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The Mathematica Book, version 5.0
Browsable Index
\[AAcute]
( ),
998,
1354
\[ABar]
( ),
998,
1354
Abel equations, DSolve,
873,
1129
Abel's Theorem,
820
Abends,
61,
479
Abort, Throw,
350,
1304
Abort,
371,
1048,
1075
$Aborted,
371,
1048,
1325
Aborting calculations,
62
AbortProtect,
371,
1075
Aborts,
370
Above, overscript,
180
OverscriptBox,
445,
1235
\above (TeX), FractionBox,
445,
1155
Above parenthesis, \[OverParenthesis]
( ),
997
Abramov algorithm, DSolve,
1071,
1129
RSolve,
1071,
1269
Abs,
31,
34,
745,
746,
813,
1075
Abscissa, Axes,
134,
512,
1086
Absent from expression, FreeQ,
268,
1156
Absent from list, Complement,
127,
1109
FreeQ,
124,
1156
Absolute coordinates,
505,
531
Absolute error, Accuracy,
727,
1077
Absolute invariant, KleinInvariantJ,
787,
1190
Absolute size, for points, AbsolutePointSize,
500,
1076
Absolute value, Abs,
31,
34,
745,
746,
1075
notation for, \[LeftBracketingBar]
( ),
1002
AbsoluteDashing,
501,
1075
in three dimensions,
525
AbsoluteOptions,
145,
490,
581,
1075
AbsolutePointSize,
500,
1076
in three dimensions,
525
AbsoluteThickness,
501,
1076
in three dimensions,
525
AbsoluteTime,
710,
1076
AbsoluteTiming,
711,
1076
Abut boxes, RowBox,
445,
1267
\accent (TeX), OverscriptBox,
445,
1235
Accent grave (`), as context mark,
392,
1015
in package names,
640
Accented characters,
190,
998
Accents,
998
Account, of user, $UserName,
716,
1339
AccountingForm,
435,
1076
Accumulate, FoldList,
243,
1151
Accumulate (Version 1 function), see FoldList,
1402
Accumulating expressions, Reap,
355,
1259
Accuracy, in examples,
xv
in timings, $TimeUnit,
711,
1338
increasing, SetAccuracy,
736,
1277
numerical,
33,
727,
952
Accuracy,
727,
1077
AccuracyGoal,
958,
976,
1077
Action, in notebooks,
49
Activating 2D forms,
430
Activating textual input,
177
Active,
448,
595,
607,
1077
Active cells,
54
Active element, ButtonBox,
448,
595,
1092
Active elements in notebooks,
54
Active links, Links,
662,
1198
Active text, in notebooks,
56
\[ACup]
( ),
998,
1354
Adamchik techniques, Sum,
1071,
1296
Adams methods, NDSolve,
979,
1068,
1216
Adaptive integration procedure,
953
Adaptive procedure, in NDSolve,
966,
1216
Adaptive sampling, in plots,
137
Add, without carry, BitXor,
756,
1090
Add-in programs,
657
Add-ons, location of files for,
1063
Addition, of elements to lists, Append,
125,
288,
1080
patterns involving,
270
Plus (+),
29,
1244
Additive cellular automata, CellularAutomaton,
946,
1101
AddTo (+=),
305,
1029,
1077
Adjoint, Conjugate,
746,
1111
AdjustmentBox,
455,
1078
Adjustments, to formatting,
449
Adobe character encoding,
421
\[ADoubleDot]
( ),
190,
998,
1354
Advanced topic sections,
xv
\[AE]
( ),
998,
1354
\ae (TeX), \[AE]
(),
998
\AE (TeX), \[CapitalAE]
( ),
998
Agemo, \[Mho]
( ),
994
Aggregating brace, \[OverBrace]
( ),
997
\[AGrave]
( ),
190,
998,
1354
\[AHat]
( ),
998,
1354
AIFF format, exporting, Export,
569,
1141
importing, Import,
570,
1176
Airy functions, AiryAi,
776,
1078
derivatives of, AiryAiPrime,
776,
1078
Airy's differential equation, DSolve,
872,
1129
AiryAi,
775,
776,
1078
AiryAiPrime,
775,
776,
1078
AiryBi,
775,
776,
1078
AiryBiPrime,
775,
1078
Alarm, Pause,
710,
1241
Albedo,
547
\[Aleph]
( ),
192,
993,
1354
Algebraic algorithms, GroebnerBasis,
805,
1168
Algebraic computation,
63
Algebraic curves,
822
Algebraic equations,
88
Solve,
820,
1285
Algebraic expressions, internal representation of,
234,
279
parts in,
234
patterns for,
261,
279
pieces of,
73
Algebraic extensions,
751
Algebraic geometry,
845
Algebraic numbers,
809,
826
Algebraic operations on polynomials,
803
Algebraic simplification,
63
Simplify,
68,
813,
1282
Algebraic transformations,
67
Algebraic variables,
66
Algebraic varieties, GroebnerBasis,
805,
1168
Algebraics,
817,
1079
Algorithms, algebraic,
223
algebraic, GroebnerBasis,
805,
1168
complexity of,
76
in Mathematica,
219,
1066
monitoring,
977
precision in numerical,
733
time complexity of,
76
Alias (Version 1 function), see $PreRead,
1402
Aliases, conventions for,
1353
HTML,
1353
SGML,
1353
TeX,
1353
user defined,
987
user defined, InputAliases,
613,
1178
\[AliasIndicator]
( ),
1009,
1354
Aliasing, of sound, SampleRate,
172,
1270
Alignment, in numerical output,
437
in tables, TableAlignments,
442,
1299
of buttons,
452
of columns, ColumnAlignments,
449,
1107
of expressions, ShowContents,
455
of GridBox, GridBaseline,
449,
1166
of inline cells, CellBaseline,
605,
1097
of numbers in tables, PaddedForm,
440,
1235
of rows, RowAlignments,
449,
1267
of subscripts, ScriptBaselineShifts,
457,
1272
\[AlignmentMarker]
( ),
451,
1008,
1354
Aliquant, Mod,
749,
1213
All, ForAll,
847,
1152
All,
125,
136,
1040,
1079
All expressions, pattern for, Blank (_),
259,
1090
All parts of expressions,
238,
1041
applying functions to, MapAll (//@),
245,
1205
Allocating memory, in MathLink,
667
\[Alpha]
( ),
175,
990,
1354
Alphabet, generating, CharacterRange,
413,
417,
1102
Alphabetic characters, test for, LetterQ,
413,
1193
Alphabetizing, of strings, Sort,
411,
1286
Alternation, Or (||),
87,
1233
patterns involving,
269
Alternatives, patterns involving,
269
Alternatives (|),
269,
1028,
1079
Always, ForAll,
847,
1152
AmbientLight,
545,
1079
Ambiguities, in special characters,
985,
1031
in TraditionalForm,
194
Ampersand, double (&&), And,
87,
1079
Ampersand (&), Function,
249,
1159
Amplitude, in elliptic functions, JacobiAmplitude,
782,
1189
of sound,
172,
566
Analog input,
51
Analysis of variance,
794
Analytic continuation,
769
AnchoredSearch,
651,
1079
And, bitwise, BitAnd,
756,
1089
And (&&),
87,
347,
1028,
1079
argument evaluation in,
1046
evaluation in,
347
\[And]
( ),
183,
985,
1001,
1354
And bar, \[Nand]
( ),
1001,
1215
\[Angle]
( ),
192,
996,
1354
Angle bracket, \[LeftAngleBracket]
( ),
191,
1002
Angle of view, ViewPoint,
152,
153,
532,
1319
Angles,
32
\[Angstrom]
( ),
192,
984,
994,
1355
Angular momentum, in quantum mechanics,
760
Animate,
170
Animate Selected Graphics menu item,
617
Animate selection, SelectionAnimate,
588,
1274
Animation,
51,
170,
617
of three-dimensional rotation,
170,
536
AnimationDirection,
617,
1080
AnimationDisplayTime,
617,
1080
Animations, exporting, Export,
567,
1141
Annotated names,
989
Annotated operator,
476
Annotation, of input, ShowAutoStyles,
613,
1280
Annotations, in graphics,
560
Anonymous functions, Function (&),
248,
1159
ANOVA (analysis of variance),
794
ANSI prototypes,
677
Anti-derivative, Integrate,
859,
1182
Antilogarithm, Exp,
31,
1137
Antique fonts,
992
Antisymmetry, Signature,
760,
1282
Any expression, pattern for, Blank (_),
259,
1090
Apart, spacing characters,
1008
Apart,
69,
70,
802,
1069,
1080
API, for Mathematica,
657
APL, catenate in, Join,
126,
1190
compress in, Select,
251,
1273
grade in, Ordering,
129,
255,
1233
grade in, Sort,
127,
1286
iota operator in, Range,
119,
1255
ravel in, Flatten,
130,
1150
reduce in, Apply (@@),
243,
1081
reshape in, Partition,
128,
292,
1240
shape in, Dimensions,
120,
916,
1124
Appell hypergeometric function, AppellF1,
781,
1080
AppellF1,
780,
781,
1080
Append,
125,
236,
288,
1080
Appending, to files, PutAppend (>>>),
624,
1253
to lists, Append,
125,
288,
1080
to lists, Sow,
355,
1286
to notebooks, CellPrint,
575,
1100
to strings, StringInsert,
408,
1291
AppendTo,
306,
1081
Apple events,
658
Apple key, \[CloverLeaf]
( ),
1009
AppleTalk,
658
Applicability, regions of, Assumptions,
867,
1084
Applicability of transformation rules, Condition (/;),
265,
1111
Application, precedence of function,
1023
Application directory, $InstallationDirectory,
637,
1330
Application packages,
59,
97,
109
Apply (@@),
243,
1025,
1081
levels in,
1041
Applying functions, by name, Apply (@@),
243,
1081
to all parts of expressions, Map (/@),
244,
1205
to lists, Apply (@@),
243,
1081
to specific parts of expressions, MapAt,
246,
1205
with side effects, Scan,
247,
1271
\approx (TeX), \[TildeTilde]
( ),
1003
Approximate differentiation,
791
Approximate formulas, derivation of from data, Fit,
926,
1149
Series,
94,
884,
1276
Approximate functions, InterpolatingFunction,
930,
1182
Approximate numbers, Real,
722,
1258
Approximately equal, \[TildeEqual]
( ),
1003
Approximation, rational, ContinuedFraction,
754,
1112
Approximation of functions, FindFit,
108,
1146
Fit,
926,
1149
Interpolation,
930,
1183
on grids, ListInterpolation,
934,
1201
Series,
94,
883,
1276
Approximations, algebraic, Series,
94,
883,
1276
numerical, N,
30,
728,
1214
Arbitrary length, lists in MathLink,
670
Arbitrary-precision functions,
731
Arbitrary-precision numbers,
33,
731
in MathLink,
675
in plots,
138
input of,
729
Arc trigonometric functions,
31,
761
ArcCos,
31,
761,
1081
ArcCosh,
761,
1081
ArcCot,
761,
1081
ArcCoth,
761,
1081
ArcCsc,
761,
1081
ArcCsch,
761,
1082
Architecture, of Mathematica system,
44
processor, $ProcessorType,
717,
1336
Arcs, of circles, Circle,
496,
1103
ArcSec,
761,
1082
ArcSech,
761,
1082
ArcSin,
31,
761,
1082
ArcSinh,
761,
1082
ArcTan,
31,
761,
1082
ArcTanh,
761,
1082
Area, Integrate,
81,
1182
Arg,
34,
746,
813,
1083
Argand diagrams, ParametricPlot,
161,
1237
argc, argv, $CommandLine,
716,
1327
argc, in MathLink,
679
Argument of complex number, Arg,
34,
746,
1083
Arguments,
230
constraining types of,
264
conventions for,
1039
default values for,
274,
1050
dropping for printing, Shallow,
432,
1279
evaluation of,
332,
1045
evaluation of in assignments,
342
function names as,
240
functions with variable numbers of,
273
in pure functions,
249
named,
276
non-standard evaluation of,
1045
on Mathematica command line, $CommandLine,
716,
1327
optional,
1050
options as,
133,
1039
overriding non-standard evaluation of, Evaluate,
1047,
1136
positional,
276
preventing evaluation of,
336
preventing evaluation of, Unevaluated,
339,
1315
scoping of names for,
387
sequences of,
273
to external functions,
662
transformation rules as,
276
unevaluated,
336
warning about number of,
61
argv array,
698
argx message,
480
\[ARing]
( ),
190,
998,
1355
Arithmetic,
29
in finite fields,
31,
749
interval, Interval,
740,
1184
machine,
728,
737
speed of,
77
Arithmetic difference equations, RSolve,
96,
891,
1269
Arithmetical functions, higher,
749
ArithmeticGeometricMean,
788,
1083
Arity, of functions,
273
Arnoldi methods, Eigenvalues,
1069,
1131
ARPACK, Eigenvalues,
1069,
1131
Arrange, Sort,
127,
1286
Arrangement, of output,
444
Array,
119,
250,
283,
289,
896,
916,
1083
Array automata, CellularAutomaton,
942,
1101
Array origins,
666
\arraycolsep (TeX), ColumnSpacings,
449,
1108
ArrayDepth,
290,
916,
1083
ArrayQ,
267,
290,
916,
1083
ArrayRules,
898,
922,
1084
Arrays,
42
as lists,
307
as matrices,
899
as tensors,
915
color, RasterArray,
498,
1255
creation of,
283
creation of, Table,
115,
1299
exporting, Export,
643,
1141
extensible,
307
extracting elements from,
117
formatting of,
439,
443
formatting of, GridBox,
445,
1167
importing, Import,
643,
1176
in C,
668
in MathLink,
665
input of,
186
interpolation of, ListInterpolation,
934,
1201
List,
40,
1199
multidimensional,
116
origin of, Mod,
749,
1213
plotting,
159,
517
reading from data files, ReadList,
644,
1257
sparse,
307
sparse, SparseArray,
295,
1287
testing for, ArrayQ,
267,
1083
with continuous indices as functions,
309
Arrow (->), Rule,
64,
299,
1269
Arrow characters,
1006
Arrow keys,
180
Arrows, control,
455
Art, computer,
11
Artificial intelligence, in simplification, Simplify,
69,
1282
\[AscendingEllipsis]
( ),
997,
1355
ASCII,
xv,
419,
421
in MathLink,
679
Aspect ratios, of geometrical figures,
495
of parametric plots,
163
AspectRatio,
134,
151,
163,
495,
509,
1084
for three-dimensional plots,
535
AspectRatioFixed,
616,
1084
Assertions,
268
simplification with, Simplify,
72,
815,
1282
Assignments,
303,
1051
associated with particular objects,
316,
1051
chains of,
313
compared with equality tests,
84
compared with replacements,
65
delayed, SetDelayed (:=),
311,
1278
evaluation in,
311,
336,
340,
1047
immediate, Set (=),
311,
1277
local,
378
local variables in,
379
of downvalues directly, DownValues,
322,
1128
of upvalues directly, UpValues,
322,
1317
of values for symbols, Set (=),
39,
1277
ordering of,
310
preventing evaluation in,
343
testing for, ValueQ,
268,
1317
tracing, Trace,
357,
1310
Assistance,
58
in notebook front end,
57
Associated packages,
205
Associative functions,
326
in patterns,
271
Associativities, of operators,
1031
table of,
1024
Associativity,
255
in pattern matching,
261
of operators,
470
Assume real variables,
813
Assuming,
818,
1084
Assumptions, about complex variables, ComplexExpand,
812,
1110
in simplification, Simplify,
72,
815,
1282
Assumptions,
867,
1084
$Assumptions,
818,
1325
Asterisk, Times (*),
29,
1306
Asterisk (*), as string metacharacter,
58,
411
Astronomical data, importing, Import,
208,
1176
Astronomy, example from,
11
\asymp (TeX), \[CupCap]
( ),
1003
Asymptotes, limits near,
895
Asymptotic, \[TildeTilde]
(),
1003
Asymptotic expansions, Series,
884,
1276
Asymptotically equal, \[TildeEqual]
(),
1003
Asynchronous interrupts,
62
At sign (@),
233
as string metacharacter,
412
\[ATilde]
( ),
998,
1355
Atomic subexpressions, in simplification, ExcludedForms,
814,
1137
AtomQ,
268,
1085
Atoms,
1016
as leaves in trees,
239
lexical,
467
number in expression, LeafCount,
714,
1192
Atop, overscript,
180
OverscriptBox,
445,
1235
\atop (TeX), GridBox,
445,
1167
Attractors, strange,
981
Attributes,
327
for pure functions,
332
functions for testing,
267
in pattern matching,
271
of built-in functions,
329
of cells, CellTags,
607,
1100
used in matching patterns,
1050
Attributes,
271,
328,
1052,
1085
AU format, exporting, Export,
569,
1141
importing, Import,
570,
1176
Audio, exporting, Export,
569,
1141
importing, Import,
570,
1176
Audio output,
171
representation of,
565
Auditory system, human,
172
Aut, Xor,
87,
1324
Author's address,
iv
Authorization, of network licenses,
1058
AutoCAD format, exporting, Export,
569,
1141
importing, Import,
570,
1176
AutoIndent,
613,
1086
AutoItalicWords,
613,
1086
Autoload directory,
1065
Autoloading, of packages,
60,
401
Automata, cellular, CellularAutomaton,
942,
1101
Automatic,
136,
1086
Automatic evaluation, of cells, InitializationCell,
608,
1178
Automatic grouping, CellGrouping,
618,
1099
Automatic numbering,
202
Automatic options, finding values of, AbsoluteOptions,
145,
490,
1075
Automatic styles, ShowAutoStyles,
613,
1280
Automatic variables,
378
Autoplectic sequences,
980
Autoscaling, in plots, PlotRange,
508,
1243
AutoSpacing,
454,
1086
Average, Mean,
109,
924,
1209
Avoiding evaluation,
336
Axes, in contour plots,
520
in density plots,
520
in three-dimensional graphics,
549
in two-dimensional graphics,
512
labeling of three-dimensional, AxesLabel,
552,
1087
options for,
512
positions of three-dimensional, AxesEdge,
551,
1087
tick marks on, Ticks,
134,
512,
1305
Axes,
134,
151,
511,
512,
549,
1086
AxesEdge,
551,
1087
AxesLabel,
134,
151,
512,
552,
1087
AxesOrigin,
134,
512,
1087
AxesStyle,
512,
550,
1087
Axis,
451
Azimuth, Arg,
746,
1083
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