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.

Discrete Calculus »

Sum, Product (modified) — indefinite sums and products and major new algorithms

DifferenceDelta  (  )   ▪  DiscreteShift  (  )   ▪  DiscreteRatio  (  ) 

GeneratingFunction  ▪  DifferenceRoot  ▪  SumConvergence  ▪  Casoratian  ▪  ...

New Integer Sequence Functions »

FindSequenceFunction — find functional forms for integer sequences

FindGeneratingFunction — find generating functions

RSolve (modified) — solve a system of recurrence equations

RecurrenceTable  ▪  LinearRecurrence  ▪  FindLinearRecurrence

GeneratingFunction  ▪  DiscreteConvolve  ▪  DirichletConvolve  ▪  ...

New Number Theory Functions »

PrimeOmega, PrimeNu — number of distinct prime factors

MangoldtLambda  ▪  LiouvilleLambda  ▪  DirichletCharacter

PrimeZetaP  ▪  RiemannR  ▪  DirichletL  ▪  DivisorSum  ▪  ...

New Combinatorial Functions »

FactorialPower  ▪  Hyperfactorial  ▪  ...

FiniteGroupCount, FiniteAbelianGroupCount — numbers of groups of given order

Boolean Computation »

BooleanFunction — general Boolean functions

BooleanCountingFunction — symmetric Boolean functions

BooleanMinterms  ▪  BooleanMaxterms  ▪  BooleanTable  ▪  ...

Equivalent  ( ⧦ )   ▪  Xnor  (  )    ▪  Majority

BooleanConvert — convert between Boolean formats (CNF, DNF, ESOP, NOR, BFF, ...)

BooleanMinimize — find a minimal Boolean form

SatisfiableQ — test a Boolean expression for satisfiability

Conjunction  ▪  Disjunction  ▪  SatisfiabilityCount  ▪  TautologyQ

New Special Functions »

AngerJ  ▪  WeberE  ▪  DawsonF  ▪  BarnesG  ▪  LogBarnesG

HurwitzZeta  ▪  HurwitzLerchPhi  ▪  Haversine  ▪  InverseHaversine

New Q-Functions »

QBinomial  ▪  QFactorial  ▪  QGamma  ▪  QHypergeometricPFQ  ▪  QPochhammer  ▪  QPolyGamma  ▪  ...

New Utility Functions

SquareWave  ▪  TriangleWave  ▪  SawtoothWave  ▪  FindDivisions

DiracComb  ▪  HeavisidePi  ▪  Log10  ▪  Log2

New in Optimization »

MinValue, MaxValue — minimum, maximum values

NMinValue  ▪  NMaxValue  ▪  FindMinValue  ▪  FindMaxValue

ArgMin, ArgMax — position of minimum, maximum

NArgMin  ▪  NArgMax  ▪  FindArgMin  ▪  FindArgMax

New in Fourier Analysis »

FourierSeries — truncated complex Fourier series to any order

FourierSinSeries  ▪  FourierCosSeries  ▪  FourierTrigSeries

FourierCoefficient — n ^th coefficient in a Fourier series

FourierSequenceTransform  ▪  InverseFourierSequenceTransform

New in Polynomials & Algebra »

CoefficientRules  ▪  FromCoefficientRules  ▪  MonomialList  ▪  ...

Root  (modified)   ▪  RootApproximant  (modified)   ▪  SeriesCoefficient  (modified)   ▪  ...

New Operations on Lists and Matrices »

UpperTriangularize, LowerTriangularize — extract parts of a matrix

SymmetricMatrixQ — test whether given matrix is symmetric

DiskMatrix  ▪  CrossMatrix  ▪  DiamondMatrix  ▪  BoxMatrix  ▪  ...

New in Differential Equations »

NDSolve (modified) — new support for delay differential equations

DifferentialRoot — symbolic representation of solutions to linear differential equations

Wronskian — test linear independence of functions or ODE solutions

FunctionExpand  (modified)   ▪  DifferentialRootReduce  ▪  ...

Convolutions »

Convolve  ▪  DiscreteConvolve  ▪  DirichletConvolve

New in Statistical Model Analysis »

LinearModelFit — construct a linear regression model from data

NonlinearModelFit — construct a nonlinear regression model

GeneralizedLinearModelFit  ▪  LogitModelFit  ▪  ProbitModelFit  ▪  FittedModel