MATHEMATICA GUIDE

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.

ReferenceReference

Probability & Statistics »

Probability compute probabilities for general events

Expectation compute expectations for general expressions

EstimatedDistribution automatically estimate parameters in a distribution from data

Distributed() Conditioned() ▪ NExpectation ▪ MomentConvert ▪ ...

New Properties for Distributions »

SurvivalFunction survival function for a distribution

Moment general moment for a distribution

HazardFunction ▪ LogLikelihood ▪ Cumulant ▪ MomentGeneratingFunction ▪ ...

New Parametric Distributions »

StableDistribution stable distribution

MaxStableDistribution ▪ BinormalDistribution ▪ ErlangDistribution ▪ DirichletDistribution ▪ GompertzMakehamDistribution ▪ ...

New Nonparametric Distributions »

SmoothKernelDistribution nonparametric kernel density estimate-based distribution

EmpiricalDistribution ▪ HistogramDistribution ▪ ...

New Derived Distributions »

TransformedDistribution transformation of an existing distribution

OrderDistribution ▪ MarginalDistribution ▪ CopulaDistribution ▪ ...

New Hypothesis Testing »

DistributionFitTest test for goodness-of-fit to a distribution or data

LocationTest test means or mean differences of one or two datasets

VarianceTest ▪ LocationEquivalenceTest ▪ VarianceEquivalenceTest ▪ KolmogorovSmirnovTest ▪ AndersonDarlingTest ▪ MannWhitneyTest ▪ ...

Graphs & Networks »

Graph construct a graph from vertices and edges

GraphData, ExampleData collection of theoretical and empirical graphs

CompleteGraph ▪ GridGraph ▪ CompleteKaryTree ▪ ButterflyGraph ▪ ...

AdjacencyGraph ▪ IncidenceGraph ▪ AdjacencyMatrix ▪ ...

UniformGraphDistribution ▪ BarabasiAlbertGraphDistribution ▪ ...

New in Styling and Labeling of Graphs »

HighlightGraph highlight vertices, edges, or whole subgraphs

GraphStyle ▪ VertexStyle ▪ EdgeStyle ▪ VertexLabels ▪ EdgeLabels ▪ ...

New Predicates and Properties »

IsomorphicGraphQ test whether two graphs are isomorphic

GraphQ ▪ DirectedGraphQ ▪ ConnectedGraphQ ▪ EulerianGraphQ ▪ ...

New Graph Measures and Metrics »

VertexCount ▪ VertexDegree ▪ VertexInDegree ▪ GraphDistance ▪ ...

ClosenessCentrality ▪ BetweennessCentrality ▪ PageRankCentrality ▪ ...

New Graph Computations »

FindShortestPath find the shortest path from the source to one or all vertices

FindEulerianCycle ▪ FindHamiltonianCycle ▪ GraphDiameter ▪ ...

ConnectedComponents ▪ KCoreComponents ▪ VertexOutComponent ▪ ...

FindClique ▪ FindEdgeCover ▪ BreadthFirstScan ▪ ...

New Built-in Control Systems Functionality »

TransferFunctionModel transfer-function model object

StateSpaceModel ▪ ToContinuousTimeModel ▪ ToDiscreteTimeModel ▪ ...

SystemsModelStateFeedbackConnect ▪ OutputResponse ▪ ...

Classical Analysis and Design »

RootLocusPlot plot pole locations as function of parameter

BodePlot ▪ NyquistPlot ▪ GainPhaseMargins ▪ SingularValuePlot ▪ ...

State-Space Analysis »

ControllabilityMatrix gives the controllability matrix

ControllabilityGramian ▪ ObservabilityMatrix ▪ ObservabilityGramian ▪ ...

MinimalStateSpaceModel ▪ InternallyBalancedDecomposition ▪ ...

State-Space Design »

KalmanEstimator Kalman filter-based optimal observer

LQGRegulator linear quadratic Gaussian optimal regulator

StateFeedbackGains ▪ EstimatorGains ▪ DiscreteLQRegulatorGains ▪ ...

New in Computational Finance »

FinancialDerivative financial derivative valuations

FinancialBond financial bond valuations

TimeValue time value of money computations

EffectiveInterest ▪ Annuity ▪ AnnuityDue ▪ Cashflow ▪ ...

New Built-in Wavelet Analysis »

ContinuousWaveletTransform gives the continuous wavelet transform

DiscreteWaveletTransform gives the discrete wavelet transform

DaubechiesWavelet ▪ LiftingWaveletTransform ▪ WaveletThreshold ▪ ...

StationaryWaveletPacketTransform ▪ WaveletScalogram ▪ ...

New Permutation Functionality »

Cycles disjoint cyclic notation for permutations

PermutationCycles ▪ PermutationListQ ▪ RandomPermutation ▪ ...

PermutationSupport ▪ PermutationMax ▪ ...

PermutationProduct ▪ InversePermutation ▪ PermutationPower ▪ PermutationOrder

Permute ▪ FindPermutation ▪ PermutationReplace

New Group Theory Capabilities »

PermutationGroup representation for a permutation group

GroupOrder number of elements in a group

GroupElements ▪ GroupElementQ ▪ ...

GroupGenerators ▪ GroupMultiplicationTable ▪ CayleyGraph

GroupOrbits ▪ GroupStabilizer ▪ GroupStabilizerChain ▪ ...

SymmetricGroup ▪ CyclicGroup ▪ DihedralGroup ▪ ...

MathieuGroupM24 ▪ JankoGroupJ2 ▪ RudvalisGroupRu ▪ ...

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

New in Special Functions »

MarcumQ Marcum's Q function

OwenT ▪ WignerD ▪ BellY ▪ RankedMin ▪ RankedMax

Fast Exact Linear Algebra »

LinearSolve fast methods for integer and rational inputs

NullSpace ▪ MatrixRank ▪ Inverse ▪ LeastSquares ▪ ...

PseudoInverse ▪ Det ▪ Dot ▪ ...

New in Matrix Decompositions »

HessenbergDecomposition (modified) — Hessenberg decomposition for a matrix pair

SchurDecomposition (modified) — Schur decomposition for a matrix pair

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