New in 7.0: Mathematics & Algorithms

Mathematica 7 represents another major achievement in Mathematica's long history of innovation in mathematics and algorithms. Building on the broad capabilities of Mathematica, as well as several recent R&D breakthroughs at Wolfram Research, Mathematica 7 for the first time makes possible systematic computation in a sequence of longstanding mathematical and algorithmic areas.

(OrangeLink[Discrete Calculus », paclet:guide/DiscreteCalculus])

(RefLink[Sum, paclet:ref/Sum]), (RefLink[Product, paclet:ref/Product]) (modified) — indefinite sums and products and major new algorithms

(OrangeLink[New Integer Sequence Functions », paclet:guide/IntegerSequences])

(RefLink[FindSequenceFunction, paclet:ref/FindSequenceFunction]) — find functional forms for integer sequences

(RefLink[FindGeneratingFunction, paclet:ref/FindGeneratingFunction]) — find generating functions

(RefLink[RSolve, paclet:ref/RSolve]) (modified) — solve a system of recurrence equations

(OrangeLink[New Number Theory Functions », paclet:guide/NumberTheory])

(RefLink[PrimeOmega, paclet:ref/PrimeOmega]), (RefLink[PrimeNu, paclet:ref/PrimeNu]) — number of distinct prime factors

(OrangeLink[New Combinatorial Functions », paclet:guide/CombinatorialFunctions])

(RefLink[FiniteGroupCount, paclet:ref/FiniteGroupCount]), (RefLink[FiniteAbelianGroupCount, paclet:ref/FiniteAbelianGroupCount]) — numbers of groups of given order

(OrangeLink[Boolean Computation », paclet:guide/BooleanComputation])

(RefLink[BooleanFunction, paclet:ref/BooleanFunction]) — general Boolean functions

(RefLink[BooleanCountingFunction, paclet:ref/BooleanCountingFunction]) — symmetric Boolean functions

(RefLink[BooleanConvert, paclet:ref/BooleanConvert]) — convert between Boolean formats (CNF, DNF, ESOP, NOR, BFF, ...)

(RefLink[BooleanMinimize, paclet:ref/BooleanMinimize]) — find a minimal Boolean form

(RefLink[SatisfiableQ, paclet:ref/SatisfiableQ]) — test a Boolean expression for satisfiability

(OrangeLink[New Special Functions », paclet:guide/SpecialFunctions])

(OrangeLink[New Q-Functions », paclet:guide/QFunctions])

New Utility Functions

(OrangeLink[New in Optimization », paclet:guide/Optimization])

(RefLink[MinValue, paclet:ref/MinValue]), (RefLink[MaxValue, paclet:ref/MaxValue]) — minimum, maximum values

(RefLink[ArgMin, paclet:ref/ArgMin]), (RefLink[ArgMax, paclet:ref/ArgMax]) — position of minimum, maximum

(OrangeLink[New in Fourier Analysis », paclet:guide/FourierAnalysis])

(RefLink[FourierSeries, paclet:ref/FourierSeries]) — truncated complex Fourier series to any order

(RefLink[FourierCoefficient, paclet:ref/FourierCoefficient]) — n(^th) coefficient in a Fourier series

(OrangeLink[New in Polynomials & Algebra », paclet:guide/AlgebraicTransformations])

(OrangeLink[New Operations on Lists and Matrices », paclet:guide/NewIn70ListsAndMatrices])

(RefLink[UpperTriangularize, paclet:ref/UpperTriangularize]), (RefLink[LowerTriangularize, paclet:ref/LowerTriangularize]) — extract parts of a matrix

(RefLink[SymmetricMatrixQ, paclet:ref/SymmetricMatrixQ]) — test whether given matrix is symmetric

(OrangeLink[New in Differential Equations », paclet:guide/DifferentialEquations])

(RefLink[NDSolve, paclet:ref/NDSolve]) (modified) — new support for delay differential equations

(RefLink[DifferentialRoot, paclet:ref/DifferentialRoot]) — symbolic representation of solutions to linear differential equations

(RefLink[Wronskian, paclet:ref/Wronskian]) — test linear independence of functions or ODE solutions

(OrangeLink[Convolutions, paclet:guide/IntegralTransforms])

(OrangeLink[New in Statistical Model Analysis », paclet:guide/StatisticalModelAnalysis])

(RefLink[LinearModelFit, paclet:ref/LinearModelFit]) — construct a linear regression model from data

(RefLink[NonlinearModelFit, paclet:ref/NonlinearModelFit]) — construct a nonlinear regression model