Index The alphabetization is character-by-character, including spaces; numbers and symbols come first. All fonts are treated equally.

The index entries refer to the sections or subsections and are hyperlinked. The index entry for a subject from within the exercises and solutions are hyperlinked mostly to the exercises and not to the corresponding solutions.

"subject in action" refers to examples or solutions of exercises making very heavy use of subject, or could be considered archetypical use of subject.

Index entries are grouped, at most, one level deep. Index entries containing compound names, such as Riemann­Siegel, are mentioned on their own and not as a subentry under the first name.

Built-in functions are referenced to the section in which they are first discussed. Built-in functions and functions defined in the standard packages appear in Courier bold (example: Plot). Functions defined in the Mathemat­

ica GuideBooks appear in Courier plain (example: DistributionOfBends).

Numbers and Symbols @@@ Apply 711 < Less 545 Blank 277,567 <= LessEqual 545

I + I. PDE in - dimensions 14 BlankNullSequence 569 ,; Less Equal 545 Degree 173 BlankSequence 569 { List 299 I 172 CompoundExpression 409 } List 299

d! GoldenRatio 175 /; Condition 588 /@ Map 737 e E 174, 874 Cross 778 //@ MapAll 740 00 Infinity 178 0 D 308 .. MessageName 400 Tf Pi 172. 874 I Divide 162 Not 561 y EulerGiiillllla 176 Dot 777 Not 561 r, Zeta 645 Equal 551 Optional 580 {j KroneckerDelta 718 Equal 551 II Or 561

& Function 336 v Or 561 Mathematica input forms and output << Get 437 % Out 3

forms > Greater 545 [ [ Part 202 >= GreaterEqual 545 ]] Part 202

: := Alias 512 "' GreaterEqual 545 [ Part 202

Alternatives 585 ? Information 397 D Part 202 && And 561

?? Information 397 Pattern 277. 567 A And 561 dl Integrate 282 ? PatternTest 586 @@ Apply 711

1004

+ Plus 160 Power 160

>> Put 437 >>> PutAppend 438

Repeated 584 RepeatedNull 584

I. ReplaceAll 611 II. ReplaceRepeated 612 -> Rule 611 .... Rule 611 : > RuleDelayed 611 , .. RuleDelayed 611

SameQ 556 Set 281

. - SetDelayed 281,876 # Slot 338 ## SlotSequence 338 <> StringJoin 438

Subtract 162 I: TagSet 319

* Times 160 X Times 160 != Unequal 552 =!= UnsameQ 556

Unset 292 UpSet 317

: = UpSetDelayed 317 @ Prefix notation 297

Infix notation 298 II Postfix notation 297

Context marker 4 7 5 String quotes 152

A

Abort 422 AbortProtect 422 Aborts

avoided- 422 because of memory constraints 423 because of time constraints 423 catching- 423, 526 intentionally induced- 791 neutralized - 650 of evaluations 422 protecting from - 422 recovering from - 423

Abs 185 Absolute value

of numbers 184 of options 30 I

AbsoluteOptions 302 Accumulation, of singularities 265 Ackermann function 432 Addition

associativity of- 305 commutativity of- 304 of attributes 304 of elements to lists 727 of exact and inexact numbers 163 of expressions 160 of function definitions 285 of lists and numbers 306 of matrices 750 resulting from subtraction 162

Additional branch cuts 190 built-in functions 489 potential exercises I 03

Adjacent commas 410 words 870

Aeolian sand ripples 1 06 Algebra packages, all - 496 Algebra'InequalitySolve' 66 Algebra 'PolynomialContL

nueFractions' 776 Algebraic

branch points 227 numbers 64 treatment of analysis problems 68

Algebraization of expressions 68 Algorithm

bead sort - 82 Euclidean - !50 for filling jugs 104 mergesort - 7 34

Algorithms complexity of- 734 for sorting 734 for symbolic linear algebra 826 monitoring- 734, 756

Alias 512 Aliases for functions 512 AlignBrackets 939 All 205 AllPossibilities 879 AllPossibleFactors 970 AllSyntacticallyCorrect~

Expressions 599 Alternative arguments 585 Alternatives 585

Amitsur-Levitzky identity 878 Analytic continuation of arctan 227 And 561 And. logical - 561 Angle

of a point in the plane 181 unit of- 173

Animation creating an - 89 of an iterated map 349 of charging an icosahedron 90 of interlocked tori 89 of polyhedra constructions 704 of polypaths 642 of the Gauss map 44

Annotation 495 Annotation, of packages 495 Annulus 106 Antisymmetrization 873 Apollonius circles 34 Append 728 AppendTo 728, 879 Application, function - 170 Apply 711 Applying

functions 711 new heads to expressions 711 replacement rules 610

Approximate zeros 151 Approximation, best - for overdeter-

mined systems 823 Arccos 181 ArcCosh 183, 227 ArcCot 182 ArcCoth 183, 227 ArcCsc 182 ArcCsch 183 ArcSec 182 ArcSech 183, 227 ArcSin 181 Arcsine, the function - 181 ArcSinh 183 ArcTan 181 ArcTanh 183 Arctrig functions 180 Area, rectangle of maximal - I 05 Arg 185 Argument of numbers 184 Arguments 713 Arguments

alternative- 585

Index

Index

and heads 145 arbitrary number of- 160, 569 avoided evaluation of- 501 default - 583 definitions associated with - 321 evaluation of - 501 exchanging heads and - 7 41 expected number of- 404 extracting - 713 for !vlathematica 109 fulfilling conditions 588 functions with many - 569 functions with no - 569 held- 313 "incorrect" - 399 later to be defined - 405 matrix- 550 multiple - 280 multiple - in pure functions 337 of a head 145 of prescribed type 277 of pure functions 342 of specified type 277 omitted - 580 optional - 580 optional - of arithmetic functions

583 repeated- 583 sequence of - 412 splicing in - 340 symbolic - 405 threading functions over- 780 to functions 571 "inappropriate" - 405 unevaluated - 312, 369 "unexpected" - 399 unexpected number of- 404 vector- 549 with a certain head 277 with certain properties 586 with faked heads 383 with prescribed head 277 wrong number of - 512 zero- 280

Arithmetic all - expressions 876 avoiding definitions for- functions

317 functions 28 operations with arbitrary expressions

149 operations with numbers 156 precedences of- operations 158

Array 707 Arrays

formatting of- 720 of numbers 707 with a given head 707

Artifacts, machine arithmetic - 270 Aspect ratio, misconceptions about

pleasing - 175 Assignments

cached- 323 complexity of- 323 delayed - 281 failed- 284, 309, 433, 587 for compound heads 328 for formats 329 for numerical values 326 immediate- 281 immediate versus delayed- 283,

430 indirect - 328 leading to recursions 644 numerical - 326 of messages 408 of values 281 recursions in - 283 recursive - 283 scoping in - 459 to parts of a function 317 to parts of expressions 742 to symbols and expressions 281

Associative functions 305 functions in pattern matching 602

Asymptotic solution of PDEs 100 Atom, photon emitted from an excited

- 108 Atomic expression 560 AtomQ 560 Atoms

in d dimensions 108 of expressions 560

Attribute emulating the- Flat 662 the- Constant 308 the- Flat 305 the - HoldAll 313 the- NHoldAllComplete 315 the- HoldFirst 313 the - HoldRes t 313 the- Listable 306 the - Locked 309 the- NumericFunction 307 the- Oneidenti ty 306

the- Orderless 304 the- Protected 309

Attributes 304 Attributes

and definitions 305 and pattern matching 601 and patterns 60 I and replacements 621 for associativity 305 for avoiding evaluation 313 for commutativity 304 for numeric functions 307 for protection 31 0 for temporary symbols 453 in the evaluation process 50 I inheritance of- 986 interacting - 607 meaning of all - 304 of all system functions 766 offunctions - 304 of pure functions 342 removing - 3 10

Autoloading 494, 879 Automatic 581 Automatic switch to high-precision

1005

numbers 427 Autonumericalization 151 Autosimplitications 149, 151, 162 Auxiliary variables, avoided- 5, 879 Axiom, the computer algebra system

102

B

Bach brackets 873 Ball, base- pieces 104 Banach-Tarski paradox 103 Bands in periodic potentials 100 Baseball pieces 104 BaseForm 220 Bases

equivalent - 1 07 for representing numbers 220

Basins of attraction 354 Bayley, D. H, 101 Bead sort algorithm 82 BeadSort 83 Begin 475 Begin, of contexts 4 75 Bell inequalities 100 Benford's tule 869 Benney equation 14

1006

Bicycle motion 103 Billiard, Sinai - 30 Binary

representions of numbers 217 splitting 81

Binary bracketing 880 Binomial theorem q- and h-version

646 Birthday paradox 990 Bit operations 490 Blank 277, 567 BlankNullSequence 569 BlankSequence 569 Bloch-Floquet theory 100 Block 450 Block matrices 878 Boiling points 885 Boltzmann constant I 08 Bolyai

digits 81 expansion 81

BolyaiRoot 81 Boolean

functions 562 operations 561 variables 539

Borwein, J. M. 101 P. B. 101

Bound states in tubes 100, 107 Box

filling curve 93 typeset - types 861

Braces for lists 3 in Mathematica 3

Bracketing, binary- 880 Brackets

Bach- 873 counting closing - 870 in Mathematica 3

Branch cuts additional - 190 canceling- 243, 251 end points of- 227 in Mathematica and in mathematics

190 of 1 I (z4 ) '14 227 of analytic functions 188 of inverse hyperbolic functions 188 of inverse trigonometric functions

227 of logarithm and power functions

188

of mathematical functions 188 of nested functions 227 overlapping - 251

Branch points of I I (z4) 114 227 of inverse hyperbolic functions 188 of inverse trigonometric functions

227 of logarithm and power functions

188 of nested functions 227

Branching constructs 563 Bridges, collapsing- 105 Bubbles, rising- 105 Buchberger, B. 100 Built-in, functions 398 Burridge-Knopoff model 12 Bytecount 425

c

Caching in action 323 in Mathematica 329

Calculations aborting - 422 interrupting - 448 matrix- 802 monitoring - 442 overview of- 7 phase transitions in - 106 rule-based - 630 showing intermediate steps in - 442 symbolic - without variables 106 timing- 331 timing of symbolic versus numeric -

804 tracing - 444 under memory constraints 423 under time constraints 423

Calculus packages 497 q-- 646

Camassa-Holm differential equation 648

CamassaHolmOperator 674 Campbell-Baker-Hausdorff formula

663 Camphor scraping 105 Canary song modeling I 06 Canceling branch cuts 243 Canonical form

of differences 162

of polynomials 27 5 of quotients 162

Cantor series 355 Car

license plate of author's- 169 modeling- traffic jams 104 path of- wheels 104

Carnot cycle 107 Cases 598, 723 Cases versus Select 598 Castle rim function 228 Cat, falling - I 03 Catching

aborts 423, 526 messages 424 zeros in linear algebra 827

Cauchy theorem 11 Cayley

group 367 multiplication 367

Cayley-Hamilton theorem 847 CayleyHamiltonTrueQ 847 CayleyTimes 367 CellPrint 402 Cells

analyzing - 860 counting - 860 initialization - I printing 402 types of - 860 wide- 200

ChainedPlatonicBody 83 Chains

hanging - I 05 sliding- 107 unlocking - I 06

Chaitin, G. J. I 09, 397 Challenge

ISSAC 1997 system challenge 109 problems 107 $100- 109

Change, for $1 879 Changing

mathematical research I 0 I money 879 system functions 311 system values temporary 459

Chapter analysis 860 ChapterOverview 495 Characteristic polynomial 848 CharacteristicPolynomial

848 Characters 769

Index

Index 1007 --------~·--··------------

Characters forming a Mathematica scrabble 784 forming multiple function names

771 frequency of- 858 named- 441 of strings 769 representing operators 969 special - 146

Charges moving- 108 nomadiating I 07 on a wire 108

Check 424 CheckAbort 423 Checking

consistency of the references 869 for aborts 423 for functions used too early 869 for messages 424 for misspellings 407 inputs 404 spacings 870 the number of arguments 404

Chemical elements 885 Church, A. 336 Circle, circumscribed - 65 Circles

Apollonius - 34 touching - 34

Circumscribed circle 65 Citations, consistency of- 869 Classical mechanics

Hilbert space formulation of- I 08 stabilizing- I 08

Classical orbits 26 Clear 292 ClearAttributes 310 Clearing

function definitions 292 symbol values 292

Closed form numbers 105 Clusters modeling I 07 Coding style 6 Coefficients

of polynomials 824 q-Binomial 665

CofactorExpansion 826 Coin

falling- 104 rotating - 104

Collapsing bridges 105 numeric expressions 172

Collisions of variable names 488, 488 Combinators I 06 Commas

adjacent 410 separating arguments 145

Comments, density of- 870 Common

patterns 571 pitfalls in patterns matching 616 subexpressions 746 warning messages 511

Commutative functions 304 functions in pattern matching 601

Comparisons numerical - 540 of expressions 761 of Mathematica with a skilled human

98 of numbers 545 of output forms 14 7 of programming techniques 869 of trace implementations 807 sloppiness in - 546 using numerical techniques 735

Compilation, explicit - 26 Compiler 26 Complement 761 Complements, of sets 761 Complex 151 Complex

conjugation 184,616,639 number characteristics 184 numbers 151 numbers as default domain 164 sorting - numbers 632

Complexinfinity 177 Complexity

of array constructions 710 of eliminating double elements 762 of list constructions 71 0 of list manipulations 888 of pattern matching 618, 630 of sorting 734

ComposeList 358 Composition 359 Compositions of functions 145, 346 Compound heads 145 CompoundExpression 409

Computable numbers 105 Computations, timing - 331 Computer

quantum - 423 ultimate- 107

Computer algebra and creativity 100 and mathematical research 101 as a tool 101 general-purpose - systems 102 impacts of - 100 quotes about - I 00 references to - systems I 02

Computer algebra systems axiom 102 Form 102 Maple 102 Mathematica MuPAD 102 REDUCE 102

Computer mathematics 70, 101 Condition 588 Condition number of matrices 808 Condition versus PatternTest

591 Conditions

for patterns 588 in scoping constructs 590 positioning of- 588

Conformal maps of genus one regions 106 series expansion of - 71

Conf ormalMapSquareToUni t'·. Disk 71

Conjugate 185 Conjugates, Ferrer- 879 Connecting Mathematica to other

programs 433 Connections, web - 105 Consistency of branch cuts 188 Constant 308 Constant

Boltzmann - I 08 Euler's- 21, 176 Trott's- 70 1[ !72

Constants for differentiation 308 local- 450 mathematical - 180

Contact interactions, one-dimensional - 107

1008 -----------------------------

Container,lists as universal 702 Context 469 Context

and packages 472 begin and end of a- 475 creation and symbol creation 513 current- 470 Developer'- 490 dropping- names 475 Experimental'- 492 FrontEnd' - 492 Global' - 470 remove - specifications 775 System'- 471

Contexts 472 Contexts

and packages 4 79 and symbol names 469 creating symbols in- 476 default - 4 72 needed- 487 nested- 469 path of- 472 removing- names 475 special - 489

ContextTester 480 Continuation, analytic - 227 Continued radical expansion 81 Continued fractions

neat - 70, 978 periodic- 8 special - 70, 978

Contour plots, animations using - 44 ContourPlot3D 488 Contracted tensors 873 Control structures 563 Conventions

about function names formatting - 6

Convergence of the Newton method 353

Cooking times I 06 Corrugated

modeling - roads 104 moving charge above- surfaces I 08

Cos 167 Cos function in Mathematica 167 Cosh 168 Cot 167 Coth 168 Count 770

Counting comparisons 883 first digits 869 function applications 389, 665, 665 list operations 702, 8H4 mathematics phrases 866 number of tried pattern matches 609 rule applications 646

Cover graphics of the Programming volume 89

CPU time not to be exceeded 423 used for a calculation 331 used in a session 424

Creation of contexts and symbols 513 of symbols in contexts 476 of temporary symbols 450

Creativity, and computer algebra 100 Cross 778 Cross product

components of - 715 definition of- 778 in d dimensions 779 properties of the - 779

CrossGraphics 324 Crossword puzzle 784 CrossWordConstruction 791 Crumbling paper I 03 Crystal classes, in 4D I 08 esc 167 Csch 168 Cube

contracted and expanded - 39 in d dimensions I 04

Cube roots of a pseudodifferential operator I 07

Cumulative maximum of lists 634 Curl operator, eigenfunctions of the -

106 Curling rock 104 Curves

Hilbert- 93 nowhere differentiable- 36 space-filling- 93 tubifying 3D - 94

Custom notations 78 Cutting straight line figures I 06 Cycles of permutations 632 Cylinders

rolling- 107

Index

D

D 308 D'Hondt voting 875 Damping, oscillator with - II Data

analyzing - 885 exporting- 492 fitting- 823 importing - 492

Date 426 Date, current- 426 DeRham's function 23 Debugging

Mathematica expressions 442 variable localization 468

Decimal expansion 220 Decomposition, Schmidt - 78 Default 604 Default

arguments 583 arguments of arithmetic functions

161 domain of functions 164 level specifications 560 method 826 option values 581 values for pattern matching 604

Definition 434 Definitions

adding - automatically 334 and attributes 305 associated with arguments 318 auto-replacing- 292 changing when loading packages

879 complexity of creating - 323 complexity of extracting - 323 displaying - 433 dynamically g~nerated - 689 evaluation of- 290 for expressions 321 for noncommutative multiplication

662 for numerical values 326 for specialized integration 329, 593 for symbols 326 formatting- 329 generating special case - 329 indirect generation of - 322 internal form of- 321 lookup time for - 323 making function - 275

Index

modeling - 624 not associated with heads 318 object -miented - 318 of built-in functions 876 order of application of- 50 I precedence of various - 50 I programmatic generation and

destruction of- 789 recursive - 568, 592 saving- 433 self-changing - 689 specific versus general - 289 types of- 321 using side effects in- 756 viewed as rules 321

Degenerate cases of arithmetic operations 161

Degree 173 Degree unit of angle 173 Delete 725 DeleteCases 725 DeleteFile 438 Deleting

elements by pattem 725 elements from lists 724 files 438 numbers iteratively 871 stored output 437

Denominator 216 Denominators of numbers 216 Density matrices, eigenvalues of a

grand canonical - I 08 Dependence

mathematical - 560 structural - 560

Dependencies 773 Dependencies of function definitions

773 Depth 204 Depth, of expressions 204 deRham'"Points 24 Derivative

fractional - 103 ordered- 647

Det 803 Determinant

multidimensional- 874 of a matrix 803

Developer- 490 Developer'SetSystemOptions

492 Developer'SystemOptions 491 Developer'$MaxMachine-..

Integer 428

Diagonal matrices 713 DiagonalMatrix 714 Diagrams, Greechie - 1 07 Difference, finite - weights 645 Differentiability in the complex plane

674 Differential equation

Camassa-Holm - 648 D' A! am bert - I 08 rewritten as iterated integrals 349 Schri:idinger- I 07 wave- 108

Differential equations asymptotic solutions of - I 00 expressed as integral equations 350 nonlinear - with superposition

principle 106 renormalization group-based solution

of- 100 Differentiation

fractional - 103 of functions 308 of generalized constants 308 of parametrized matrices 647

Digit sum 10, 28,218 DigitCount 221 Digih

counting - 221 distribution of first - 869 of Bolyai expansions 81 of integers 217 of machine arithmetic 426 of numbers 217 of real numbers 217 of JT 69 relevant for comparisons 552 sum of- 10, 28, 33,218

Dimension of a quantum particle path 107

Dimensions 802 Dimensions

of expressions 802 of nested lists 802 of tensors 802

Dirac matrices 873 DiracTrace 924 Directedinfinity 177 Directions

in infinity 177 of table outlines 720

Dirichlet function 32 Disconnected sheets of a Riemann

surface 241

Discontinuities of analytic functions 188

Discontinuous limit 32

1009

Discrete mathematics packages 497 Discretization, perfect- 661 Disks. Jensen - 22 Dispatch 628 Displayed, form of expressions 143 Dissection, of polygons 107 Distribute 783 Distribution

age - ofreferences 864 of built-in function names 770 of cited joumals 899 of family names 105 of initials 870 of letters 867 of messages per function 401 of typeset boxes 861

Distributive law for noncommutative multiplication 662

Divide 162 Division

of expressions 162 of matrices 7 50 of numbers 162

DivisionFreeRowReduction 826

DLA cluster 107 Do 416 Do loop 416 Dolphins I 06 Dot 777 Dot product 777 Doublestruck letters 4 DownValues 322 Down values

and function definitions 321 manipulating - directly 789 monitoring - 772

Dreitlein, J. I 00 Dripping tap 104 Drop 725 Drop, shape of a - I 04 Dropping

context names 4 7 5 elements from lists 724

Ducci's iterations 872 Dynamic

programming 329 scoping 450

Dyson equation 388

1010

E

E 174,874 Earthquake modeling 12 Effect, side- in definitions 756 Eggs, cooking times for- 106 Eiffel tower 54 Eigenmesh 814 Eigensystem 808 Eigenvalues 808 Eigenvalues

distances between - 18 of a grand canonical density matrix

108 of matrices 18, 808 of sums of matrices I 07 prime numbers as - 107 simple- problem 878

Eigenvectors 808 Elastic rods 105 Electric field under a Lorentz

transformation 820 Electrons, spin of- 108, 809 Element

chemical - 885 of a set 559

Elementary functions 164 Elliptic functions 73 Elliptic integrals from integration 593 EllipticE 594 EllipticK 594 Empty list 709 End 475 End, of contexts 475 End points, of branch cuts 227 Enumerating, rational numbers I 05 Equal 551 Equal, overloading - 658 Equality

extended - testing 645 numerically undecidable - 540 of expressions 551 of high-precision numbers 553 of machine numbers 552 of mathematically identical

expressions 557 of numbers 551 of numerically similar expressions

762 structural - 556

Equation Benney- 14 Dyson- 388

Schriidinger - 56, 107 wave- 108

Equation solving numerical - 22 using Solve 817

Equations abstract evolution - 845 in Mathematica 546, 551 Kohn-Sham - 100 linear- 817 manipulating - 645 overdetermined linear - 823 solving - 817 underdetermined linear - 818

Errors in Mathematica 403 syntax- 403 versus warnings 403

Essential singularity of exponential function 165

Euclidean algorithm 150 Euler

constant 17 4 identity 174

EulerGamma 176 Evaluate 315 Evaluation

aborted - 429 aborting an - 422 avoiding - 311 avoiding -in patterns 408 exceptions from standard - 507 forcing - 315 infinite - 281 iterative - 433 nonstandard 562 of Boolean functions 562 of iterators 416, 507 of multiple iterators 416 of patterns 290 order of - 499 process of- 499 recursive - 281, 432 sequence 178, 652 standard procedure of- 501 tracing an - 444 under memory constraints 423 under time constraints 423 using side effects in - 756

Eveness, of integers 541 EvenQ 541 Everything, is an expression 143

Evolution equations 845 from ancestors I 05

Exact numbers 147, 543 zero 149

ExactNumberQ 543 Exceptions, from standard evaluation

507 Exp 167 Expand 275 Expansion

ID Fourier- 31 Bolyai- 81 decimal - 220 of hyperbolic expressions 874 of logical expressions 562 of polynomials 275 of polynomials using rules 644 of sums of roots 62 of trigonometric expressions 276,

874 Experimental mathematics 70, 100 Experimental' 492 Exponential function

essential singularity of- 165 in Mathematica 167 of matrices 840

Exponentiation of expressions 160 repeated - 367

Expressions all arithmetic - 876 all possible - 644 all syntactically correct - 599, 644 analyzing- 200, 896 antisymmetric - 873 atomic- 560 canonical ordering of - 197 changing parts of- 627 changing parts of- fast 742 compound - 409 converting - to strings 413 converting strings to- 412 counting leaves of- 213 depth of - 204 displayed- versus internal - 143 elements of- 208 equality of- 551 evaluating held - 315 everything is an- 143 extracting unevaluated parts from -

312

Index

Index

forcing evaluation of- 315 frozen- 311 headsof- 144,214 held- 311 identical - 556 identity of- 556, 761 indetenninate- 159, 178,269 inert- 315 large- 200 length of- 211 levels of - 208 multiple - 409 notebooks as - 853, 869 numerical - 541 options of - 299 ordered - 558 outline of - 198 pmts of - 202 printing - 403 replacements in- 610 representations of- 143 selecting- 598 selecting parts of an - 564 semantically meaningless- 149, 403 silently large - 512 simplification of- 330 size of - 424 structure of - 200 symbolic 143 syntactically correct- 153, 405 testing if - have values 560 testing the absence of - 560 testing the presence of- 559 that are numbers 541 that give messages 405 too big for fonnatting 20 I treefonn of- !56 unevaluated- 312,533,743 unvisibly held - 312 with nested heads 145 with values 560 writing - in outlined form 198 writing - in short form 198

Extending Equal 645 Solve 829

Extensibility, reason of Mathematica's - 143

Extraction of all function definitions 323 of heads 284 of parts 202

F

Faces of Mathematica 7 Factor 275 Factorial

function 81 user-defined 81

Factorization of polynomials 275 of trigonometric expressions 276

Factors for Mathematica I 09 of polynomials 275

Failed, assignments 284, 433, 587 Failing, operations 405 Falling

ball 103 buttered toast I 04 cat 103 coin 104 leaves 104, 104

False 539 False

functions returning True or - 540 the truth value - 539

Family names, distribution of- I 05, 870

Ferrer conjugates 648, 879 diagrams 648

FerrerConjugate 972 FeynCalc 80 Fibonacci chain map 224 Field

electromagnetic - under a Lorentz transformation 820

invariants 821 knotted- configurations 107 lines 75 magnetic - 7 5 particle in a - 56 strength tensor 820 transformations 821

Field lines, magnetic - 105 File operations 438 FileNames 849 Files

deleting - 438 names of - 849 operations on - 438 reading from - 437, 853

saving definitions to - 438 saving to - 437

Filling jugs 104 lists 742

Finite difference weights 645 First 724 First

digits of data 869 element of expressions 724 element of lists 724

1011

Fixed points of function applications 353

FixedPoint 353 FixedPointList 353 Flat 305 Flatten 754 FlattenAt 757 Flattening of nested lists 754 Flexibility, reason of Mathematica's-

143 Floating objects, position of- I 03 Flowers, polyhedral - 43 Flying kite I 04 Fold 356 Folding proteins 106 FoldList 356 Foldy-Wouthuysen transformations

108 For 565 For loop 565 Forest fire model 27 Fonn, the computer algebra system

102 Fonnatting

conventions of the GuideBooks 5 for brevity 922 ideal- 876 Mathematica code 6, 876 of arrays 720 of tables 721 of too big expressions 201 wrappers 147

Formula Campbell-Baker-Hausdorff- 663 Frobenius- 878 Mei sse! - for primes 879 Soddy- 34

FORTRAN code generation 944 fonn 876

Foundations, of Mathematica 143

1012

Fountains, water falling from - I 03 Fourier coefficients I 05 Fourier series, Gibbs phenomena in -

31 Fourier transform of greatest common

divisors 25 Fractal

of Newton basins 354 post sign 42 tree 46

Fractals from iterations 47 Fractal Tree 46 Fractional

derivative I 03 differentiation I 03 integration 103 iteration I 03 part 222

FractionalPart 222 Fractions

automatically collapsing- 163 denominator of - 216 exact- 216 irreducible- 163 numerator of- 216 reduced - 150

FreeQ 560 Frequency analysis 869 Friction 103 Frobenius formula 878 FromDigi ts 220 FrontEnd' 492 Frozen, expressions 311 FullDefinition 434 FullForm 143 Function 336 Function

Ackermann - 432 analytic - vanishing for almost all

real values 227 analytic - vanishing for lzl > 1 227 analytic - vanishing for lzl * 1 227 analytic - vanishing outside the unit

interval 227 anonymous - 336 application 170 castle rim - 228 de Rham's- 23 Dirichlet - 32 inverse - 180 pure- 336 reconstruction from series terms I 06 Riemann Zeta - 645

sawtooth - 228 self-reproducing - 338 special analytic - I 03 staircase - 228 Takeuchi - 333 Zeta- 645

Function application extracting all -s 323 infix form of- 170, 298 input forms of - 297 postfix form of- 170, 297 prefix form of - 297 recursive - 281 repeated - 3 50

Function definitions automatic generation and destruction

of- 789 automatic generation of- 334 avoiding certain - 317 clearing - 292 complete - 434 counting - applications 389, 665 degenerate cases of - 161, 7 36 dependencies of- 773 for compound heads 328 for numerical values 326 for various cases 285 generality of- 289 immediate versus delayed - 293 indirect generation of- 322 internal forn1 of- 321 mixing delayed and immediate-

287 modeling - 625 multiple - 290, 369 multiple matching- 289 object -oriented - 317 ordering of- 290 pitfalls of - 283 removing special - 292 simple- 279 special numerical - 327 traditionally formatted- 75 unusual - 363, 364

Functional programming constructs 777 programs 879

Functional equation de Rham's function 23 of Riemann Zeta function 645 of Siamese Sisters curve 818

FunctionDefinitionsTester 480

Functions aliases of- 512 all - that hold arguments 314 all - with options 765 all built-in- 398 application of- 297 applied to lists 306 arctrig - 180 arithmetic - 28 associative - 305 attributes of- 304 bandlimited - I 06 Boolean - 539 built-in versus user-defined- 275 changing heads of - 711 commutative- 304

Index

conditionally defined- 588 continuous but not differentiable 36 counting - applications 389 counting - calls 703, 884 defining- 281 definitions of- 433 differential algebraic constant - 227 differentiation of- 308 direct and inverse - 183 disappearing in definitions 876 discussed in this book 895 domain of- definition 164 dumped- 961 easily removable- 297 elementary - 164 elliptic- 73 ending with Q 540 equality of pure- 375 exponential - 16 7 failing 405 finding - programmatically 938 frequency of the occurrence of- 851 from the standard packages 496 functions of- 359 general - of matrices 844 higher order- 359 hyperbolic- 167 inverse- 105, 360 inverse hyperbolic - 183 inverse trigonometric - 180 invertible by Mathematica 361 investigating all system - 763 iterated- 228 iteration of- 347 listing all built-in - 398 logarithmic - 167

Index

mapping- directed 742 mapping- everywhere 740 mapping- over lists 737 multi valued- 227 multivariate - I 06. 282 names of all Mathcmatica - 398 naming conventions for- 3 nowhere differentiable - 36 number of built-in- 398 numeric - 307, 541 obsolete - 406. 964 of linear algebra 826 of matrices 839 options of- 298 overloading - 806 pattems in- definitions 277 piecewise-defined - 563 protected - 766 recursive definitions of- 433 repealed application of- 346 returning True or False 540 retuming unevaluated for inappropri

ate arguments 597 scoping in - with iterators 449 separability of- 652 setting attributes of- 304 setting options of-- 302 system - as strings 770 testing - 540 that generate functions 341 that remember their values 329 that rctum numbers 307 that take level specifications 564.

598. 750 threading - over arguments 780 to be treated especially 524 top ten used - 849 trigonometric- I 67 undocumented - 406 unprotected buill-in - 297 unusual analytic - 227 used too early 869 user-defined factorial - 81 with attributes 766 with certain attributes 766 with level specifications 877 with long names 771 with ma~y arguments 287 with many attributes 768 with many options 299 with options 626. 769 with palindromic names 771

with short names 769 with values 524

Fundamental theorem of algebra 22

G

Gaits modeling 105 Galilei in variance I 08 Game

house of the Nikolaus - 635 paradoxical - I 04 Scrabble - 784 Sorry- 592

Gamma function. fast integer evaluation of- 81

Gamma matrices 573. 873 Gases in equilibrium 107 Gauss map 44, 352 Gaussian primes 544 Gayley, T. 964 Gear teeth I 04 Genealogical tree I 05 General 400 General

definitions 289 information about Mathematica messages 400 overview l

Generality. of paltems 290 Generalized

cross product 779 scalar product 779 table 918 Weierstrass function 36

Generation of evaluation outlines 444 of function definitions 334 of subsets 871

Generic cases 702 Genetic code 105 Geometric theorem proving 65 Geometry packages 497 Get 437 Gibbs phenomena 31 Global variables 470 Global- 470 Global 'Trace 806 GluedPolygons 702 GluedPolygonsAnalysis 884 Glide!. K. 397 Golden ratio 175

GoldenRatio 175 Gotha (in Thuringia) 784 Gothic letters 4 Goto 456 GramDet 958 Grammar. leaming- 105 Graphics

as expressions 30 I of polyhedral flowers 43 of polynomial roots 23 packages 497 with legends 886

1013

Graphics'ContourPlot3D' 775 Graphics'Legend' 886 Gravitational potential of polyhedra

103 GrayRhombusesPartition 5 Greater 545 GreaterEqual 545 Greatest common divisor 25 Greechie diagrams 107 Greek letters

in inputs 4 problem suggestions I 07

Greuel, G.-M. 100 GroebnerBasis in action 65 Grouping, of numbers 875 Groups

generated by pure functions 872 of identical elements 736, 933 of the genetic code I 05 tetrahedral - 917

Growth of icicles 104 of lists 710 of snowflakes I 04

GuideBooks analyzing the - by program 860 consistency of references of the -

869 index creation for the - 869 statistics of the - 860

Gutzwi!ler-Maslov theory 26

H

Hand, optimal - I 05 Harmonic numbers 21 Hash 884 Hash values 884 Head 144

1014

Heads 214 Heads

and arguments 145 as a level specification 214 changing - of expressions 711 compound- 145 exchanging- and arguments 741 extracting - 284 faked- 366 function definitions for compound -

328 of exact numbers 147 of expressions 144 of inexact numbers 147 with arguments 145 with hold attributes 314

Heat conduction 108 engine 107

Held arguments 313 patterns 577

HeldPart 312 Helicopter noise 106 Help browser 25

HoldPattern 409, 577 Holc!Rest 313 Horse, modeling - gaits 105 Hourglass I 06 House of the Nikolaus 635 Hurwitz problem 103 Huygen's principle 108 Hydra, fighting a- 106 Hydrogen, orbitals I 08 Hyperbolic

cube 39 functions 167

Hypothesis, Riemann - 662

I 172 Icicle growth 104 Icosahedron

animation, of charging an - 90 made from reflected polygons 704 made from triangles 704

Ideal formatting 6 Identities

differential matrix - 878 for matrices 840 in tanh 874

Heptagons, forming polyhedra 704 Hermite polynomials 648 Hexagons, polyhedra made from -High-precision

705 Identity

automatic - comparisons 546 logistic map iterations 24

High-precision arithmetic in action 24 in equality testing 540 in iterator calculations 419 principles of- 24, 194

High-precision numbers, inputting -153, 196

Hilbert, D. I 09 Hilbert

curve in 3D 93 matrix 18, 803 space formulation of classical

mechanics 108 HilbertCurve3D 93 History of a session 429 Htirselgau (in Thuringia) 839 Hold 311 HoldAll 313 HoldAllComplete 315 HoldFirst 313 HoldForm 312

Amitsur-Levitzky - 878 Euler- 174 Legendre - 64 matrix 713 of expressions 556, 761 Ramanujan - 64

IdentityMatrix 713 If 563 If

Hilbert knew Mathematic a I 09 misuse of- 564 the programming construct 563

IgnoreCase 439 Im 185 Imaginary part

numerically present - 546 of numbers 184 spurious - 546

Imaginary unit 171 Impacts of computer algebra 100 Impossible matrix 883 In 429 Indefinite, integration 282

Indeterminate 178 Indeterminate expressions 178 Index

contractions 873 creation 869

Index

creation of the - for the GuideBooks 869

Inequalities Bell- 100 multiple- 547 numerically undecidable - 540 resolving - 66 solving- 66 stating - 545 visualizing - 67

Inequality 547 Inert, expressions 315 Inexact numbers

checking for- 543 heads of- 147 inputting- 153 machine versus high-precision - 195

InexactNumberQ 543 Infinite

evaluation 281 iteration limits 432 recursion limits 432

Infinity 178 Infinity

arithmetic with - 178 as an expression - 177 flavors of- 177

Infix notation 170, 298 Information 397 Information, getting all built-in- 415 Inheritance

in Mathematica 882 of properties 986

Initials, distribution of- 870 Inner 779 InPlaneTori 87 Input 448 Input

copyable- 414 numbering of- 429

Input-to-text ratio 862 Inpu tForm 144 Inputs

evaluating all - 857 formatting of- 5 generating messages 404

Index

grouping in - 879 history of - 430 ideally fonnatted- 876 in notebooks I interactive - 448 line length of- 870 numbering - 429 numbering of- I semantically meaningful versus

syntactically meaningful - 404 shortcuts for- 523 white space in- 870

InputString 448 Inputting high-precision numbers !53 Insert 728, 728 Inserting, elements into lists 727 Integer 149 Integer

faked- 585 part 222 testing for being - 541

IntegerDigits 217 IntegerPart 222 IntegerQ 541 Integers

digit sums of- 10,218 digits of- 217 even- 541 factoring - 545 fast multiplication of- I 0 Gaussian - 544 in different bases 220 odd- 541 partition of- 80 primality of - 544 quadraticity of- I 06

Integrals elliptic - 593 product - 106 undone- 68 user-implemented - 593 variables in - 365

Integrate 282 Integration

fractional - 103 indefinite - 282 pattern-based specialized- 329, 593 product - 106 recursive - 329

Interactive, inputs 448

InterCall 433 Interesting

differential equations 16 problems 103

Intennediate steps, in calculations 442 Internal

fonn of expressions 143 form of function definitions 321

Internal' 493 Interrupt 448 Intersection 761 Invariant, field-s 821 Inverse 803 Inverse

functions 360 functions and direct functions 183 matrix 803 trigonometric functions in the

complex plane 227 Inverse functions, built-in- 361 InverseFunction 361,830 Inversion

matrix - 106, 803 of functions 360 of matrices 803

Irreducible fractions 163 polynomials 275

ISSAC system challenge 1997 109 Iterated

digit sum 28 logarithms 351 polygon reflections 702

IteratedDigitSum 28 Iteration

identifying- 447 versus recursion 447

Iterations avoiding - in pattern matching 651 counting Newton - 354 Ducci's- 872 fractional - 103 in ReplaceRepeated 623 limiting - 433 of functions 34 7 of logarithms 351 of polygon reflections 702 of power functions 350 of secant functions 169 Stieltjes - 872

Iterator1ess programs 869 lterators

1015

construction of multiple - 715 discrete and continuous - 3 maximum number of steps in - 428 multiple- 715

J

number of steps in - 418 optimized- 717 possible- 417 scoping, in - 421 syntaxof- 416 undecidability of number of steps in

- 419

Jacobi functions 772 Janhunen,P. 944 JensenDisks 22 Join 760 Joining

iterators 715 lists 760 strings 438

Journals as sources of exercises I 07 most cited - 869

Jugs, filling- 104 Jumping

instructions 456

K

Kepler problem 108 tiling 40

Kite, flying a- 104 Klauder phenomena 108 Kleene, S. 336 Knots

as field configurations 1 07 tie- 106

Kohn-Sham equations I 00 Kolakoski sequence 881 Krattenthaler, C. 99 Kronecker

product 779 symbol 718

KroneckerDelta 718

1016

L

L-systems in 3D 93 L'H6pital's rule 59 Label 456 Lake, K 101 Lambda calculus 336 Landau S. 10 I Large calculations

in quantum field theory 80 string-oriented- in Mathematica

784 Largest number 427 Last 724 LeafCount 213 Leaves

falling - I 04, I 04 of expressions 213

Legendre identity 64 Length 211 Length

of expressions 211 of integers 221 of lists 211, 802

Less 545 LessEqual 545 Letters

doublestruck- 4 from different fonts 4 Gothic- 4 Greek- 4

Level 209 Level

all -s of an expression 227 analyzing notebook -s 863 counted from top and from bottom

227 definition of a - 208 definitions associated with - 1 318 functions that take - specifications

564,598,750 functions with - specifications 877 lowest- 209 negative- 209 of an expression 208 specifications 209 uppermost - 209

Levi-Civita tensor 714. 873 Levici vi tac 922 Levitron I 04 Lexical, scoping 450 Lexicons, numbers as - 69 Liapunov exponent 24 Libraries, numerical - 26

Light rays in a water vertex I 08 Limiting

iterations 433 memory use of calculations 423 recursions 432 time of calculations 423

Limits discontinuous - 32 of Mathematica 99 simple- 59

Linear equations 817 Linear algebra

and data types 802 comparisons 804 in Mathematica 802 packages 497 symbolic - 826

LinearAlgebra 'Orthogonal·· i za tion' 808

LinearSolve 817 LinearSolve in action 832 Lines, approximately intersecting -

823 Linkages I 05 List 299 List

empty- 709 operations in action 784, 851

Listable 306 Lists

adding elements to - 727 applying functions to - 306 as matrices 802 as tensors 721 as universal containers 702 as vectors 802 changing elements of- fast 742 counting elements in - 770 creating - 707 cyclically rotating - 729 definition of- 299 deleting elements from - 724 dropping elements from - 724 extracting elements from - 723 fast creation of- 755 first element of- 724 flattening nested- 754 general operations on- 750 generating - 597 in linear algebra 802 inse1ting elements into - 727 joining - 760

largest element of- 735 last element of - 724 manipulating elements of- 729 manipulating named - 728 manipulations of- 723 mapping functions over- 737 nested- 802 partitioning- 757 removing -s iteratively 726 removing multiple elements in -

725, 876 reordering - 730 reversing - 729 selecting elements from - 723 smallest element of - 7 35 sorting - 730 splitting - into sub lists 736

Literal equality 556 patterns 579

Loading packages definitions changing when - 879 details of - 4 79

Localization of variables 449, 456, 883, 883

Locked 310 Locked symbols 310 Log 167, 167 Logarithm

iterated - 351 natural - 167 nested- 351

LogicalExpand 562 Logistic map 24, 105 Longest

function names 771 messages 773

Loop for- 565 while- 565

Loops, programming - 565 Lorentz

gas 29 transformation 104, 819

LorentzTrafo 820 Losing game 104

M

Machine equality of- numbers 552 integers 428 real numbers 426

Index

Index

Machine arithmetic artifacts 270 largest number of- 427 number of digits in - 426 smallest number of- 428 use of- 194 values of- 426

Magic squares 831 Magnetic field

in an air gap 75 lines 75, 105 under a Lorentz transformation 820

Magnitude of numbers 184, 427 Map 737 Map

conformal - 7 L I 06 Fibonacci chain - 224 Gauss - 44, 352 logistic - I 05

MapAll 740 MapAt 742 Mapindexed 744 Maple the computer algebra system

102 Mapping

functions 737 functions everywhere 741

Maps functions as - 336 iterated 745

MapThread n2 Mathematica

and creativity I 00 and mathematical research I 0 I application library 80 as a programming language 397 as a tool 101 as an interpreted language I 0 basic principle of- 143 counting - 866 enws in - 403 expressions in - 143 foundations of- 143 functions in - 275 fundamentals I global options of- 491 impacts of- I 00 introduction into -language principles learning - I 00

length of function names in - 770 linear algebra in- 701 lists in- 701 matrices in - 70 I naming conventions of-online help in - 397 operators in - 879 overview of- I overview of mathematics in - 7 overview of numerics in - 7 overview of programming in - 80 overview of symbolics in - 54 programming in - 80 replacement rules in - 539 short input forms of- 523 syntax 3 version used 426 version-related 425 what - cannot do 99 what - could do better 98 what - does well 98

Mathematics counting - phrases 866 experimental - 70, I 00

MathTensor 80 MathWorld 107 Matrices

adding- 750 arithmetic operations on - 750 condition number of- 808 creation of- 707 creation times of - 710 detcnninants of- 803 diagonal - 713 diagonalization of- 810 differentiation of parametrized ~ dimensions of- 802 Dirac- 873 eigenvalues of- 808 eigenvectors of- 808 exponentials of square - 840 exponentiating - 839 extracting elements from - 723 extracting sub- 723 forn1atting - 720 functions of- 839 identity - 713 in Mathematica 550 inverse - 803 Lorentz transformation - 819

memory needs of- 710 multiplying- 750 Pauli- 809 powers of square - 839 pseudoinverses of- 823 raising - to powers 839 roots of square - 839 rotation - 777 special - 713 subtracting - 750 transposing- 751 with symbolic entries 18, 804

Matrix block- 878 differential - identities 878 difficulty of- inversion 106 functions 839 Hilbert - 803 identities 877 inversion 106, 878 Redheffer - 57 square root 878 trace of a - 806 Vandermonde- 56 virtual - 883

MatrixCos 841 MatrixCosh 845 MatrixExp 840

MatrixForm 720 MatrixPower 839 Ma trixQ 550, 551 MatrixSinh 845 MatrixSqrt 845 Max 735 Maxima 634

647 Maximum element of a list 735 memory of calculations 423 number of iterations 433 number of recursions 432 of numbers 735 time of calculations 423

MaxMemoryUsed 424 Maxwell equations I 07, 820 MContainer 613 Measurements

mutual unbiased - I 07 of Riemann sutfaces I 06

Medial parallelogram 65 Median! 874

1017

1018

Meissel formula for primes 879 Melting points 885 MemberQ 559 Members, of ancestor generations I 05 Memory

-constrained calculations 423 freeing - 437 sharing - 424 used in a session 424

MemoryConstrained 423 MemoryinUse 424 Mergesort 734 Message 408 MessageList 431 MessageName 400 Messages 399 Messages

allowing - 407 catching - 424 collecting issued - 431 common warning - 511 correct phrasing of - 404 error and warning - 399 for symbolic expressions 405 from comparision functions - 540 general - 400 how many - per function 40 I implementing new - 408 issued in argument testing 597 issued three times 406 longest - 773 names of - 403 searching - 767 spelling warning - 407 suppressing - 407 temporarely disabled- 513 text of all - 399 usage- 399 used by many functions 408 user-defined - 408 warning - 403 warning versus error - 403

Meta-mathematics 397 Metabolic rate I 03 Metacharacters 296, 397 Method 826, 877 Method

determining option 826 Newton- 353 power- 812 Szegti's- 71

Methods of linear algebra 826

Min 735 Minimal element of a list 735 Minimum of a set 735 Minus 162 Mirroring, polygons iteratively - 702 Miscellaneous packages 497 Miscellaneous ·chemical··.

Elements· 885 Misconceptions, about pleasing aspect

ratios 175 Model

Burridge-Knopoff- 12 forest fire - 27 traffic jam - 104

Modeling a woodpecker toy I 04 canary songs I 06 corrugated roads I 04 earthquakes 12 function definitions 625 monopoly I 05 popcorn 105 swarm formations I 05

Modular programming 479 Module 450 ModulePowerSum 452 Moessner's process 871 Money, changing - 879 Monitoring

definitions applications 619,665 determinant calculations 805 expression evaluation 444 pattern matching 619 Sort 734 sorting 732 variable localizations 456

Monopoly game 105 Moore-Penrose inverse 823 Multidimensional determinant 874 MultiDimensionalDet 874 Multiple

arguments 280 with same digits 884

Multiplication associativity of- 305 by zero 149, 179 commutativity of- 304 fast integer - 10 FFr-based - 10 matrix- 777 noncommutati ve - 645, 952 of matrices 750

ofnumbers 151 overloading - 613 resulting from division 162 with approximate zeros !51

Multi valued functions in Mathematica 188

Index

inverse trigonometric functions as -180,227

nested powers as - 227 Multivariate functions, definitions of-

282 MuPAD, the computer algebra system

102 Mutual unbiased, measurements I 07 Mylar balloon I 03

N

N 170 N-functions 3 NAG 26 Names 398 Names

all built -in function - 398 colliding - 488 collision of variable - 482 context part of - 469 conventions about function - 3 longest built-in function- 770 longest function - 771 of all attributes 767 of all options 765 of characters 441 offiles 849 of functions with attributes 766 of functions with options 765 of messages 403 of package functions 496 of patterns 570 of temporary variables 453 of value-carrying symbols 764 person - in function - 3 temporary - 453 unique- 455

Naming conventions in Mathematica 3 of local variables 450 of patterns 278

Nearly integers 8 Needed packages 479 Needs 479, 487

Index

Negative 548 Negative

numbers 548 specific heat I 08 symbolic expressions !58

Neighbors of words 870 Nest 346 Nested

analysis of- expressions 197 digit sum 28 functions 346 heads 145 logarithms 351 radicals 64. 173 replacement rules - 623 roots 81 scoping 652

NestedTriangles 872 NestList 346 NestWhile 351 NestWhileList 350 Netlib 26 Newton

fractal of - basin 354 method for root finding 353

Nikolaus, house of the - 635 Noise, helicopter- 106 Nonhermitian Hamiltonians I 07 NonNegative 548 Nonnegative numbers 548 Nonradiating oscillating charges 107 Nonuniqueness in solving equations

817 NormalPlaneTori 87 Not 561 Not, logical - 561 Notation

custom- 78 infix - 170, 298 postfix - 170, 297 prefix- 297

Notebooks analyzing - 852 as Matlzematica expressions 853 wide- 200

Nothing as a result 443 as a set 709

Novels versus poems I 06 Null 410,443 Number, condition - of matrices 808 Number theory packages 497

Numbering of inputs 429 of inputs and outputs

NumberQ 541 Numbers

absolute value of - 184 algebraic - 64, !59 argument of- 184 as lexicons 69 closed-form - I 05 comparing - 545 complex- 151 complex conjugation of- 184 computable - I 05 default sorting of of complex- 731 digits of- 217 enumerating rational- 105 equality of high-precision - 553 equality of machine - 552 exact- 543 exact versus inexact - 195 formatting of- 155 grouping- 875 harmonic - 21 imaginary part of - 184 in different bases 217 inexact- 543 inputting- 155,514 integer - 149 largest machine- 427 machine - 426 machine integer- 428 magnitude of- 184 nearly integer- 8 negative - 548 nonnegative - 548 Pi sot- 8 positive- 548 prime - I 07, 544, 726 rational - !50 real- !50 real part of - 184 representation of- 147 smallest - 428 sorting - 632, 730 splitting complex - 187 Stirling - 717 with numerical imaginary parts 546 with periodic continued fractions 8 with unusual continued fractions

70,978 NumberTheory 'Primitive··.

Element- 473

Numerator 216 Numerators of numbers 216 Numeric expressions

declaring - 307 testing - 541

Numerical function definitions 327 functions 307 libraries 26 linear algebra 804 mathematics packages 498 techniques in comparisons 555 testing expressions for being

potentially - 541

1019

value of symbolic expressions 170 Numericalization

hidden- 540 in comparisons 555 in iterators 419 through collapsing !51 to arbitrary many digits 194 using N 170

NumericalMath'ApproxL mations' 487

NumericalMath 'Optimize··. Expression- 749

NumericFunction 307 NumericQ 541 Nutshell, syntax in a­NValues 326

0

Objects, fast moving - I 04 Obsolete functions 406 Octagons, forming polyhedra 704 Octahedron made from reflected

polygons 704 Odd numbers 541 Oddness, of integers 541 OddQ 541 Off 407,442 on 407,442 On versus Trace 447 One-dimensional contact interactions

107 One-liner 879, 948 Oneidentity 306,605 OneStepRowReduction 826 Online help 397 OpenMath 102 Operate 359

1020

Operations arithmetic - !56 logical - 561 set-theoretical - 761

Operator characters representing -s 969 curl- 106 exponentiation 663 precedence of -s 879 product 645

Optimal hand 105 Optimizations, no- 10 Option

Automatic- value 581 processing 626 repeated - setting 626 strings as - values 49 I

Optional 580 Optional arguments 580 Options

acquiring values 626 all- 765 and rules 626 defaults of- 298 finding- settings programmatically

938 finding possible - settings 877 frequency of- 861 in general 298 inheritance of- 986 of expressions 299 of functions 299 of functions and expressions 301 of linear algebra functions 826 of Mathematica 491 of notebooks 861 of system functions 765 setting - 298 system- 491 with delayed values 769

Or 561 Or, logical - 561 Order

of evaluating arguments 50 I of evaluation 499 of substitutions in replacements 877

Ordered derivative 64 7 OrderedQ 559 Ordering

canonical - 559 in output forms 156

of function definitions 290 relations 545 testing- 558

Orderless 304 Orthogonal trajectories in potential

force fields 108 Oscillator

harmonic - I 08 nonlinear - II

Out 3 Outer 780 Outer product 779 Output

comparing - forms 14 7 deleting stored - 437 ordering in - !56

OutputForm 144 Outputs

history of- 430 numbering of- I

Overloading system functions 830 Overview of Mathematica 7 OwnValues 326

p

Package for chemical elements 885 for legends in graphics 886 for polynomial continued fractions

776 Packages

annotation of- 495 as subprograms 469 autoloaded - 879 built-in functions from - 879 consistency check of- 879 dependencies in - 773 details of loading- 479 exported variables of- 497 for algebra 496 for calculus 497 for discrete mathematics 497 for geometry 497 for graphics 497 for linear algebra 497 for numerical mathematics 498 for statistics 498 functions exported from - 496 large- 80 miscellaneous - 497 number theory - 497

standard - 4 79, 496 start-up - 489, 850 template of- 4 79

Packed arrays 491 Packing of Platonic solids I 06 Painlevc transcendents 99 Palindromes 77 I , 771 Paper

crumbling- I 03 cutting 106 tearing - 10 3

Paradox, Banach-Tarski - 103 Paradoxical game I 04 Parametrization

sphere- 37 torus- 37

Parentheses for grouping 3 in Full Form 226

Part 202 Part

assignment 742 extraction 202 numbering -s 744

Index

repeated versus multiple - extraction 366

replacing -s of expressions 627 Part versus Take 723 Partition 757 Partitioning

integers 80 lists 757

Partitions all possible- 758 generated from rules 872

PartitionsLists 872 Parts, of nested expressions 204 Pascal's triangle, q-- 667 Path

of car wheels 104 of quantum particles I 07

Pattern 277, 567 Pattern matching

and attributes 60 I argument substitution in - 279 complexity of- 618 failed- 616 for functions 285 in action 630 in associative functions 601 in commutative functions 60 I

/nJex

in rule applications 610 monitoring- 608,613,631 nonunique - 572 order of - 94 7 unique- 572

PatternRealization 948 Patterns

abbreviations for- 277 alternative - 5 85 and attributes 60 I avoiding evaluation in - 577 binding of- 877 evaluation of- 290 for repeated arguments 583 for variable arguments 567 generality of- 571 held- 577 in function definitions 277 in replacement rules 612 inert- 579 literal- 579 matching an empty argument

sequence 569 meaning of- variable 279 most common- 571 multiple-named - 278 named- 278, 570 nonmatching- 616 of prescribed head 277 realizations of- 279, 877 repeated - 572 restricting- 586 simple- 277 sophisticated - 587 special treatment of- 578 unevaluated - 408, 577, 614 verbatim - 579

PatternsAndAttributes 609 PatternTest 586 PatternTest versus Condition

591 Pauli matrices 809 PDEs

numerical solution of- 14 with peakon solutions 648 with Sierpinski solution 16

Pentagons forming polyhedra 703 graphic of subdivided- 40 iteratively reflected- in 3D 703

Perfect discretization 661 Periodic decimal numbers 219

Periodicity, of trigonometric functions 174

Permutations 751 Permutations

cycles in - 632 of indices 922 oflists 751 rule-based generation of- 671 signature of- 714

Perturbation, supersingular I 08 Pfaff forms 99 Phase

of complex numbers 184 transitions in calculations 106

Phase shift 17 Phenomena

Gibbs- 31 Stokes- 100

Photon, emitted from an excited atom 108

Phrases, in texts 106 Phylogenetic tree 105 Pi 172 Piano, moving a - 104 Picard's theorem 166 Piecewise defined functions 563 Piles of blocks 104 Pisot numbers 8 Piston, movable - 108 Pitfalls

in assignments to iterator variables 421

in expected simplifications 192 in pattern nonmatching 616

Platonic solids packing - I 06 rotated- 49

Plot 300 Plots of simple functions 300 Plus 160 Poems versus novels 106 Polygons

dissecting - I 07 gluing - together 702 iteratively reflected- in 3D 703

Polyhedra classical - 703 formed by reflected polygons 703 generating new - 703 made from heptagons 704 made from hexagons 705 made from octagons 704 random- 52

Polyhedral flowers 53 PolyLog 76 Polymorphism 601 Polynomial

characteristic - 848 inequalities 66 testing for being a - 549

PolynomialQ 549 Polynomials

characteristic - 848 expanding- 275 factoring- 275 Hermite - 648 irreducible- 275 Laguerre - 365 orthogonal - 105 power of- with few terms 276 systems of - 58 testing - 549 with real roots I 06 zeros of- 23

Polypaths 639 Popcorn, modeling- 105 Position 208 Position

of floating objects I 03 of subexpressions 208

Positive 548 Positive numbers 548 Postfix notation 170, 297 Potential

gravitational - of polyhedra 103

1021

of computer mathematics tools I 01 random 2D - 13 with orthogonal trajectories I 08

Power 160 Power

function 160 function for matrices 839 method 812 of Mathematica 109 tower 367

Powers expanding -in polynomials 275 of polynomials with few terms 276

PowerSum 449 Precedences 158, 879 Prefix notation 297 Prepend 728 PrependTo 728

1022

Primality testing 544 Prime

checking for being - 544 Gaussian - numbers 544 numbers in arithmetic progressions

565 sieve 726

PrimeQ 544 Prince Rupert's problem 104 Print 403 Printing

arbitrary cells 402 as a debugging tool 505, 619 expressions 402

Probability distributions for references 90 I packages for - 498

Problem Hurwitz- 103 Kepler- 108 Prince Rupert's- 104 stable marriage - 106

Problem-solving environments I 00 Problems, sources of- I 07 Process

Moessner's- 871 of evaluation 499

Product 449 Product

integral I 06 noncommutative - 662 operator - 662 square root as infinite - 357

Products cross- 778 dot- 777 finite- 449 generalized dot - 779 outer- 779 symbolic - 449

Programming comparing - styles 806 dynamic - 329 functional- 713, 890 functional - constructs 777 pattern and rule-based - 630 procedural - 713, 890 string-based - 784 styles 713, 890 with lists 869

Programs analyzing Mathematica - 882

changing - programmatically 665 examples of - 80 generic - 60 I iteratorless - 869 larger- 83 nesting depth of- 859 nicely formatted - 876 that print themselves 440

Proposals, for computations I 02 Protect 310 Protected 309 Protein folding I 06 Proving trigonometric identities 64 Pseudocompiler 26 Pseudodifferential operator I 07 Pseudoinverse 823 Pseudoinverse

matrix 823 properties of -s 823

Pseudoperiodic trajectories 13 Pseudorandom, trees 873 Puns, calculating - I 03 Pure functions

attributes of - 342 definition of- 336 differences of- 882 equality of- 557 inversion of- 361 scoping in - 454 with one and two arguments 877

Put 437 PutAppend 438

Q

q-Binomial 665 binomial theorem 646 hypergeometric functions 99 Pascal triangle 667

Q-functions for testing properties 540 returning not a truth value 651

qBinomial 665 qFactorial 665 Quadrati city, of integers I 06 Quantum cellular automata 828 QuantumCellularAutomata 828 Quotes

about computer algebra 100 about Mathematica 100

around strings 3, 152 visibility of string - 491

Quotient

R

Radians 167 Radiation, absent - I 07 Radicals

as expressions 159 nested- 173

Rain, running in the- I 03 Ramanujan identities 64 Random

number generator I 05 polyhedra 52

Random walk in multidimensional lattices 105

Range 707 Rank

of built-in functions 849 of cited journals 869 of tensors 722

Rational 150 Rational

enumerating - numbers I 05 numbers 150

Ray tracing 99 Rays

in a billiard 30 in a water vertex I 08

Re 185 Reading

files 437 notebooks 860 packages 853

ReadList 853 Real 150 Real numbers

head of- 150 in patterns 277 inputting- 153

Real part of numbers 184 RealDigi ts 217 Realizations, of patterns 279 Rectangles touching a rectangle I 05 Recursion

identifying - 44 7 in assignments 644 versus iterations 447

Index

Index

Recursive definitions 568, 592 evaluation 281

Redheffer matrix 57 REDUCE, the computer algebra

system 102 Reduced fractions 150 References

about computer algebra systems I 02 age distribution of - 864 consistency of - 869

Refractive index 108 Reintroducing, symbols 296 Relations

between elementary functions and their inverses 182

containedness - 559 ordering - 545

Relativistic train 104 transformations 819

ReleaseHold 315 Remembering function values 329 Remove 294 Removed 295, 535 Removed symbols 295 Removing

built-in functions 297 context names 475 elements from lists 724 special function definitions 292 symbols 294

Renormalization group -based solution of differential equations I 00

Reordering of lists 730 Repeated 584 Repeated

option setting 627 patterns 583

RepeatedNull 584 Replace 611 ReplaceAll 611 ReplaceList 617 Replacement rules

and function definitions 322 applying - 611 building- 746 dispatched - 628 in action 630 monitoring the application of- 633 nested- 623 scoping in - 621

Replacements all possible - 617 and attributes 621 and patterns 621 applying - 611 compiling - 628 failed- 616 many- 628 monitoring- 612 of parts 627 of subexpressions 610 order of - 612 order of substitutions in - 877 repeated - 611

ReplacePart 628 ReplaceRepeated 612 Representation of numbers 14 7 Reserved words 3 Residue theorem II Resources used in a session 424 Rest 724 Restticted patterns 586 Results

abbreviated - 198 suppressing - 409

Reverse 729 Ridges, in sand 1 03 Riemann

hypothesis 662 Zeta function 645

Riemann surfaces experimentally detetmining - 106 of inverse trigonometric functions

188 of nested fractional powers 227 with disconnected sheets 227

Rising bubbles 105 River basins I 05 Rock, curling - 104 Rolling

ball 105 cylinder 104

Roots nested- 81 of differentiated polynomials 22 of polynomials 811

RotatedBlackWhiteStrips 5 RotatedSideWireFrame 49 RotateLeft 730 RotateRight 730 Rotation

around an axis 778

coin-s 104 matrices 777

RowReduce 837 Rule 611 Rule

Benford's - 869 l'Hopital's- 59

RuleCondition 680 RuleDelayed 611 Rules

applying- 611 as internal form of function

definitions 322 for replacements 610

1023

immediate and delayed - 610 monitoring the application of- 631 returned from Solve 818

RulesToCycles 632 RunEncode 630 Running, in the rain 103

s

Sagrada Familia 54 SameQ 556 SameTest 762 Sand

aeolian - ripples 106 flow in an hourglass 106 ridges 103

Save 438 Saving

data to files 438 function definitions 434

Sawtooth function 228 Schmidt decomposition 78 SchmidtDecomposition 78 Schrodinger equation, with prime

eigenvalues 107 SchubertRelation 915 Scoping

comparing - constructs 456 conditions in -constructs 590 dynamic - 450 for nonsymbols 513 in assignments 459 in iterators 42], 449 in pure functions 454 in replacement rules 621 in subprograms 450

1024

Scoping continued in summation 449 iterators as - constructs 416 lexical - 450 nested 652, 883 of vmiables 883 timings of constructs 463

Scrabble game 784 Scraping, camphor- I 05 Searching messages 767 Sec 167 Secants, iterations of - 169 Sech 168 Select 564, 723 Select versus Cases 598 Selecting expressions 598 Self-reproducing, function 338 Semantically meaningless expressions

403 Semialgebraic set 66 Semicolon 409 Separability

of functions 652 of wave equation I 07

Sequence 339, 575 Sequence

Kolakoski - 881 of arguments 339,412

Sequences from pattern matching 57 5 Series

Cantor- 355 examples of- expansions 59 improved - expansion I 03 to function I 06

Serif typeface, in traditional form 148 Session

CPU time used in a - 424 freeing memory in a- 437 history in a - 397 histor~ of a - 430 inputs of a - 430 line numbers in a - 429 memory used in a - 424 reducing memory needs of a- 424 resources used in a- 424

Set 281 Set

sum-free - 869 theoretic operations 761

SetAttributes 305 SetDelayed 281, 876

Setting options 302 system options 491 values 281 values of expressions 281 values of symbols 281

Shadowing, of symbol names 487 Shallow 198 Shape

of a cracking whip I 05 of a drop 104

Share 424 Sheets

disconnected - of a Riemann surface 241

of Riemann surfaces 251 Short 198 Short form of expressions 198 Siamese sisters 818 Sierpinski triangle, PDE with -

solution 16 Sieve, prime - 726 Signature 714 Signature, of permutations 714 Simplification

apparently missing - 192 by pointed rewriting 595 missing- 62 missing expected - 192 of expressions 330 of logical expressions 562 pointed - 490 through common subexpressions

746 wrong- 192

Simplify 330 Simpson's rule 105 Sin 167 Sinai billiard 30 Singularities

accumulation of - 228, 265 detecting - 827 essential - 166

Sinh 168 Size of expressions 213, 425 Skeleton 198 Sliding chain 107 Slot 338 SlotSequence 338 Snowflake growth I 04 Siiddy formula 34 Sofroniou. M. 944 Solutions, best - for overdetermined

systems 823

Solve 817 SolveMagicSquare 836 Solving

linear equations 817 matrix equations 830

Solving equations results of- 818 using Solve 817

Sorry, the game - 592 Sort 731, 876 SortComplexNumbers 632 Sorting

algorithm for built-in- 734 complexity of of built-in - 734 data 730 default- of complex numbers 731 lists 731 modeling - with rules 632 monitoring - 732

Spacing check 870 Special characters, for built-in

functions 146

Index

Special functions, naming conventions of- 3

Special values of trigonomet1ic functions 172

Specific definitions 289 negative - heat l 08

Specification, of levels 209 Speed

of numerical calculations 26 reduced - of arithmetic functions

317 Spelling

errors 407 waming 407

Sphere, parameterized - 37 Split 736 Splitting 634 Splitting

binary- 81 lists into sublists 736

Spurious imaginary part 546 Sqrt 160 Square

confonnal map of a - 71 subdivision of- a 104

Square root as an infinite product 357 formatting of- !58 function 160 of a matrix 878

Index

Squares forming polyhedra 703 iteratively reflected- in 3D 703

Stable marriage problem I 06 Staircase function 228 Standard

evaluation procedure 50 I form output 144

StandardForm 144, 146 Stmt of contexts 475 Start-up packages 489, 850, 960 State after package loading 965 Statistics packages 498 Step function, bad choice of a - 563 Steps, of a calculation 442 Stepwise defined functions 563 Stern-Gerlach experiment I 08 Stieltjes iterations 872 Stirling, numbers 717 Stokes phenomena I 00 String 152 String

characters of a- 769 inputting a- !52 letters in a- 439 manipulations 438 metacharacters 296 modifying a - 438 outputting expressions as a - 413

StringJoin 438 StringLength 438 StringPosition 439 StringReplace 439 StringReverse 439 Strings

as function arguments 296 as option names 491 as option values 491 changing characters in - 438 characters of- 769

of system functions 770 reversing - 438

StringTake 439 Stub 767 Subdivision of pentagons 40 Subprograms, packages as - 469 Subsequence s in texts I 06 Subset generation 871 Substitutions, order of- in replace-

ments 877 Subtract 162 Subtraction

of expressions 162 of matrices 750

SubValues 328 Suggestions from messages 540 Sum 449 Sum of digits 10, 28, 33,218 Sum-free set 869 Summation

convention about - 873 of symbolic terms 449 tern1-by-term - versus - at once 712 variable scoping in - 449

Sums finite- 449 involving special functions 61

Sun dial 104 Superposition principle for nonlinear

differential equations 106 Suppressing results 409 Surface with many holes 38 Surfaces, Riemann - 227 Surprises, teaching - l 05 Swarm modeling 105 Switch 599 Symbol 162 Symbol

Kronecker - 7 18 thehead- 161

concatenating- 438 Symbolic linear algebra 826 converting- to expressions 411,412 Symbols converting - to held expressions 411 all built-in - 398 from expressions 413 as expressions 161 intertwined - 784 attributes of - 304 joining- 438 counting all built-in- 493 manipulating- 771 created inside Module 453,883 matching - 296 creation of- and contexts 513 metacharacters in - 397 creation of- in contexts 476 of all Mathematica functions 398 declared to be numeric 541

definitions associated with - 321 inside Block 450, 883

locked- 310 long - names 512 numbers as - 514 numerical - 171 protected - 309 reintroducing - 296 reintroducing removed- 295 removed- 295, 535 removing- 294 shadowing of- 487 temporary - 453

102S

temporary changing values of - 450 unchangeable - 310 unique- 450 with values 764, 772, 876

Symmetry used in 3D graphics 90 Syntactically correct, expressions 153 Syntax

elementary - principles 3 errors 403

System options 491 System' 471 Systems, computer algebra - 1 02 Szego's method 71

T

Table 597, 707 Table 872 Table, "symbolic" - 405 TableAlignments 721 TableDepth 720 TableDirections 720 TableForm 720 TableHeadings 720 Tables

aligning row and columns in - 721 creation of- 597. 707 displaying - 721 formatting of - 720 generalized - 918 of data 885

TableSpacing 721 TagSet 319 TagSetDelayed 319 Take 723 Take versus Part 723 Takeuchi function 333 Takeuchi T 333 Taking parts of expressions 202. 723

1026

Tan 167 Tan function

definition of the - 167 inside arctan 227

Tanh 168 Tannhiiuser 839 TanPowerintegrate 330 Tap, dripping- 104 Taylor series coefficients I 05 Teaching surprises I 05 Tearing paper 103 Teeth, gear- 104 Template, of a package 479 Temporary 453 Temporary

changing system values 459 values of symbols 450 variables 453

TensorRank 722 Tensors

creating - 707, 721 dimensions of- 802 dual field strength - 822 field strength - 820 formatting - 721 Levi-Civita- 714, 873 lists as - 721 multidimensional - 722 rank of- 722 totally antisymmetric- 714, 873

Testing for being a matrix 550 for being a number 541 for being a numerical quantity 541 for being a polynomial 549 for being a vector 549, 549 for being an atomic expression 560 for being an even integer 541 for being an exact number 543 for being an inexact number 543 for being an integer 541 for being an odd integer 541 for being explicitly true 540 for being identical 556 for being mathematically identical

551 for being ordered 558 for being prime 544 for containing an expression 559 for having a value 560 functions 540

Sort 876 the absence of expressions 560

Tetrahedral group 917 Text

analyzing - 866 printing - 403 printing - in cells 402

Texts, subsequences in - I 06 Theorem

binomial - 646 Cauchy- II Cayley-Hamilton - 847 fundamental - of algebra 22 geometric - proving 65 Picard's 166 q-Binomial - 665 residue- II

Thread 780 Threading, over arguments 780 Through 360 Tie knots I 06 Tiling, Kepler - 40 Time

current - 426 maximal - for a computation 423 used for an evaluation 331 uses in a session 424

TimeConstrained 423 Times 160 TimeUsed 424 Timing 331 Timings

ideal steak cooking - 106 of array constructions 709 of computations 331 of function applications 323 of functional list manipulations 742 of integer arithmetic I 0 of linear algebra operations 804 of list creations 755 of machine versus high-precision

calculations 427 of summation 712 of symbolic versus numeric

calculations 804 of unioning 762 of variable localizations 464 of various list operations 888

Tippe top 104 Toast, falling buttered - I 04 ToExpression 411

ToHeldExpression 412 Top ten functions used 849 Tori, animation of interlocked - 89 Torus, parametrized - 37 ToString 413 Tower, Eiffel - 54 Toy, walking- 106 Tr 806 Trace 444 Trace

comparisons of- implementations 807

of matrices 806 of product of Dirac matrices 873

Trace versus On 447 Tracing evaluations 444 TraditionalForm 144, 146 Traffic jam modeling I 04 Trail systems I 04 Train, relativistic - 104 Trajectories

chaotic- 13 of quantum particles I 07 of vortices 7 4 potential with orthogonal - I 08 pseudoperiodic - 13

Transformation, Lorentz - I 04, 819 Transformations

evaluation as applying- 501 Foldy-Wouthuysen- 108

Transpose 751 Transposing matrices 751 Transpositions, all possible - 752 Tree

genealogical - I 05 phylogenetic - I 05

Tree form of big expressions 200 of expressions 143

TreeForm 144 Trees, pseudorandom - 873 Triangle

area 65 q-Pascal - 667

Triangles forming polyhedra 704 points and lines in - I 00 with touching vertices 50

Triangulation of surfaces 99 TrigExpand 277 TrigFactor 276

Index

Index

Trigonometric functions all- 167 autosimplification of - 172 expanding - 276 expressed through logarithms and

square roots 188 factoring - 276 iterated - 169 periodicity of- 174 rewriting- 276 special values of- 172

Trott's constant 70 True 539 True

functions returning - or False 540 the truth value- 539

TrueQ 540 Truncation for display 198 Truth values 539 Tubes

along nondifferentiable curves 94 constructed from points 870

Turing, A. 397 Typeface in traditional form 148 Types of fonts and letters 4 Typesetting 73, 146

u

Ultimate laptop I 07 Unchangeable, variables 309 Underdetermined linear systems 818 Unequal 552 Unevaluated 313,366,512 Unevaluated

in action 763 passing arguments - 3 12 patterns 577 surviving - 522

Union 725,761 Unique 455 Unique symbol names 455 Universality, reason of Mathematica's

- 143 Unlocking chains 1 06 Unprotect 310 UnsameQ 556 Unset 292 UpSet 317 UpSetDelayed 317 UpValues 322 Utilities'Annotation 495

Utility packages 498

v

ValueQ 560 Values

inside Block 514 internal form of- 326 of expressions 321 of symbols 326

Vandermonde matrix 56 VandermondMatrix 56 Variables

assignments to- 326 auxiliary- 4 clearing - 292 clearing many- 296 collision of- names 482 context of- 469 created inside Block 450, 883 created inside Module 453, 883 creating new- 455 dummy- 338 dummy integration - 557 from all packages 497 genericity assumptions about - 405 in different contexts 513 in packages 469 in pure functions 337 inside scoping constructs 453 localization of- 456, 883 number of - in contexts 4 71 of all contexts 494 protected - 309 removed - 295 removing many- 296 scoping of - in assignments 459 scoping of- in iterators 449 scoping of - in subprograms 450 shadowed - 488 strange - 405 symbolic calculations without- 106 temporary - 45 3 to avoid 458 unchangeable - 309 unique- 455

VariablesTester 480 Vector

algebra 777 as a list 549 four- 819 testing for being a- 549

1027

VectorQ 550,551 Vectors, unioning- 876 VectorUnion 876 Verbatim 580 Verbatim patterns 579 Version-related data 425 Vieta polynomial 61 Virtual matrix 883 Visible, form of expressions 143 Visualizations of inequalities 67 Vortex motion 7 4 Voting, d'Hondt- 875

w

Wagner, R. 839 Walk, random- 105 Walking toy 106 Warnings

about using experimental functions 492

in Mathematica 403 versus errors 403

Water dripping- 104 dripping- drops l 03 falling from fountains 103 waves 103

Wave equation modeling - using Huygens' principle

108 separability of- I 07

Web connections I 05 resources for problems 107

Website on mathematical constants 180

Weekday of teaching surprises 105 Weierstrass function 36 Weight, finite difference-s 645 WhatsGoingOnWithContexts'

482 Which 564 While 565 While loop 565 Whip, cracking- 105 Wild cards in strings 397 Wine bottle labels, bubbles in - 106 Wire, charged - I 08 With 450 Woodpecker, modeling a- toy 104

1028

Words different 865 most frequent - 866

WriteRecursive 746 Wronskian 805 WronskiDet 958

X

Xor 562 Xor, logical - 561

z

Zeilbergcr, D. 10 I Zero

approximate - !51, 289 arguments 280 exact- 149 test 827

Zeros in multiplication 179 of univariate polynomials 23 real - of nearby polynomials I 06

ZeroTest 827 Zeta 645 Zipf' s law 855

$

$-functions 3, 399, 425

$Aborted 429 $Context 470 $ContextPath 472 $CreationDate 426 $DisplayFunction 431 $Failed 405 $HistoryLength 430 $IterationLimi t 433 $Line 429 $MachineEpsilon 426 $MachinePrecision 426 $MaxMachineNumber 427 $MinMachineNumber 428 $RecursionLimit 432 $Version 426

Index