 1219

\ni (TeX), \[ReverseElement] (), 1004

Nielsen functions, PolyLog, 772, 1246

Nim addition, BitXor, 756, 1090

NIntegrate, 103, 951, 952, 954, 957, 1068, 1219

         implementation of, 1068

\nleq (TeX), \[NotLessEqual] (), 1004

\nless (TeX), \[NotLess] (), 1004

NMaximize, 106, 951, 974, 1219, 1220

         implementation of, 1068

NMinimize, 106, 974, 1220

         implementation of, 1068

\[NoBreak] (), 459, 460, 1008, 1379

\nobreak (TeX), \[NoBreak] (), 460

Node ID, $MachineID, 718, 1331

Nodes, in expression trees, 237

\nolinebreak (TeX), \[NoBreak] (), 460

Nome, in elliptic functions, EllipticNomeQ, 782, 1133

Non-blocking reads, in MathLink, 701

Non-differentiable functions, limits of, 894

Non-local returns, Throw, 354, 1304

Non-printing characters, 1008

Non-theorem, \[LeftTee] (), 1001

\[NonBreakingSpace] (), 459, 1008, 1379

NonCommutativeMultiply (**), 1026, 1220

NonConstants, 853, 1220

None, 136, 1220

Nonlinear differential equations, DSolve, 871, 1129

Nonlinear fitting, 109

         FindFit, 108, 929, 1146

Nonlinear PDEs, 971

NonNegative, 1220

NonPositive, 1221

Nonsingular linear systems, 909

Nor, 87, 1221

\[Nor] (), 1001, 1379

Norm, \[LeftDoubleBracketingBar] (), 1002

Norm, 119, 1221

Normal, 94, 296, 827, 888, 1221

Normal form, for singularities, GroebnerBasis, 805, 1168

         Jordan, JordanDecomposition, 915, 1190

         of polynomials, PolynomialReduce, 805, 1247

Normal window frame option, 621

NormalDistribution, 794

NormFunction, 929, 966

Not, bitwise, BitNot, 756, 1090

Not (!), 87, 1028, 1221

\[Not] (), 1001, 1380

\not= (TeX), \[NotEqual] (), 1003

Notation, for expressions, 233

         in Mathematica, 203

         in notebooks, 35

         mathematical, 193

         scientific, 729, 1021

Notations, without meanings, 471

\[NotCongruent] (), 1003, 1380

\[NotCupCap] (), 1003, 1380

\[NotDoubleVerticalBar] (), 1005, 1380

Note, for button, ButtonNote, 597, 1094

Notebook, unformatting, 572

Notebook, 576, 1221

Notebook commands, 578

Notebook computers, styles for, ScreenStyleEnvironment, 197, 1272

Notebook directories, 622

Notebook files, syntax in, 1038

Notebook interface, 26, 49

         animated graphics in, 170

         interactive input with, 478

Notebook option inspector, 574, 601

Notebook-based interface, test for, $Notebooks, 715, 1334

Notebook-to-TeX conversion, TeXSave, 210, 1302

NotebookApply, 585, 1222

NotebookAutoSave, 618, 1222

NotebookClose, 591, 1222

NotebookConvert, 1403

NotebookCreate, 591, 592, 1222

NotebookDelete, 585, 1222

NotebookDirectory, 592

NotebookFind, 584, 1223

NotebookGet, 578, 580, 1223

NotebookLocate, 585, 1223

NotebookML, exporting, Export, 212, 1141

         importing, Import, 212, 1176

NotebookObject, 579, 1224

NotebookOpen, 578, 591, 1224

NotebookPath, 592

NotebookPrint, 591, 1224

NotebookPut, 578, 579, 580, 1224

NotebookRead, 585, 1225

Notebooks, 26, 44, 49

         active elements in, 54

         and packages, 205

         buttons in, 54

         compared to packages, 61

         controlling from the kernel, 581

         converting to HTML, HTMLSave, 211, 1171

         converting to TeX, TeXSave, 210, 1302

         generating output in, StylePrint, 478, 575, 1295

         input and output in, 174

         options for, 577

         organization of, 49

         previous results in, 38

         setting options for, SetOptions, 581, 1278

         setting up from kernel, 578

         structure of on different computers, 47

Notebooks, 579, 1225

$Notebooks, 715, 1334

NotebookSave, 591, 1225

NotebookSelection, 591, 1225

NotebookWrite, 585, 1225

\[NotElement] (), 191, 1004, 1380

\[NotEqual] (), 182, 1003, 1380

\[NotEqualTilde] (), 1003, 1380

\[NotExists] (), 1001, 1380

\[NotGreater] (), 1004, 1380

\[NotGreaterEqual] (), 1004, 1380

\[NotGreaterFullEqual] (), 1004, 1380

\[NotGreaterGreater] (), 1004, 1380

\[NotGreaterLess] (), 1004, 1380

\[NotGreaterSlantEqual] (), 1004, 1381

\[NotGreaterTilde] (), 1004, 1381

\[NotHumpDownHump] (), 1003, 1381

\[NotHumpEqual] (), 1003, 1381

\notin (TeX), \[NotElement] (), 1004

\[NotLeftTriangle] (), 1005, 1381

\[NotLeftTriangleBar] (), 1005, 1381

\[NotLeftTriangleEqual] (), 1005, 1381

\[NotLess] (), 1004, 1381

\[NotLessEqual] (), 1004, 1381

\[NotLessFullEqual] (), 1004, 1381

\[NotLessGreater] (), 1004, 1381

\[NotLessLess] (), 1004, 1381

\[NotLessSlantEqual] (), 1004, 1381

\[NotLessTilde] (), 1004, 1382

\[NotNestedGreaterGreater] (), 1004, 1382

\[NotNestedLessLess] (), 1004, 1382

\[NotPrecedes] (), 1005, 1382

\[NotPrecedesEqual] (), 1005, 1382

\[NotPrecedesSlantEqual] (), 1005, 1382

\[NotPrecedesTilde] (), 1005, 1382

\[NotReverseElement] (), 1004, 1382

\[NotRightTriangle] (), 1005, 1382

\[NotRightTriangleBar] (), 1005, 1382

\[NotRightTriangleEqual] (), 1005, 1382

\[NotSquareSubset] (), 1005, 1382

\[NotSquareSubsetEqual] (), 1005, 1382

\[NotSquareSuperset] (), 1005, 1383

\[NotSquareSupersetEqual] (), 1005, 1383

\[NotSubset] (), 1004, 1383

\[NotSubsetEqual] (), 1004, 1383

\[NotSucceeds] (), 1005, 1383

\[NotSucceedsEqual] (), 1005, 1383

\[NotSucceedsSlantEqual] (), 1005, 1383

\[NotSucceedsTilde] (), 1005, 1383

\[NotSuperset] (), 1004, 1383

\[NotSupersetEqual] (), 1004, 1383

\[NotTilde] (), 1003, 1383

\[NotTildeEqual] (), 1003, 1383

\[NotTildeFullEqual] (), 1003, 1383

\[NotTildeTilde] (), 1003, 1384

\[NotVerticalBar] (), 1005, 1384

Nounifying (holding), 336

Novell networks, 658

\nprec (TeX), \[NotPrecedes] (), 1005

NProduct, 103, 951, 957, 1226

\nsim (TeX), \[NotTilde] (), 1003

NSolve, 104, 821, 951, 959, 1068, 1226

         implementation of, 1068

\nsubseteq (TeX), \[NotSubsetEqual] (), 1004

\nsucc (TeX), \[NotSucceeds] (), 1005

NSum, 103, 951, 957, 958, 1226

         implementation of, 1068

NSumExtraTerms, 958

NSumTerms, 958

\nsupseteq (TeX), \[NotSupersetEqual] (), 1004

\[NTilde] (), 190, 998, 1384

\[Nu] (), 175, 990, 1384

Nudging expressions, 455

Null, 1056, 1226

\[Null] (), 1008, 1384

Null list, 1022

NullRecords, 646, 648, 1227

NullSpace, 907, 908, 910, 1227

         implementation of, 1069

NullWords, 646, 648, 1227

Number, of lines, $Line, 703, 1331

Number, 646, 1227

Number marks, 1021

Number of elements, Length, 236, 1192

Number of occurrences, Count, 124, 261, 1115

Number of terms, Length, 75, 1192

Number representation, continued fraction, ContinuedFraction, 754, 1112

Number sign (#), Slot, 249, 1284

Number theory, 772

         and Diophantine equations, 843

         functions in, 749

         L-series in, LerchPhi, 774, 1193

         theorems in, 818

         theorems in, Simplify, 73, 1282

Number-theoretic transforms, Times (*), 1067, 1306

NumberForm, 435, 437, 1227

NumberFormat, 436, 1228

Numbering, of equations, 202

         of lines, CellLabelAutoDelete, 607, 1099

         of lines in notebooks, 50

         of parts in expressions, 234

         of sections, 202

NumberMarks, 634, 730, 1228

$NumberMarks, 730, 1334

NumberMultiplier, 436, 1228

NumberPadding, 436, 1228

NumberPoint, 436, 1228

NumberQ, 267, 723, 724, 1228

Numbers, 29, 722

         accuracy of, 727

         algebraic, 809, 826

         arbitrary-precision, 30, 33, 731

         arbitrary-precision in MathLink, 675

         bases of, 438, 725, 1021

         equality testing for, 732

         exact, 30, 722

         fixed-precision, 737

         floating-point, Real, 30, 722, 1258

         formatting tables of, 440

         functions of complex, 746

         heads of, 723

         high-precision, 728

         implicit, NumericQ, 724, 1229

         input forms for, 1021

         input of, 644, 729

         internal storage of, 1067

         low-precision, 728

         machine-precision, 737

         output of, 435

         padding in output of, 437

         patterns for, 279

         precision in output, 435

         precision of, 727

         random, Random, 747, 1254

         rational, 30

         rational, Rational, 722, 1255

         real, Real, 30, 722, 1258

         strings consisting of, DigitQ, 413, 1123

         testing for, NumberQ, 267, 1228

         testing for even, EvenQ, 267, 1137

         testing for odd, OddQ, 267, 1230

         testing for types of in patterns, 724

         tests for types of, 723

         truncation of, Chop, 730, 1103

         types of, 722

         variation of machine precision in, 738

NumberSeparator, 436, 1229

NumberSigns, 436, 1229

Numerator, 74, 1229

Numerators, expansion of, ExpandNumerator, 801, 1138

Numeric keypad, 26

Numeric quantities, testing for, NumericQ, 267, 724, 1229

Numerical analogs of symbolic functions, 951

Numerical analysis, 740

Numerical calculations, 29, 722

Numerical computation, optimized, Compile, 213, 1109

Numerical data, 107, 109, 924

Numerical derivatives, 791

Numerical differential equations, 105, 961

         representation of solutions to, 105

Numerical differentiation, 791

Numerical errors, 737

Numerical evaluation, 30, 102, 727, 1043

Numerical factors, in polynomials, FactorTerms, 797, 1144

         pulling out, FactorTerms, 797, 1144

Numerical functions, 745

         approximate, Interpolation, 932, 1183

Numerical input, 1021

Numerical integration, 82, 954

         NIntegrate, 103, 954, 1219

         path of, 955

         recursion in, 956

         sampling of functions in, 956

         singularities in, NIntegrate, 954, 1219

Numerical mathematics, 102, 951

         uncertainties of, 952

Numerical matrices, patterns for, 280

         testing for, MatrixQ, 267, 1208

Numerical maximization, NMaximize, 106, 974, 1219

Numerical minimization, errors in, 953

         FindMinimum, 973, 1148

         NMinimize, 106, 974, 1220

Numerical optimization, 106

Numerical overflow, testing for, Check, 482, 1102

Numerical precision, 727

         in compiled functions, 373

         in examples, xv

Numerical products, NProduct, 103, 957, 1226

Numerical root finding, 960

         FindRoot, 104, 1149

Numerical solution of differential equations, NDSolve, 961, 1216

Numerical solution of equations, 87, 959

         FindRoot, 960, 1149

Numerical solution of polynomial equations, NSolve, 959, 1226

Numerical summation, 83

         errors in, 953

         NSum, 103, 957, 1226

Numerical values, defining, 320

Numerical vectors, patterns for, 280

         testing for, VectorQ, 267, 1318

NumericFunction, 329, 724, 1043, 1229

NumericQ, 267, 724, 1044, 1229

NValues, 1052

\nwarrow (TeX), \[UpperLeftArrow] (), 1006