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 areas—together with new basic scientific and mathematical methodologies created at Wolfram Research—makes possible an ever-increasing rate of algorithm innovation in Mathematica.

(OrangeLink[New Mathematical Functions », paclet:guide/NewIn60MathematicalFunctions])

Major New Numerics Capabilities

(RefLink[FindMinimum, paclet:ref/FindMinimum]), (RefLink[FindMaximum, paclet:ref/FindMaximum]) (modified) — now support constrained nonlinear optimization

(RefLink[FindFit, paclet:ref/FindFit]) (modified) — now supports constrained nonlinear fitting

(RefLink[Minimize, paclet:ref/Minimize]), (RefLink[Maximize, paclet:ref/Maximize]), (RefLink[LinearProgramming, paclet:ref/LinearProgramming]) (modified) — now support integer programming

(RefLink[NIntegrate, paclet:ref/NIntegrate]) — now supports efficient high-dimensional integration

(RefLink[Interpolation, paclet:ref/Interpolation]), (RefLink[InterpolatingPolynomial, paclet:ref/InterpolatingPolynomial]) (modified) — generalized to higher dimensions

(OrangeLink[New Matrix & Linear Algebra Functions », paclet:guide/NewIn60MatrixAndLinearAlgebraFunctions])

(RefLink[Band, paclet:ref/Band]) — symbolic representation of generalized banded matrices & arrays

(RefLink[ArrayFlatten, paclet:ref/ArrayFlatten]) — generalized block matrix constructor

(OrangeLink[New Symbolic & Algebraic Computing Functions », paclet:guide/NewIn60AlgebraicComputing])

(RefLink[FullSimplify, paclet:ref/FullSimplify]) (modified) — now supports general equational theorem proving

(RefLink[SeriesCoefficient, paclet:ref/SeriesCoefficient]) (modified) — now supports symbolic series

(RefLink[Expand, paclet:ref/Expand]), (RefLink[Apart, paclet:ref/Apart]), (RefLinkPlain[..., paclet:guide/NewIn60AlgebraicComputing]) (modified) — now automatically thread over equations

(OrangeLink[New Statistics Capabilities », paclet:guide/NewIn60Statistics])

(RefLink[Mean, paclet:ref/Mean]), (RefLink[Variance, paclet:ref/Variance]), (RefLinkPlain[..., paclet:guide/NewIn60Statistics]) (modified) — now support symbolic distributions

(RefLink[PDF, paclet:ref/PDF]), (RefLink[CDF, paclet:ref/CDF]) — probability density function, cumulative distribution function

(OrangeLink[New Data Analysis Capabilities », paclet:guide/NewIn60NumericalDataHandling])

(RefLink[Nearest, paclet:ref/Nearest]) — find nearest neighbors in multidimensional data

(RefLink[FindClusters, paclet:ref/FindClusters]) — cluster analysis for numerical, Boolean, string, etc. data

(OrangeLink[New Computational Geometry Capabilities », paclet:guide/ComputationalGeometry])

(RefLink[PolyhedronData, paclet:ref/PolyhedronData]) — database of properties of regular polyhedra

New in Discrete Math

(RefLink[GraphPlot, paclet:ref/GraphPlot]), (RefLink[GraphPlot3D, paclet:ref/GraphPlot3D]), (RefLink[LayeredGraphPlot, paclet:ref/LayeredGraphPlot]) — lay out graphs of any size

(RefLink[GraphData, paclet:ref/GraphData]) — database of named graphs and their properties

(RefLink[TreePlot, paclet:ref/TreePlot]) — display trees

(RefLink[FindShortestTour, paclet:ref/FindShortestTour]) — solve traveling salesman problems

New in Computational Systems

(RefLink[TuringMachine, paclet:ref/TuringMachine]) — general 1D, 2D, etc. Turing machines

(RefLink[CellularAutomaton, paclet:ref/CellularAutomaton]) (modified) — extended to allow more general rules

(OrangeLink[New Mathematical Data Sources », paclet:guide/MathematicalData])

(OrangeLink[New in Number Theory & Integer Functions », paclet:guide/NewIn60NumberTheoryAndIntegerFunctions])

(RefLink[AlgebraicNumber, paclet:ref/AlgebraicNumber]) — implicit representation of a general algebraic number

(RefLink[RootApproximant, paclet:ref/RootApproximant]) — find an algebraic approximation to a number

(OrangeLink[New Random Generation Functions », paclet:guide/RandomNumberGeneration])

Some Functions with Major New Algorithms