The Mathematica Guidebooks

# Index of the GuideBooks

Symbols, A-C | D-E | F-H | I-J | K-M | N-P |Q-S | T-W | X-Z | Download index (1.5 MB .pdf)

## Q

`q`-

• Binomial P.5.Sol.8, S.1.Ex.30
• binomial theorem P.5.Ex.8
• derivative P.5.Ex.8, S.1.6.4
• Factorial N.1.Ex.2
• Hermite polynomials S.2.Ex.7
• hypergeometric functions P.1.3
• logarithm S.1.Ex.19
• Pascal triangle P.5.Sol.8
• product from q-series S.1.Ex.30
• series to q-product S.1.Ex.30
• Taylor series S.1.6.4
• trigonometric functions N.1.Ex.2

`Q`-functions

• for testing properties P.5.1.1, S.1.Ex.32
• returning not a truth value P.5.Ex.15

`qBinomial` P.5.Sol.8

`qCos` N.1.Sol.2

QES conditions S.1.Ex.22

`qFactorial` P.5.Sol.8

`qHermite` S.2.Sol.7

`qSin` N.1.Sol.2

• equation G.1.Ex.19, S.1.Ex.32
• irrationals N.1.1.3
• map N.1.3

• ODEs solvable by ~ S.1.7.1
• weights N.1.8

Quadrilaterals, in 3D contour plots G.3.Ex.19

Quantifier elimination S.1.2.3

Quantifiers S.1.2.3

Quantum

• Carnot cycle P.1.Sol.1
• carpet N.1.Sol.35
• cellular automata P.6.5.1
• event enhanced ~ mechanics G.2.3.1
• Hamilton-Jacobi equation N.1.10.1
• harmonic oscillator S.3.Ex.8
• mechanical angular momentum G.3.2
• mechanical time evolution G.2.2.2
• mechanics N.1.10.1, N.1.10.2, N.1.Ex.35, S.1.Ex.21, S.2.3, S.2.6, S.2.10, S.2.Ex.9, S.2.Ex.10, S.2.Ex.11, S.3.0, S.3.1, S.3.3, S.3.5, S.3.Ex.10
• potential N.1.10.1
• random walk N.1.Sol.32
• well G.3.1, S.3.Ex.10

`QuantumCellularAutomata` P.6.5.1

Quaquaversal tiling G.2.3.1

Quartic

• oscillator N.1.Ex.5, N.1.Ex.24, S.1.Ex.21, S.2.10, S.3.Ex.1
• plane curves S.1.Ex.28
• polynomial N.1.11.2

Quasi-random numbers N.1.7

Quasicrystals

• Meyer construction of ~ G.1.1.1
• visualization of ~ G.1.5.5

`QuasiMonteCarlo` N.1.7

`QuasiNewton` N.1.9

Quintic

• Lagrange's ~ S.1.Sol.24
• solving ~ polynomials S.3.13

Quotential derivative S.1.Ex.1

Quotes

• around strings P.1.1.2, P.2.2.1
• from E. Mach Pr
• from M. W. Crofton S.1.9.1
• visibility of string ~ P.4.6.6

`Quotient` N.2.1

Quotient

• differential equation for ~ S.1.Ex.4
• of elliptic integrals S.3.Ex.16
• of intervals N.1.1.2
• of numbers N.2.1
• of ODE solutions S.1.Ex.4
• of polynomials S.1.2.2
• of series S.1.6.4

## R

`RademacherPartitionPApproximation` N.2.Sol.12

Radial-azimuthal, animation of a ~ transition G.3.Ex.12

• absent ~ P.1.Sol.1
• from a dipole G.1.4
• from moving charges G.3.Ex.4, S.1.Ex.29
• Sommerfeld's ~ condition S.3.Sol.10

• as expressions P.2.2.2
• canonicalization of numerical ~ S.1.5
• denesting ~ N.2.Ex.3, S.1.1
• nested ~ P.2.2.4, G.1.5.6, G.2.3.7
• trigonometric functions in real ~ S.1.Ex.18

Rain, running in the ~ P.1.Sol.1

Rainbow G.1.1.2, G.1.Ex.7

`RainbowImage` G.1.Sol.7

Ramanujan

• 's factorial expansion S.1.Ex.30
• 's master theorem S.1.8
• identities P.1.2.3, S.1.Ex.18, S.3.Ex.24, S.3.Ex.24
• series for pi N.1.1.1
• theta functions S.3.0
• tau function N.2.Ex.14

`RamanujanEllipticA` S.3.0

`RamanujanEllipticB` S.3.0

`RamanujanEllipticC` S.3.0

`Random` G.1.5.6

Random

• 2D graphics G.1.5.6
• 3D graphics G.2.Sol.1
• analytic function N.1.Sol.2
• average area of a ~ triangle S.1.9.1
• average distance between ~ points S.1.Ex.35
• complex numbers G.1.5.6
• contour plots of ~ functions N.1.2
• curves G.1.5.6
• determinants S.1.Ex.44
• expressions G.1.Ex.16
• Fibonacci recursion N.1.1.1, N.1.3
• flea exchanges N.2.Ex.6
• fractals G.3.Sol.8
• friezes G.1.5.6, N.2.1
• functions G.1.Ex.16, G.3.Sol.8, S.1.Ex.16
• Helmholtz equation solutions S.3.Ex.13
• integers G.1.5.6
• intersections of ~ planes G.2.Ex.12
• letter arrangement G.1.5.6
• matrices G.1.5.6, G.1.5.6, G.2.1.2
• number generator P.1.Sol.1
• parking of cars N.1.Ex.27
• permutations G.1.5.6, G.2.3.1, N.1.Ex.27, N.2.Sol.14, S.3.Sol.25
• perturbations of iterations N.1.Ex.1
• points in a sphere S.3.Ex.1
• polygons G.3.Ex.12
• polyhedra P.1.2.2, G.2.Ex.18, G.2.Sol.1
• polynomials S.1.2.1
• potential G.1.Ex.17, N.1.Ex.11
• programs G.1.Ex.16
• rational functions N.1.3
• real numbers G.1.5.6
• rotation matrices G.2.1.2
• rotations N.1.Sol.28
• searches G.3.Sol.8, S.3.Sol.9
• smooth ~ transitions G.2.Sol.18
• stirring N.1.Sol.28
• sums G.1.5.6, N.1.Ex.25
• superposition of waves G.3.1
• surfaces G.3.Sol.9
• textures N.1.Ex.32
• two particle collisions N.1.Ex.25

Random numbers

• complex ~ G.1.5.6
• generating ~ G.1.5.6, N.1.Ex.25
• integer ~ G.1.5.6
• iterated ~ G.1.Ex.17
• real ~ G.1.5.6
• reproducible ~ G.1.5.6
• seeded ~ G.1.5.6
• state of the generator of ~ G.1.5.6

Random walk

• average ~ excursion shape N.1.Ex.27
• colliding ~ G.1.Ex.14
• in multidimensional lattices P.1.Sol.1
• long ~ in 3D G.2.Ex.9
• modeling a ~ G.1.5.6
• of reflection projections N.1.Sol.18
• on a Sierpinski triangle G.1.Ex.14
• on a sphere G.2.Ex.9
• probabilities for returns in a ~ S.3.5
• quantum ~ N.1.Sol.32
• rotated ~ G.1.5.6
• second arcsine law of ~ N.1.Ex.27
• self-intersection free ~ G.2.3.2
• tubes, along ~ G.2.3.2

`RandomCluster` G.1.Sol.1

`RandomFunction` S.1.Sol.16

`RandomGeode` G.2.2.2

`RandomIFS` G.1.5.6

Randomized

• arithmetic N.1.Ex.23
• field lines G.2.Sol.1
• iterations N.1.Ex.1

Randomness

• graphics containing ~ G.1.5.6
• testing ~ G.1.5.6

`RandomPlatonicSolidCluster` G.2.Sol.16

`RandomSpike` G.1.5.7

`RandomTetrahedronGrowth` G.2.3.1

`Range` P.6.1.1

Rank

• of built-in functions P.6.6
• of cited journals P.6.Ex.4
• of tensors P.6.2

`Raster` G.3.2

`Rational` P.2.2.1

Rational

• enumerating ~ numbers P.1.Sol.1
• functions S.1.3
• numbers P.2.2.1
• numbers from real numbers N.1.1.3
• solution of Painlevé equations S.1.Ex.3

Rational numbers, as a type P.2.2.1

`RationalFunctions` S.1.2.2

Rationalization, of real numbers N.1.1.3

`Rationalize` N.1.1.3

`Rationals` S.1.1

Rauzy tessellations G.1.1.1

Ray

• Cartesian ~ G.1.Sol.7
• tracing P.1.3

Rayleigh sums S.3.Ex.1

Rayleigh-Schrödinger perturbation theory S.2.Ex.10

Rays

• colored ~ G.2.Ex.17
• in a billiard P.1.2.1, G.1.Ex.13
• in a spherical mirror G.1.1.1
• in a supercircle S.1.Ex.25
• in a water drop G.1.Ex.7
• in a water vertex P.1.Sol.1
• multiple-reflected ~ G.1.Ex.13, S.1.Ex.25

`Re` P.2.2.5

• data from the web N.1.1.5
• files P.4.4.1
• notebooks P.6.6
• packages P.6.6
• recommended ~ A.1.1

`ReadList` P.6.6

`Real` P.2.2.1

Real numbers

• as a type P.2.2.1
• in patterns P.3.1.1
• inputting ~ P.2.2.1
• variables assumed to be ~ S.1.1

Real part

• of expressions S.1.4
• of numbers P.2.2.5
• of polynomial roots S.1.5

`RealDigits` P.2.4.2

Realizations, of patterns P.3.1.1

`Reals` S.1.1

Reciprocity law N.2.2

`ReciprocityLaw` N.2.2

`Rectangle` G.1.1.1, G.1.3.1, G.1.3.1, G.3.2

Rectangles

• containing a graphic G.1.3.1
• Green's function for ~ S.3.Ex.12
• in graphics G.1.1.1
• packings of ~ G.1.Ex.12
• touching a rectangle P.1.Sol.1
• with inscribed graphics G.1.3.1

Recurrence equations S.1.8

Recurrence relation

• of associated Legendre polynomials S.2.6
• of first kind Chebyshev polynomials S.2.7
• of Gegenbauer polynomials S.2.4
• of Hermite polynomials S.2.2
• of Jacobi polynomials S.2.3
• of Laguerre polynomials S.2.5
• of Legendre polynomials S.2.6
• of second kind Chebyshev polynomials S.2.8

Recurring decimals N.2.Ex.5

Recursion

• identifying ~ P.4.5
• in assignments P.5.Ex.5
• versus iterations P.4.5

Recursive

• coefficient calculations N.1.Sol.24
• definitions P.5.2.1, P.5.2.2, G.2.4, N.1.Sol.24
• evaluation P.3.1.1

Redheffer matrix P.1.2.3

`Reduce` S.1.5

REDUCE, the computer algebra system P.1.Ex.2

Reduced

• fractions P.2.2.1
• polynomials S.1.2.2
• residue system N.2.Sol.12

`ReducedDifferentiatedPolynomial` S.3.Sol.18

`ReduceToPrincipalQuintic` S.3.13

Reductions, algebraic ~ S.1.2.2

References

• about computer algebra systems P.1.Ex.2
• age distribution of ~ P.6.6
• consistency of ~ P.6.Ex.4
• of the GuideBooks In
• on parametrized surfaces G.2.Sol.1

Refractive index P.1.Sol.1, G.1.Ex.7, N.1.3

Regularization

• numerical ~ N.1.Ex.6
• Zeta function ~ S.1.Sol.15, S.3.Sol.15

Reinhardt, K. G.1.1.4

Reintroducing, symbols P.3.1.2

Relation

• completeness ~ S.2.1
• Legendre ~ S.1.2.2

Relations

• between divisor sums S.1.Ex.17
• between elementary functions and their inverses P.2.2.5
• between harmonic numbers S.3.0
• between orthogonal polynomials S.2.9
• between zeros of differentiated polynomials S.3.Sol.18
• containedness ~ P.5.1.2
• contiguous ~ S.3.7
• Newton ~ S.2.Ex.5
• ordering ~ P.5.1.1
• Vieta ~ S.1.2.2, S.1.5, S.2.Ex.5

Relatively prime G.3.Ex.1

Relativistic

• oscillator S.2.Ex.7
• train P.1.Sol.1
• transformations P.6.5.1, S.1.Ex.29

`ReleaseHold` P.3.3

Remainder, Lagrange ~ N.1.Ex.15

Remembering function values P.3.5

`Remove` P.3.1.2

`Removed` P.3.1.2, P.4.Sol.10

Removed symbols P.3.1.2

Removing

• built-in functions P.3.1.2
• context names P.4.6.4
• elements from lists P.6.3.1
• special function definitions P.3.1.2
• symbols P.3.1.2

`RenderAll` G.2.1.3, G.2.1.5

Rendering

• hidden edges G.2.Ex.15
• intersecting polygons G.2.1.5
• of 3D graphics G.2.1.5
• of 3D polygons G.2.1.5
• of concave polygons in 3D G.2.1.1, G.2.Ex.20
• only visible polygons G.2.1.5

Renormalization group

• -based solution of differential equations P.1.3
• temptation of ~ In

Reordering

• of lists P.6.3.3
• of polynomials S.1.2.1
• of sequences S.1.6.4

`Repeated` P.5.2.2

Repeated

• changes in ~ timings N.1.1.4
• option setting P.5.3.1
• patterns P.5.2.2
• rule application P.5.3.1

`RepeatedNull` P.5.2.2

`Replace` P.5.3.1

`ReplaceAll` P.5.3.1

`ReplaceList` P.5.3.1

Replacement rules

• and function definitions P.3.4
• applying ~ P.5.3.1
• building ~ P.6.3.3
• dispatched ~ P.5.3.2
• in action P.5.3.3
• monitoring the application of ~ P.5.3.3
• nested ~ P.5.3.1
• scoping in ~ P.5.3.1

Replacements

• all possible ~ P.5.3.1
• and attributes P.5.3.1
• and patterns P.5.3.1
• applying ~ P.5.3.1
• compiling ~ P.5.3.2
• failed ~ P.5.3.1
• in action G.1.6
• many ~ P.5.3.2
• monitoring ~ P.5.3.1
• of parts P.5.3.1
• of subexpressions P.5.3.1
• order of ~ P.5.3.1
• order of substitutions in ~ P.6.Ex.17
• random G.1.5.6
• repeated ~ P.5.3.1

`ReplacePart` P.5.3.1

`ReplaceRepeated` P.5.3.1

Representation

• CCR ~s S.1.2.2
• momentum ~ S.2.Sol.7
• of numbers P.2.2.1
• Schwinger ~ N.1.Ex.5
• Zeckendorf ~ N.2.Ex.13

Reproducibility

• of random numbers G.1.5.6
• of shown results In

Reptiles, Escher's ~ G.1.5.8, G.2.Sol.19

Reserved words P.1.1.1

`Residue` S.1.6.5

Residue

• generalized ~ S.1.6.5
• logarithmic S.1.Ex.41
• of functions at poles S.1.6.5
• theorem P.1.2.1

Resistances, all possible ~ S.1.6.4

Resistor network

• description of ~ N.1.Ex.20
• finite ~ N.1.4
• infinite ~ S.1.6.2
• linear ~ S.1.6.4

Resonances

• in a quantum well S.3.Sol.10
• in cylinder scattering S.3.Sol.13
• in square well scattering G.3.1

Resources

• needed for the GuideBooks In
• used in a session P.4.2.2

`Rest` P.6.3.1

Restricted

• patterns P.5.2.2
• plot range G.1.1.3, G.2.1.5, G.3.1
• search ranges N.1.9
• solution ranges N.1.10.1
• three-body problem N.1.10.1

`Resultant` S.1.2.2

Resultants

• identities for ~ S.1.Sol.37
• of polynomials S.1.2.2
• of polynomials with large coefficients S.3.13

Results

• abbreviated ~ P.2.3.1
• avoiding storage of ~ N.1.11.1
• form of displayed ~ In
• formatting of ~ In
• reproducibility of shown ~ In
• suppressing ~ P.4.1.1
• with hidden data G.1.1.1, N.1.2, N.1.3

Retarded time G.3.Ex.4, S.1.Ex.29

`Reverse` P.6.3.3

`RGBColor` G.1.1.2

Rhombii, subdivision of ~ G.1.5.5

Riccati, differential equations S.1.7.1

Richardson theorem S.1.2.1

Ridges, in sand P.1.Sol.1

Riemann

• curvature tensor S.1.6.1
• expanding sphere S.2.5
• hypothesis P.5.Sol.7
• sphere G.2.3.7, G.3.Ex.11, N.1.11.2, S.2.5, S.3.Ex.3
• Zeta function P.5.Ex.7, S.3.Ex.15

Riemann surfaces

• experimentally determining ~ P.1.Sol.1
• faithfulness of ~ N.1.11.2
• of algebraic functions N.1.11.2
• of cube roots G.2.3.7, G.3.3
• of cubics S.1.Ex.23
• of elliptic integral ratios S.3.Ex.16
• of hypergeometric functions S.3.Ex.16
• of inverse trigonometric functions P.2.2.5
• of inverse Weierstrass's functions S.3.Ex.3
• of Mathieu characteristics S.3.11
• of nested fractional powers P.2.Ex.6
• of nested logarithms G.2.3.7
• of oscillator energies S.2.10
• of pendulum oscillations S.3.Ex.4
• of `ProductLog` S.3.10
• of simple functions G.2.3.7
• of square roots G.2.3.7, S.1.6.6
• of the bootstrap equation S.3.Ex.21
• of the incomplete Gamma function S.3.2
• of the inverse error function S.3.Ex.16
• of the Kepler equation G.2.Ex.21
• over a Riemann sphere G.2.3.7
• tetraview on ~ G.2.Ex.21
• with disconnected sheets P.2.Ex.6

Riemann-Siegel formula S.3.Ex.15

`RiemannSiegelTheta` S.3.Ex.15, S.3.Sol.15

`RiemannSiegelZ` S.3.Ex.15, S.3.Sol.15

`RiemannSpherePolynomialVisualization` S.2.5

`RiemannSurface` N.1.11.2

Riesz-Fischer, theorem S.1.8

Riffle shuffles N.2.Ex.6

Ring shift modeling N.2.Ex.6

Ringcoil N.1.11.1

Rings, Borromaen ~ G.2.2.1

Risch algorithm S.1.6.2

Rising bubbles P.1.Sol.1

River basins P.1.Sol.1, G.1.1.1

Rivin, I. G.2.3.10

Robbin's, integral identity S.1.6.2

Robbins, conjecture Pr

`RobbinsIntegralIdentityTest` S.1.6.2

Robin boundary condition N.1.10.2

Rock, curling ~ P.1.Sol.1

Rocket, with discrete propulsion S.3.Ex.5

Rod packings G.2.1.2

Rodrigues's formula

• of associated Legendre polynomials S.2.6
• of first kind Chebyshev polynomials S.2.7
• of Gegenbauer polynomials S.2.4
• of Hermite polynomials S.2.2
• of Jacobi polynomials S.2.3
• of Laguerre polynomials S.2.5
• of Legendre polynomials S.2.6
• of orthogonal polynomials S.2.1
• of second kind Chebyshev polynomials S.2.8

Rogosinsky sum S.2.4

Rolling

• ball P.1.Sol.1, G.2.Sol.6
• circles G.1.1.2
• cylinder P.1.Sol.1

`Root` S.1.5

Root finding

• algorithms S.1.6.4
• numerical ~ N.1.8
• symbolic ~ S.1.5
• timings of ~ N.1.8
• Weierstrass ~ method N.1.Ex.15

`RootLinePicture` N.1.Sol.15

`RootPointPicture` N.1.Sol.15

`RootReduce` S.1.5

`Roots` S.1.5

Roots

• conditions on polynomial ~ S.1.2.3
• iterated ~ N.1.8
• minimal distance between polynomial ~ N.1.8, S.1.Ex.2
• multiplicity of ~ N.1.8
• nearly integer ~ S.1.5
• nested ~ P.1.2.4, N.1.Ex.37
• of differentiated polynomials P.1.2.1, S.3.Ex.18
• of Gaussian integers G.1.1.1
• of orthogonal polynomials S.2.9
• of polynomials P.6.5.1, S.1.5, S.1.Ex.6
• of polynomials and their derivative S.3.Ex.18
• ordering of ~ S.1.5
• parameterized ~ N.1.Sol.15, S.1.2.3
• primitive ~ S.1.9.2
• sensitivity of polynomial ~ N.1.8
• smoothness of ~ S.1.5
• sum of ~ S.1.6.2
• transforming ~ to radicals S.1.5

`RootsPrincipalQuintic` S.3.13

`RootSum` S.1.6.2

Ropes, bent ~ G.1.5.6

Rotated

• 2D graphics objects G.1.1.1
• 3D graphics objects G.2.1.2
• labels in graphics G.1.1.3
• text in 2D graphics G.1.1.1

`RotatedBlackWhiteStrips` P.1.1.2

`RotatedSideWireFrame` P.1.2.2

`RotateLabel` G.1.1.3

`RotateLeft` P.6.3.3

`RotateRight` P.6.3.3

Rotation

• 2D ~ matrices G.1.1.1
• 3D ~ matrices G.2.1.2
• 4D ~ matrices G.2.Ex.21
• around an axis P.6.4.3
• coin ~s P.1.Sol.1
• infinitesimal ~ matrices S.1.6.3
• matrices P.6.4.3
• possible crystal ~s N.2.2
• random ~ matrices G.2.1.2

Roughening, of a surface G.2.Sol.9

`Round` N.1.1.1, N.1.1.3

Rounding

• numbers N.1.1.3
• precision and accuracy N.1.1.1

`RowReduce` P.6.5.2

Rudin-Shapiro sequence G.1.5.2

`Rule` P.5.3.1

Rule

• Benford's ~ P.6.Ex.1
• l'Hòpital's ~ P.1.2.3

`RuleCondition` P.5.Sol.13

`RuleDelayed` P.5.3.1

Ruler

• and compass constructions S.1.9.2
• on two fingers N.1.Ex.11

Rules

• applying ~ P.5.3.1
• as internal form of function definitions P.3.4
• for input formatting P.1.1.2
• for replacements P.5.3.1
• immediate and delayed ~ P.5.3.1
• monitoring the application of ~ P.5.3.3
• returned from `DSolve ` S.1.7.1
• returned from `NDSolve` N.1.10.1
• returned from `NSolve` N.1.8
• returned from `Solve` P.6.5.1, S.1.5
• used by `FullSimplify` S.3.1

`RulesToCycles` P.5.3.3

`RunEncode` P.5.3.3

Runge phenomena N.1.2

Runge-Kutta method, for solving ODEs N.1.10.1

`RungeKutta` N.1.10.1

Running, in the rain P.1.Sol.1

## S

• approximation N.1.Ex.29
• in a 2D plot G.1.2.1
• in differential equation solutions S.1.Sol.5
• visualization of a ~ G.3.Ex.2

`SameQ` P.5.1.2

`SameTest` P.6.4.1, N.1.1.1

Sampling

• in `FindMinimum` N.1.9
• in `FindRoot` N.1.8
• in `FunctionInterpolation` N.1.2
• in `NDSolve` N.1.10.1
• in `NIntegrate` N.1.7
• in `Plot` G.1.2.1

Sand

• aeolian ~ ripples P.1.Sol.1
• flow in an hourglass P.1.Sol.1
• on vibrating metal plates G.3.Sol.3
• ridges P.1.Sol.1

Sandpile model N.1.3, N.2.Ex.6

Saunders pictures G.3.2

`Save` P.4.4.1

Saving

• data to files P.4.4.1
• function definitions P.4.4.1

Sawtooth function P.2.Ex.7

Scale

• graphic of a ~ G.2.1.5
• of a number N.1.1.1

`Scaled` G.1.1.1, G.2.1.1

Scaled coordinates

• in 2D graphics G.1.1.1
• in 3D graphics G.2.1.1

Scarlets G.3.1

Scattering

• chaotic ~ N.1.10.1
• Coulomb ~ S.3.Ex.13
• of four hills N.1.10.1
• on a corrugated wall S.3.Ex.13
• on a cylinder S.3.Ex.13
• on a dielectric cylinder S.3.Ex.13

Schanuel's conjecture S.1.Sol.14

Scheme, pyramidal ~ N.2.4

Scherk's fifth surface N.1.Ex.7

Schmidt decomposition P.1.2.3

`SchmidtDecomposition` P.1.2.3

Schönberg's Peano curve N.2.1

`SchoenbergPeanoCurve` N.2.1

Schröder's formula S.1.6.4

Schrödinger equation

• harmonic oscillator ~ S.2.2, S.3.Ex.5
• nonlinear ~ N.1.10.2, S.1.8
• one-dimensional ~ N.1.Ex.35, S.3.3, S.3.3
• time-dependent ~ N.1.10.2, N.1.Ex.35, S.3.3
• time-independent ~ N.1.8, S.3.3
• with prime eigenvalues P.1.Sol.1

`SchubertRelation` P.6.Sol.7

Schwartz, distributions S.1.8

Schwarz

• derivative S.1.6.3
• differential operator S.1.Ex.4, S.3.13

Schwarz-Riemann minimal surface N.1.Ex.19

Schwinger representation N.1.Ex.5

Scoping

• comparing ~ constructs P.4.6.3
• conditions in ~ constructs P.5.2.2
• dynamic ~ P.4.6.2
• for nonsymbols P.4.Ex.6
• in assignments P.4.6.3
• in iterators P.4.2.1, P.4.6.1
• in pure functions P.4.6.2
• in replacement rules P.5.3.1
• in subprograms P.4.6.2
• in summation P.4.6.1
• iterators as ~ constructs P.4.2.1
• lexical ~ P.4.6.2
• missing ~ S.1.Sol.3
• nested P.5.Ex.17, P.6.Ex.23
• of variables P.6.Ex.23
• timings of constructs P.4.6.3

Scrabble game P.6.4.4

Scraping, camphor ~ P.1.Sol.1

Screw, graphic of a ~ G.2.Sol.1

Searching

• for a long random walks G.2.Ex.9
• for Dedekind Eta function identities S.3.Ex.25
• for fractals G.3.Sol.8
• for Gamma function identities S.3.Ex.25
• for interesting functions G.3.Sol.8, N.1.Sol.34
• for interesting LTL rules N.1.Sol.32
• for jerk functions N.1.Ex.34
• for solutions of nonlinear PDEs S.3.Ex.4
• for strange attractors N.1.Ex.9
• messages P.6.4.2
• patterns in iterated maps N.1.Ex.9

`Sec` P.2.2.3

Secant method

• for root finding N.1.8
• iterated ~ N.1.Ex.13

Secants

• envelope of ~ S.1.Ex.39
• iterations of ~ P.2.2.3

Seceder model N.1.Ex.27

`Sech` P.2.2.3

Second, arcsine law N.1.Ex.27

Secular terms S.1.Ex.36

`SeedRandom` G.1.5.6

Selberg identity N.2.Ex.10

`SelbergIdentity` N.2.Sol.10

`Select` P.5.1.4, P.6.3.1

`Select` versus `Cases` P.5.2.2

Selecting

• expressions P.5.2.2
• formatting styles In
• roots S.3.Sol.19

Self-Fourier transform S.1.8

Self-intersections, of a curve S.1.Ex.28

Self-organized criticality G.1.5.6

Self-reproducing, function P.3.6

Self-similar, graphics G.1.1.1, G.1.5.9

Semantically meaningless expressions P.4.1.1

Semialgebraic set P.1.2.3, S.1.2.3, S.1.Ex.25

Semiclassical approximation S.1.Ex.21, S.3.5

Semicolon P.4.1.1

Sensitivity

• of linear equations S.1.Sol.13
• of polynomial roots N.1.8

Separability

• of functions P.5.Ex.15
• of wave equation P.1.Sol.1

Separation of variables S.2.1, S.3.11

Septic polynomial N.1.11.2

`Sequence` P.3.6, P.5.2.1

Sequence

• cut ~ N.1.Ex.27
• Farey ~ N.1.8, N.2.2, N.2.Ex.10
• Farey-Brocot ~ G.1.1.1, N.2.Ex.10
• Gale-Robinson ~ S.1.3
• integer ~s N.1.6
• Kimberling ~ N.2.Ex.1
• Kolakoski ~ P.6.Ex.21
• Lenard ~ N.1.1.5
• Odlyzko-Stanley ~ N.1.Ex.25
• of arguments P.3.6, P.4.1.2
• reordered S.1.6.4
• representation of the Dirac delta function S.1.8
• representation of the Heaviside step function S.1.8
• Rudin-Shapiro ~ G.1.5.2
• transformations N.1.Ex.6
• van Der Corput ~ N.1.7

`SequenceLimit` N.1.6

Sequences

• accelerated convergence of ~ N.1.6, N.1.Ex.6
• divergent ~ N.1.Sol.6
• extrapolating ~ N.1.6
• from pattern matching P.5.2.1
• guessing ~ S.2.Sol.3
• integer ~ N.1.6
• limits of ~ N.1.6
• of digits N.2.Ex.5
• substitution ~ N.1.5

`Series` S.1.6.4

Series

• arithmetic of ~ S.1.6.4
• Cantor ~ P.3.7
• cardinal ~ G.2.2.2
• divergent ~ S.1.6.4
• Eisenstein ~ S.1.Ex.17
• examples of ~ expansions P.1.2.3
• expansions of analytic functions S.1.6.4
• failure of ~ expansion S.3.Sol.1
• for elliptic functions S.3.Ex.4
• Fourier ~ G.3.1, S.1.Ex.44
• high order ~ S.3.Ex.1
• improved ~ expansion P.1.Sol.1
• Laurent ~ S.1.6.4
• multiplicative ~ S.1.Ex.30
• multivariate total degree ~ S.1.6.4
• of matrix functions S.1.Ex.14
• of quotient of Gamma functions S.3.Ex.1
• of theta functions S.3.Ex.12
• of Weierstrass functions S.3.Ex.3
• Puiseux ~ S.1.6.4
• q-~ S.1.6.4, S.1.Ex.30
• solution of differential equations S.1.6.4, S.1.Ex.36
• symbolic terms of a ~ S.1.8
• Taylor ~ S.1.6.4
• to function P.1.Sol.1
• using numerical techniques in ~ expansions N.1.Sol.31
• zeros of truncated ~ S.1.6.4

`SeriesCoefficient` S.1.6.4

`SeriesData` S.1.6.4

`SeriesTerm` S.1.6.4

Serif typeface, in traditional form P.2.2.1

Session

• CPU time used in a ~ P.4.2.2
• freeing memory in a ~ P.4.4.1
• history in a ~ P.4.1.1
• history of a ~ P.4.3.2
• inputs of a ~ P.4.3.2
• line numbers in a ~ P.4.3.2
• memory used in a ~ P.4.2.2
• reducing memory needs of a ~ P.4.2.2
• resources used in a ~ P.4.2.2

`Set` P.3.1.1

Set

• Julia ~ G.1.1.3, N.1.3
• semialgebraic ~ S.1.2.3
• sum-free ~ P.6.Ex.2
• theoretic operations P.6.4.1

`SetAccuracy` N.1.1.1

`SetAttributes` P.3.3

`SetDelayed` P.3.1.1, P.6.Ex.14

`SetOptions` P.3.2

`SetPrecision` N.1.1.1

Sets, number ~ S.1.1

Setting

• elements of lists P.6.3.3
• options P.3.2
• system options P.4.6.6, N.1.1.5, S.1.6.1
• the accuracy of numbers N.1.1.1
• the precision of numbers N.1.1.1
• values P.3.1.1
• values of expressions P.3.1.1
• values of symbols P.3.1.1

Sextic oscillator S.2.Ex.11

`Shading` G.2.1.3

Shadows, absence of ~ in 3D graphics G.2.1.5

Shaft, graphic of a ~ G.2.2.1

Shakespeare, W. N.1.1.5

Shallit-Stolfi-Barbé plots G.3.Ex.5

`Shallow` P.2.3.1

Shape

• ~s in 3D graphics G.2.1.5
• functions in FEM S.1.Sol.7
• of a cracking whip P.1.Sol.1
• of a drop P.1.Sol.1

`ShapeFunction` S.1.Sol.7

`ShapeFunctionPlot` S.1.Sol.7

`Share` P.4.2.2

Sheets

• disconnected ~ of a Riemann surface P.2.Sol.6
• of Riemann surfaces P.2.Sol.6, N.1.11.2, S.3.Ex.16, S.3.Ex.21

Shooting method N.1.Ex.5

`Short` P.2.3.1

Short

• form of expressions P.2.3.1
• time solution of Newton's equation S.1.Ex.24

`Show` G.1.1.1

Shuffle

• exchange ~ N.1.Ex.27
• riffle ~ N.2.Ex.6

Siamese sisters P.6.5.1

Sierpinski

• plant G.2.Ex.22
• sponge G.2.3.1, N.1.Sol.32

Sierpinski triangle

• constructing the ~ G.1.5.1
• in a magnetic field N.1.8
• PDE with ~ solution P.1.2.1
• random walk on a ~ G.1.Ex.14

`SierpinskiPicture` G.1.5.1

`SierpinskiPlant` G.2.Sol.22

`SierpinskiSponge` G.2.3.1

`SierpinskiTriangle` G.1.5.1

Sieve, prime ~ P.6.3.1

`Signature` P.6.1.2

Signature, of permutations P.6.1.2

Significance arithmetic N.1.1.1

Simplicity, defining ~ of expressions S.1.1

Simplification

• algorithmic ~ of tensors S.1.6.1, S.1.Sol.17
• apparently missing ~ P.2.2.6
• by optimization N.1.11.1
• by pointed rewriting P.5.2.2
• by togethering S.1.3
• missing ~ P.1.2.3
• missing expected ~ P.2.2.6
• of algebraic expressions N.2.Sol.3
• of algebraic numbers S.1.5, S.3.1
• of expressions P.3.5, S.1.1, S.1.Sol.1, S.3.1
• of large results S.1.7.1
• of logical expressions P.5.1.3
• of special functions S.3.1
• of tensor expressions S.1.Sol.17
• pointed ~ P.4.6.6, S.1.Sol.24
• through common subexpressions P.6.3.3, N.1.11.1
• under time constraints S.1.1, S.3.1
• using assumptions S.1.1
• using trees S.1.Sol.17
• wrong ~ P.2.2.6, S.1.1

`Simplify` P.3.5, S.1.1

`Simplify`SimplifyPseudoFunctions` S.1.8

Simpson's rule P.1.Sol.1

Simulation, molecular dynamic ~ N.1.0

`Sin` P.2.2.3

Sinai billiard P.1.2.1

Sinc function G.2.2.2, S.3.1

Sine function

• command P.2.2.3
• iterated ~ G.1.2.1
• series of the ~ N.2.2

Sine-circle map, coupled ~ N.1.Sol.32

Singular

• moduli N.1.Ex.31
• points of differential equations S.1.Ex.5
• points of surfaces G.3.3, G.3.Ex.14, N.1.8
• potential S.3.Ex.8

Singularities

• accumulation of ~ P.2.Ex.10, P.2.Sol.10
• detecting ~ P.6.5.1
• essential ~ P.2.2.3
• expansion at ~ S.1.6.4
• from ODEs N.1.10.1
• in numerical integrands N.1.7
• of curves G.3.Ex.14
• of surfaces G.3.3
• removable ~ S.1.Ex.32
• series at essential ~ S.3.Sol.1

Singularity

• logarithmic ~ S.3.Ex.12
• nonintegrable ~ S.1.Ex.21

`SingularityDepth` N.1.7

`Sinh` P.2.2.3

`SinIntegral` S.3.4

Size

• as a measure for simplicity S.1.1
• of certain integrals G.2.2.2
• of expressions P.2.3.2, P.4.2.2
• of random expressions G.1.Sol.16

`Skeleton` P.2.3.1

Slicing

• a Möbius strip G.2.Ex.14
• polygons by lines G.1.3.1
• polygons by planes G.2.1.5
• polyhedra G.2.1.5

Slide

• finding the minimum of a ~ N.1.9
• sliding down in a ~ N.1.9

Sliding

• chain P.1.Sol.1
• ruler N.1.Ex.11

`Slot` P.3.6

`SlotSequence` P.3.6

Slowly, convergent sums N.1.6

Smallest number N.1.1.1

Smith's Sturmian word theorem N.2.Ex.5

Smoothing

• a dodecahedron N.1.Ex.7
• a torus G.2.Ex.2
• algebraic ~ S.1.2.3
• contours in contour plots G.3.1
• convolution kernel N.1.Ex.13
• in graphics G.1.3.1, N.1.5
• nonsmooth surfaces G.2.Ex.2, G.2.Sol.6
• of data N.1.5
• of intersecting surfaces G.2.Sol.6, G.3.3
• of polygons N.1.3

Smoothness, of initial conditions N.1.10.2

Snail G.2.Ex.4

Snell's law G.1.Sol.7

Snowflake growth P.1.Sol.1

Soccer ball G.2.1.5

Söddy formula P.1.2.2, S.1.5, S.1.Ex.1

Sofroniou, M. P.6.Sol.16

Sokhotsky-Plemelj formula S.1.8

Solitons, of finite length S.1.8

`SolutionBallPendulum` N.1.10.1

`SolutionIcosahedralEquation` S.3.13

Solutions

• best ~ for overdetermined systems P.6.5.1, S.3.Ex.19
• checking ~ S.1.Sol.24
• exhaustive ~ S.1.5
• generic ~ S.1.5
• implicit ~ from `DSolve ` S.1.7.1
• integer ~ of linear systems N.2.Sol.2
• of differential equations N.1.10.1, S.1.7.0
• of equations N.1.8, S.1.5
• of the exercises In
• remarks on the ~ of equations S.1.5
• style of the ~ In
• verifying ~ S.1.5

`Solve` P.6.5.1, S.1.5

`SolveDelayed` N.1.10.1

`SolveMagicSquare` P.6.5.2

Solving

• differential equations N.1.10, N.1.Ex.35, N.1.Ex.36, S.1.7
• linear equations P.6.5.1
• matrix equations P.6.5.1
• polynomial equations N.1.8, S.1.2.2, S.1.5
• transcendental equations N.1.8, S.1.5
• vector ~ equations S.1.Ex.29

Solving equations

• by iterations N.1.Ex.15
• iteratively G.3.Ex.4
• numerically N.1.8
• results of ~ P.6.5.1
• using differential equations N.1.10.1, N.1.Sol.1, S.2.Sol.7, S.3.Sol.15
• using `FindRoot` N.1.8
• using `GroebnerBasis` S.1.2.2
• using `NDSolve` N.1.10.1, N.1.Sol.1, S.1.Sol.38, S.2.Sol.7, S.3.Sol.15
• using `NRoots` N.1.8
• using `NSolve` N.1.8
• using `Resultant` S.1.2.2
• using `Roots` S.1.5
• using `Solve` P.6.5.1, S.1.5

Sommerfeld condition S.3.Sol.10

Soreng, H. S.1.6.1

Sorry, the game ~ P.5.2.2

`Sort` P.6.3.3, P.6.Ex.15

`SortComplexNumbers` P.5.3.3

Sorting

• algorithm for built-in ~ P.6.3.3
• complexity of of built-in ~ P.6.3.3
• data P.6.3.3
• default ~ of complex numbers P.6.3.3
• game G.1.Ex.12
• lists P.6.3.3
• modeling ~ with rules P.5.3.3
• monitoring ~ P.6.3.3

Space curve

• knotted G.2.3.2
• plotting ~s G.2.2.1
• thickened ~ G.2.1.3, G.2.3.2

Space-filling

• curves G.1.5.9
• polyhedra G.2.3.1

Spacing check P.6.Ex.4

Sparse matrices N.1.4

Special characters, for built-in functions P.2.1

Special functions

• converting ~ S.3.1
• from integration S.1.6.2, S.3.1
• from summation S.1.6.6
• in action S.3.0
• naming conventions of ~ P.1.1.1
• of mathematical physics S.3.0
• references to ~ S.3.1
• simplification of ~ S.3.1
• web site about ~ S.3.0

Special values

• of Ramanujan lambda function S.3.Sol.24
• of Ramanujan phi function S.3.Sol.24
• of trigonometric functions P.2.2.4

Specific

• definitions P.3.1.1
• heat S.3.Ex.12
• negative ~ heat P.1.Sol.1

Specification, of levels P.2.3.2

Speckle plot G.3.1

Speed

• of numerical calculations P.1.2.1, N.1.3
• reduced ~ of arithmetic functions P.3.4

Spelling

• errors P.4.1.1
• warning P.4.1.1

Sphere

• 3D contour plot of a ~ G.3.3
• affine-distorted ~s G.2.Sol.1
• Alexander's horned ~ G.2.Ex.13
• cube-rooted ~ S.1.Ex.37
• cubed ~ S.1.Ex.37
• deforming a ~ to an egg G.2.3.3
• dielectric S.3.7
• enclosing 3D objects in graphics G.2.1.3
• in d dimensions N.1.Ex.13, S.1.6.2, S.3.Ex.1
• inversion of a ~ S.1.2.2
• nested ~s G.2.Sol.1
• parameterized ~ P.1.2.2, G.2.2.1
• random walk on a ~ G.2.Ex.9
• Riemann ~ G.2.3.7, N.1.11.2, S.2.5
• vortices on a ~ N.1.Ex.28
• with field lines G.2.Sol.1
• with handles G.3.Sol.9
• with oceans and continents G.3.Sol.13
• with random spikes G.2.2.2
• with six handles G.3.3
• with spikes G.2.2.1
• with stripes G.2.Ex.11

`SphereMoire` G.1.Sol.9

Spherical

• Bessel functions S.3.5
• harmonics S.2.Ex.1
• standing wave S.1.Ex.29

`SphericalRegion` G.2.1.3

Spindle, graphic of a ~ G.2.Sol.1, S.1.Ex.37

Spine

• curve G.2.3.4
• graphics G.3.Sol.16

Spinning top S.1.Ex.31

Spiral

• integer ~ N.1.6
• phyllotaxis ~ G.1.1.1
• prime number ~ N.2.2
• seed ~ N.1.Sol.32
• tilings N.1.8
• triangle ~ G.1.1.1
• Voderberg ~ N.1.8
• waves N.1.10.1, S.3.Ex.13

`SpiralingSpiral` G.2.2.1

Spirals G.1.1.1, G.1.3.1, G.2.1.3

`Split` P.6.3.3

`Splitting` P.5.3.3

Splitting

• binary ~ P.1.2.4
• lists into sublists P.6.3.3

Springs

• along polyhedra edges S.1.Ex.10
• in a linear chain G.1.3.2
• in triangular networks N.1.Ex.28

Spurious

• contour lines G.3.Ex.6
• imaginary part P.5.1.1, S.1.5

`Sqrt` P.2.2.2

Square

• conformal map of a ~ P.1.2.3
• gauge transformation for a ~ S.3.Ex.20
• subdivision of ~ a P.1.Sol.1
• subdivision of a ~ G.1.5.8

Square root

• as an infinite product P.3.7
• formatting of ~ P.2.2.2
• function P.2.2.2
• nested ~s N.1.Ex.37
• of a matrix P.6.Ex.18, S.1.2.2
• of differential operators S.1.Ex.33
• Riemann surface of a ~ G.2.3.7

Square well

• in an electric field S.3.Ex.10
• transmission amplitude for ~ potential G.3.1

Squares

• forming polyhedra P.6.0
• gluing sides of a ~ together G.2.3.4
• iteratively reflected ~ in 3D P.6.0
• sum of ~ N.2.1
• total least- ~ N.1.2

Squeezed, torus S.1.2.3

Stable marriage problem P.1.Sol.1

`StackedPlatonicBodies` G.2.Sol.16

Staircase

• function P.2.Ex.7
• potential N.1.Ex.5

Standard

• evaluation procedure P.4.7
• form output P.2.1
• map N.1.Ex.9

`StandardForm` In, P.2.1, P.2.1, P.6.Sol.16

Start

• of contexts P.4.6.4
• values for minimizations N.1.9
• values for root finding N.1.8, S.3.11, S.3.Sol.19

Start-up packages P.4.6.6, P.6.6, P.6.Sol.19

`StartingStepSize` N.1.10.1

State

• entangled ~ S.1.Ex.21
• Gamov ~ S.3.Ex.10

Statistics packages P.4.6.6

`Statistics`NonlinearFit` N.1.2

Steepest descent method N.1.Ex.22

Steer, of Helios' herd N.2.Ex.2

Stein's algorithm N.2.1

Steiner's

• cross cap G.2.Sol.1
• Roman surface G.3.3

Step function

• bad choice of a ~ P.5.1.4
• for mathematics S.1.8

Step potential, smoothed ~ S.3.5

Steps, of a calculation P.4.5

Stepwise

• constant potential N.1.Ex.5
• defined functions P.5.1.4, S.1.8
• defined probability distribution S.1.Ex.44

Stereographic projection

• in 3D S.3.13
• in 4D G.2.Sol.17

`StereographicProjection` S.3.13

Stern-Gerlach experiment P.1.Sol.1

Stieltjes iterations P.6.Ex.8

Stiffness matrix S.1.Sol.7

`StiffnessMatrix` S.1.Sol.7

Stirling, numbers P.6.1.2, N.2.3, N.2.Ex.1, S.3.10

Stirling's formula N.2.3

`StirlingS1` N.2.3

`StirlingS2` N.2.3, N.2.Ex.1

Stirring, random ~ N.1.Sol.28

Stochastic webs N.1.Ex.9

Stokes phenomena P.1.3

Stone

• falling ~ N.1.2, S.1.7.1
• thrown ~ S.1.Ex.10
• worn ~ G.2.Sol.1

`StoppingTest` N.1.10.1

Strang's strange figures N.1.5

Strange

• attractors N.1.Ex.9
• nonchaotic attractors G.1.5.6

Strategies

• for equation solving S.1.5
• for numerical integration N.1.7
• for symbolic integration S.1.6.2

`String` P.2.2.1

String

• characters of a ~ P.6.4.2
• inputting a ~ P.2.2.1
• letters in a ~ P.4.4.2
• manipulations P.4.4.2
• metacharacters P.3.1.2
• modifying a ~ P.4.4.2
• outputting expressions as a ~ P.4.1.2

`StringJoin` P.4.4.2

`StringLength` P.4.4.2

`StringPosition` P.4.4.2

`StringReplace` P.4.4.2

`StringReverse` P.4.4.2

Strings

• as function arguments P.3.1.2
• as option names P.4.6.6
• as option values P.4.6.6, G.1.1.1, N.1.1.5, S.1.6.1
• changing characters in ~ P.4.4.2
• characters of ~ P.6.4.2
• concatenating ~ P.4.4.2
• converting ~ to expressions P.4.1.2, P.4.1.2
• converting ~ to held expressions P.4.1.2
• from expressions P.4.1.2
• intertwined ~ P.6.4.4
• joining ~ P.4.4.2
• manipulating ~ P.6.4.2
• matching ~ P.3.1.2
• metacharacters in ~ P.4.1.1
• of all Mathematica functions P.4.1.1
• of system functions P.6.4.2
• reversing ~ P.4.4.2

`StringTake` P.4.4.2

`Stub` P.6.4.2

Sturm-Liouville problems N.1.Ex.5, S.1.Ex.6, S.1.Ex.33, S.2.1

Sturm's theorem S.3.Sol.18

Style, of text in graphics G.1.1.1

`StyleForm` G.1.1.1

Subdivision

• in `NIntegrate` N.1.7
• in `Plot` G.1.2.1
• Loop ~ G.2.Ex.6
• midedge ~ G.2.Ex.2
• of a hexagon G.1.1.1
• of a square G.1.5.8
• of intervals N.2.Ex.10
• of pentagons P.1.2.2, G.2.3.1
• of rhombii G.1.5.5
• of surfaces N.1.Ex.10
• of triangles G.1.5.4, G.2.3.10, G.2.Sol.22
• sqrt(3) ~ G.2.Ex.6
• surfaces G.2.Ex.2, G.2.Ex.6

Subluminal, tachyonic signal propagation N.1.10.2

Subprograms, packages as ~ P.4.6.4

Subsequence

• ~s in texts P.1.Sol.1
• longest common ~ N.2.Ex.6

Subset

• generation P.6.Ex.6
• sums N.2.Ex.18

Substitution sequences N.1.5

Substitutions

• order of ~ in replacements P.6.Ex.17
• tilings based on ~ G.1.5.4, G.1.5.5, G.1.Ex.22, G.2.3.1

`Subtract` P.2.2.2

Subtraction

• of expressions P.2.2.2
• of intervals N.1.1.2
• of matrices P.6.4.1
• of series S.1.6.4
• of Taylor series S.1.6.4

`SubValues` P.3.4

Suggestions

• from messages P.5.1.1, N.1.7
• to Mathematica users In

`Sum` P.4.6.1, S.1.6.6

Sum

• Fejér ~ S.2.4
• minimizing ~ of squares N.1.9
• of digits P.1.2.1, P.1.2.1, P.1.2.2, P.2.4.2, G.1.Sol.10
• of error function N.1.Ex.37
• of squares N.2.1
• of two primes N.2.Ex.12
• Rogosinsky ~ S.2.4

Sum-free set P.6.Ex.2

Summation

• Boole ~ formula N.2.4
• Borel ~ S.1.8, S.3.Ex.1, S.3.Sol.1
• convention S.1.Ex.17
• convention about ~ P.6.Ex.9, S.1.Sol.17
• Euler-Maclaurin ~ formula N.2.4
• exchanging integration and ~ S.1.8
• extended Poisson ~ formula S.1.Sol.15
• Hölder ~ S.1.6.6
• numerical ~ N.1.0, N.1.6
• of 9-free numbers S.3.Ex.11
• of approximate numbers N.1.6
• of asymptotic series S.3.Sol.1
• of divergent series S.1.8
• of symbolic terms P.4.6.1
• of Taylor series S.3.7, S.3.Sol.1
• order of summands in ~ N.1.0
• symbolic ~ S.1.6.6
• term-by-term ~ versus ~ at once P.6.1.1
• using `NSum` N.1.6
• using `Sum` S.1.6.6
• variable scoping in ~ P.4.6.1

Sums

• convergence of ~ N.1.6, S.1.8
• counting ~ N.1.1.5
• Dedekind ~ N.2.Ex.12
• distribution function for ~ S.1.Ex.44
• divergent ~ N.1.Ex.6, S.1.8, S.1.Ex.15, S.3.Ex.1
• divisor ~ S.1.Ex.17
• Fibonacci ~ S.1.6.4
• finite ~ P.4.6.1, N.1.6, S.1.6.6
• Gauss ~ G.3.2
• involving special functions P.1.2.3
• Minkowski ~ S.1.2.3
• of polynomial roots S.1.6.2, S.1.Ex.2, S.2.Ex.3
• of rounded numbers N.1.Ex.25
• of subsets N.2.Ex.18
• of zeros of Bessel functions S.3.Ex.1
• of zeros of Hermite polynomials S.2.Ex.1
• power ~ S.2.Ex.5
• products of partial ~ N.1.3
• random ~ G.1.5.6, N.1.Ex.25
• Rayleigh ~ S.3.Ex.1
• slow convergence of ~ N.1.6
• Weyl ~ G.1.3.1

Sun dial P.1.Sol.1

Supercircle S.1.Ex.25

Superconductor S.3.Ex.6

Superposition

• of lattices G.1.Sol.9, G.3.1
• of random waves G.3.1
• of solutions N.1.Sol.35
• principle for nonlinear differential equations P.1.Sol.1

Supersphere G.3.3, G.3.Ex.16, S.3.1

Suppressing

• edges in 3D graphics G.2.1.2
• results P.4.1.1

Surface

• bisector ~ G.3.3, S.1.Ex.13
• blending ~ G.2.Ex.6
• Boy ~ G.2.Sol.1
• Clebsch ~ N.1.Ex.7, S.1.Ex.27
• Cmutov ~ G.3.Ex.9, S.1.6.1
• constant negative curvature ~ S.1.Ex.9
• discriminant ~ S.1.Ex.27
• Enneper ~ S.1.6.2
• equipotential ~ G.3.3
• generalized Clebsch ~ S.1.Ex.27
• Henneberg ~ G.2.Sol.1, S.1.6.2
• periodic S.1.Ex.27
• roughening ~ G.2.Sol.9
• Scherk's fifth ~ N.1.Ex.7
• Steiner's Roman ~ G.3.3
• with many holes P.1.2.2

`SurfaceColor` G.2.1.2

`SurfaceGraphics` G.2.2.1

Surfaces

• algebraic ~ G.3.3, G.3.3
• blending ~ G.2.Ex.6
• built from polygons G.2.Ex.1
• caustics from ~ N.1.3
• clipping ~ G.2.2.1
• coloring ~ G.2.1.2, G.2.2.1
• coloring of ~ G.2.2.1
• contour ~ G.3.3, G.3.Ex.9
• cubic ~ N.1.Sol.7
• geodesics on ~ S.1.6.1
• gluing ~ together G.3.3
• implicit ~ G.3.3, S.1.Ex.37
• in 4D G.2.3.0
• interesting ~ G.2.Ex.1
• intersection of ~ with planes G.2.3.8
• making ~ transparent G.2.3.4, G.3.3
• mapped ~ G.2.Ex.11
• minimal ~ N.1.Ex.19, N.1.Ex.19, N.1.Sol.7, S.1.6.2, S.3.9
• of finite thickness G.3.Ex.18
• of genus k G.2.Ex.7
• one-sided ~ G.2.2.1, G.2.3.4
• parametricized ~ G.2.2.1, G.2.Ex.1
• projected ~ G.1.1.1, G.2.Ex.11, G.3.1
• random parametric ~ G.2.Sol.1
• references on parametric ~ G.2.Sol.1
• Riemann ~ P.2.Ex.6, G.2.3.7, G.3.3, N.1.11.2, S.1.Ex.23, S.3.10, S.3.Ex.3, S.3.Ex.16, S.3.Ex.21
• slicing ~ G.2.1.5
• smoothing ~ G.2.Ex.2, G.2.Ex.6
• subdividing ~ N.1.Ex.10
• subdivision ~ G.2.Ex.6
• textured ~ G.2.3.2, G.2.Ex.2, G.3.Ex.17
• triangulation of ~ G.2.3.4
• various 3D ~ G.2.Ex.1
• visualization of implicitly defined ~ G.3.3
• visualizing heights of ~ G.3.Ex.7
• with contour lines G.3.Ex.13
• with derivative discontinuities G.2.Sol.1
• with dodecahedral symmetry G.3.Sol.9
• with singular points N.1.8
• with singularities G.3.3
• zero-velocity ~ G.3.3

Surprises, teaching ~ P.1.Sol.1

Sutherland-Calogero model S.3.Ex.3

Swarm modeling P.1.Sol.1

Swing

• getting impetuts on a ~ S.1.Sol.10
• jumping from a ~ S.1.Ex.10

`Switch` P.5.2.2

Sylvester

• matrix S.1.2.2
• problem S.1.9.1

Sylvester expansion N.1.1.4

Sylvester-Fibonacci expansion N.2.Ex.13

`SylvesterFibonacciDigits` N.2.Ex.13

`Symbol` P.2.2.2

Symbol

• Kronecker ~ P.6.1.2
• Pochhammer ~ S.3.2

Symbolic

• calculations ~ S.1
• computer mathematics Pr
• differential equation solving S.1.7.0
• differentiation S.1.6.1
• integration S.1.6.2
• linear algebra P.6.5.1
• numerical techniques used in ~ calculations S.1.Ex.16
• summation S.1.6.6

Symbols

• all built-in ~ P.4.1.1
• as expressions P.2.2.2
• attributes of ~ P.3.3
• Christoffel ~ S.1.6.1
• counting all built-in ~ P.4.6.6
• created inside `Module` P.4.6.2, P.6.Ex.23
• creation of ~ and contexts P.4.Ex.7
• creation of ~ in contexts P.4.6.4
• declared to be numeric P.5.1.1
• definitions associated with ~ P.3.4
• inside `Block` P.4.6.2, P.6.Ex.23
• internal ~ N.2.3
• locked ~ P.3.3
• long ~ names P.4.Ex.2
• numbers as ~ P.4.Ex.8
• numerical ~ P.2.2.4
• of Mathematica G.2.3.10
• protected ~ P.3.3
• reintroducing ~ P.3.1.2
• reintroducing removed ~ P.3.1.2
• removed ~ P.3.1.2, P.4.Sol.10
• removing ~ P.3.1.2
• temporary ~ P.4.6.2
• temporary changing values of ~ P.4.6.2
• unchangeable ~ P.3.3
• unique ~ P.4.6.2
• united ~ G.3.3
• user-defined ~ In
• with values P.6.4.2, P.6.4.2, P.6.Ex.14

Symmetric, polynomials G.3.Sol.7, S.1.Sol.28, S.2.Ex.5

Symmetrized determinant S.1.Ex.20

Symmetry

• of a cube G.2.Sol.1
• used in 3D graphics P.1.2.4, G.3.Ex.9

Symposia, Mathematica ~ A.1.3

Syntactically correct, expressions P.2.2.1

Syntax

• elementary ~ principles P.1.1.2
• errors P.4.1.1

System

• Darboux-Halphen ~ S.3.Ex.23
• options P.4.6.6, N.1.1.5

`System`` P.4.6.4

Systems, computer algebra ~ P.1.Ex.2

Szebehely's equation S.1.7.2

Szegö's method P.1.2.3