This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 MATHEMATICA GUIDE Functions »|More About »
New in 8.0: Mathematics & Algorithms
Mathematica 8 adds major new areas, including probability and statistics, graphs and networks, computational finance, control systems, wavelet analysis, and group theory. Each of these areas represents major progress in the ability to work at a high level of abstraction supported by in-depth algorithmic coverage and advanced automation. This should enable rapid progress in these areas, and also in the ability to combine tools from several disjoint areas as functions are designed to fit together even across different domains.
Probability compute probabilities for general events
Expectation compute expectations for general expressions
EstimatedDistribution automatically estimate parameters in a distribution from data
SurvivalFunction survival function for a distribution
Moment general moment for a distribution
StableDistribution stable distribution
New Nonparametric Distributions
SmoothKernelDistribution nonparametric kernel density estimate-based distribution
TransformedDistribution transformation of an existing distribution
DistributionFitTest test for goodness-of-fit to a distribution or data
LocationTest test means or mean differences of one or two datasets

Graph construct a graph from vertices and edges
GraphData, ExampleData collection of theoretical and empirical graphs
HighlightGraph highlight vertices, edges, or whole subgraphs
IsomorphicGraphQ test whether two graphs are isomorphic
FindShortestPath find the shortest path from the source to one or all vertices

TransferFunctionModel transfer-function model object
RootLocusPlot plot pole locations as function of parameter
ControllabilityMatrix gives the controllability matrix
KalmanEstimator Kalman filter-based optimal observer
LQGRegulator linear quadratic Gaussian optimal regulator

FinancialDerivative financial derivative valuations
FinancialBond financial bond valuations
TimeValue time value of money computations

ContinuousWaveletTransform gives the continuous wavelet transform
DiscreteWaveletTransform gives the discrete wavelet transform

Cycles disjoint cyclic notation for permutations
PermutationGroup representation for a permutation group
GroupOrder number of elements in a group

New Equation-Solving Capabilities
Solve (modified), NSolve (modified) — solve equations and inequalities over domains
ConditionalExpression an expression defined when a condition holds
New Numerics Capabilities
NIntegrate (modified) — integration of univariate and multivariate oscillatory functions
MarcumQ Marcum's Q function
LinearSolve fast methods for integer and rational inputs
HessenbergDecomposition (modified) — Hessenberg decomposition for a matrix pair
SchurDecomposition (modified) — Schur decomposition for a matrix pair