WOLFRAM LANGUAGE GUIDE

New in 6.0: Mathematics & Algorithms

Mathematica 6.0 represented a major new level in Mathematica's distinguished twenty-year history of broad cutting-edge algorithm development. Mathematica's unified architecture and unique tradition of integrating disparate algorithmic areastogether with new basic scientific and mathematical methodologies created at Wolfram Researchmakes possible an ever-increasing rate of algorithm innovation in Mathematica.

ReferenceReference

New Mathematical Functions »

HankelH1  ▪  KelvinKer  ▪  SphericalBesselJ  ▪  ParabolicCylinderD  ▪  WhittakerM  ▪  SpheroidalS1  ▪  BesselJZero  ▪  AiryAiZero  ▪  ZernikeR  ▪  ZetaZero  ▪  ...

Major New Numerics Capabilities

FindMinimum, FindMaximum (modified) now support constrained nonlinear optimization

FindFit (modified) now supports constrained nonlinear fitting

Minimize, Maximize, LinearProgramming (modified) now support integer programming

NIntegrate now supports efficient high-dimensional integration

Interpolation, InterpolatingPolynomial (modified) generalized to higher dimensions

New Matrix & Linear Algebra Functions »

Band symbolic representation of generalized banded matrices & arrays

ArrayFlatten generalized block matrix constructor

Normalize  ▪  Orthogonalize  ▪  Projection  ▪  KroneckerProduct  ▪  ...

LeastSquares  ▪  HermiteDecomposition  ▪  RotationMatrix  ▪  ...

New Symbolic & Algebraic Computing Functions »

Discriminant  ▪  CountRoots  ▪  SymmetricPolynomial  ▪  SymmetricReduction  ▪  ...

FullSimplify (modified) now supports general equational theorem proving

SeriesCoefficient (modified) now supports symbolic series

PadeApproximant  ▪  PossibleZeroQ  ▪  HornerForm  ▪  ...

Expand, Apart, ... (modified) now automatically thread over equations

New Statistics Capabilities »

Mean, Variance, ... (modified) now support symbolic distributions

MeanDeviation  ▪  Skewness  ▪  Kurtosis  ▪  CentralMoment  ▪  ...

NormalDistribution  ▪  PoissonDistribution  ▪  ChiSquareDistribution  ▪  ...

PDF, CDF probability density function, cumulative distribution function

New Data Analysis Capabilities »

BinCounts  ▪  Tally  ▪  MovingAverage  ▪  MovingMedian  ▪  ...

Nearest find nearest neighbors in multidimensional data

FindClusters cluster analysis for numerical, Boolean, string, etc. data

EuclideanDistance  ▪  ManhattanDistance  ▪  CorrelationDistance  ▪  ...

New Computational Geometry Capabilities »

PolyhedronData database of properties of regular polyhedra

Nearest  ▪  NearestFunction  ▪  RegionPlot  ▪  RegionPlot3D

RotationTransform  ▪  AffineTransform  ▪  TransformationMatrix  ▪  ...

New in Discrete Math

GraphPlot, GraphPlot3D, LayeredGraphPlot lay out graphs of any size

GraphData database of named graphs and their properties

TreePlot display trees

FindShortestTour solve traveling salesman problems

New in Computational Systems

TuringMachine general 1D, 2D, etc. Turing machines

CellularAutomaton (modified) extended to allow more general rules

New Mathematical Data Sources »

PolyhedronData  ▪  GraphData  ▪  LatticeData  ▪  KnotData  ▪  ExampleData

New in Number Theory & Integer Functions »

IntegerPartitions  ▪  PowersRepresentations  ▪  ChineseRemainder  ▪  FrobeniusSolve  ▪  PrimitiveRoot  ▪  BellB  ▪  RamanujanTau  ▪  ...

AlgebraicNumber implicit representation of a general algebraic number

AlgebraicNumberNorm  ▪  NumberFieldDiscriminant  ▪  ToNumberField  ▪  ...

RootApproximant find an algebraic approximation to a number

Divisible  ▪  CoprimeQ  ▪  NextPrime  ▪  RandomPrime  ▪  SquareFreeQ  ▪  ...

IntegerLength  ▪  IntegerString  ▪  BitSet  ▪  BitShiftLeft  ▪  ...

New Random Generation Functions »

RandomInteger  ▪  RandomReal  ▪  RandomChoice  ▪  RandomSample  ▪  ...

Some Functions with Major New Algorithms

NIntegrate  ▪  FindMinimum  ▪  LinearProgramming  ▪  FunctionExpand  ▪  LinearSolve  ▪  DSolve  ▪  RSolve  ▪  Sum  ▪  Integrate  ▪  Series  ▪  NDSolve  ▪  Interpolation