This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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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.
Sum, Product (modified) — indefinite sums and products and major new algorithms
FindSequenceFunction find functional forms for integer sequences
FindGeneratingFunction find generating functions
RSolve (modified) — solve a system of recurrence equations
PrimeOmega, PrimeNu number of distinct prime factors
FiniteGroupCount, FiniteAbelianGroupCount numbers of groups of given order

BooleanFunction general Boolean functions
BooleanCountingFunction symmetric Boolean functions
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

New Utility Functions

MinValue, MaxValue minimum, maximum values
ArgMin, ArgMax position of minimum, maximum
FourierSeries truncated complex Fourier series to any order
FourierCoefficient n coefficient in a Fourier series
Root (modified)  ▪ RootApproximant (modified)  ▪ SeriesCoefficient (modified)  ▪ ...
UpperTriangularize, LowerTriangularize extract parts of a matrix
SymmetricMatrixQ test whether given matrix is symmetric
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  ▪ ...

LinearModelFit construct a linear regression model from data
NonlinearModelFit construct a nonlinear regression model