This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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Summary of New Features in Mathematica 8

Core Language
Integration of Wolfram|Alpha into Mathematica
type Ctrl+= anywhere in an input cell, type natural language into the box, and get back the corresponding Mathematica input
type = at the beginning of an input cell to get a single piece of data from Wolfram|Alpha
type == at the beginning of an input cell to get the full output from Wolfram|Alpha
WolframAlpha programmatically query Wolfram|Alpha and give the results in Mathematica

CompilationTarget specify the target runtime for the compiled function, including C code
Parallelization specify whether a compiled function should run in parallel
The Mathematica Compiler User Guide a tutorial on how to use the compiler effectively

LibraryFunction a function that calls into a dynamic library
Wolfram LibraryLink User Guide a tutorial on using dynamic libraries in Mathematica

Export export a Mathematica compiled function into C code
C Code Generation User Guide a tutorial on generating C code from Mathematica compiled functions

ToCCodeString convert a symbolic C expression into a string of C code
SymbolicC User Guide a tutorial on creating, manipulating, and optimizing C code from within Mathematica

CreateExecutable create an executable from C code
CreateLibrary create a library from C code
CCompilerDriver User Guide a tutorial on using available C compilers from within Mathematica

CUDAInformation enumerate all CUDA device information

OpenCLInformation enumerate all OpenCL device information

Assertion Checking
Mathematics and Algorithms
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, StateSpaceModel models of linear time-invariant systems
RootLocusPlot plot the root loci
BodePlot magnitude and phase plots of the frequency response
ControllableModelQ test whether a model is controllable
KalmanEstimator Kalman estimator with specified covariance matrices

Probability, NProbability compute probabilities for general events
Expectation, NExpectation compute expectations for general expressions
ProbabilityDistribution distribution constructed from a distribution function
Moment moments of distributions and data
Cumulant cumulants of distributions and data
DistributionFitTest test for goodness of fit to a distribution or data
LocationTest test means or mean differences of one or two datasets
VarianceTest test variances or variance ratios of one or two datasets
MultivariateTDistribution multivariate Student distribution
HistogramDistribution distribution constructed from a histogram of data
SmoothKernelDistribution distribution constructed from smoothing of data

Cycles  ▪ PermutationCyclesQ cyclic representation of a permutation
RandomPermutation randomly generated permutations
Permute  ▪ FindPermutation permute the parts of an expression
PermutationListQ  ▪ PermutationList  ▪ PermutationCycles conversion between permutation lists and their cyclic form
PermutationSupport  ▪ PermutationMax  ▪ ... points moved by a permutation
PermutationProduct  ▪ PermutationPower  ▪ PermutationOrder  ▪ ... operations with permutations
PermutationGroup permutation representation of a finite group
GroupMultiplicationTable  ▪ CayleyGraph alternative representations of a group
GroupOrder  ▪ GroupElements  ▪ GroupElementQ  ▪ ... elements of a group
GroupOrbits  ▪ GroupStabilizer  ▪ ... operations with groups
SymmetricGroup  ▪ DihedralGroup  ▪ ... named groups

Improvements to Equation Solving
Solve, NSolve new implementations, including solving over different domains

NIntegrate new methods, particularly for univariate and multivariate oscillatory integrands
Visualization and Graphics
Texture specify texture faces of polygons or other filled graphics objects

ScalingFunctions specify which scaling functions should be used when plotting with Plot, Plot3D, and other plotting functions

SmoothHistogram plot a density estimate of data
QuantilePlot quantile-quantile plot of data or distributions
ProbabilityPlot probability-probability plot of data or distributions
ProbabilityScalePlot normal plot, Weibull plot, Gumbel plot, etc.

WaveletListPlot plot wavelet transform coefficients

Improved Interactive Graphics Editing
draw and edit graphics interactively
New Application Technologies
ContinuousWaveletTransform give the continuous wavelet transform
DiscreteWaveletTransform give the discrete wavelet transform
HaarWavelet Haar wavelet family
DaubechiesWavelet Daubechies wavelet family
MexicanHatWavelet derivative of Gaussian wavelet family
GaborWavelet Gabor wavelet family
WaveletListPlot plot wavelet transform coefficients

FinancialDerivative get the pricing of financial derivatives
FinancialIndicator symbolic representation of technical indicators
TimeValue time value of money computations
EffectiveInterest effective interest rate conversions

CandlestickChart candlestick and OHLC chart of open-high-low-close prices

ImageTransformation pixelwise functional transformation of an image
EdgeDetect detect edges in an image using Canny and other methods
RandomImage generate a random image from a distribution
ImageCapture capture an image from your computer's primary camera device
ImageKeypoints find keypoints and associated feature vectors in an image
ImageCooccurrence create a texture co-occurrence matrix
TextRecognize extract text from an image
WatershedComponents watershed transform of an image
ComponentMeasurements shape and color analysis

"GraphML" graph format
"QuickTime" Export can export to the QuickTime video format
"EPS" Import now supports the Encapsulated PostScript format
Notebook and Document Enhancements
Computable Document Format (CDF) Files
create a new .cdf file
added support for saving .cdf files
"CDF" added Import and Export of Computable Document Format (.cdf) files

Printing and Layout Improvements
File Print Preview new "Print Preview" capability on Windows and Linux platforms
Improved line and page breaking and paging control

New Citation Management
Insert Citation integration with both EndNote and BibTeX citation styles
Citation Management a tutorial on managing citations in Mathematica

Improved Find & Replace Dialog
includes finding and replacing of fully typeset text, enhanced highlighting of search results, and a history of previous searches and replacements

Automatic Evaluation of Notebooks
NotebookEvaluate evaluate the cells in a specified notebook

Interface Controls Enhancements
InputField now supports horizontal scrolling and content masking
MouseAppearance context-sensitive mouse cursor appearance
Systems Interfaces & Deployment
CompilationTarget specifies the target runtime for the compiled function including C code
Parallelization specifies whether a compiled function should run in parallel
The Mathematica Compiler User Guide a tutorial on how to use the compiler effectively

LibraryFunction a function that calls into a dynamic library
LibraryLink User Guide a tutorial on using dynamic libraries in Mathematica

Export export a Mathematica compiled function into C code
C Code Generation User Guide a tutorial on generating C code from Mathematica compiled functions

ToCCodeString convert a symbolic C expression into a string of C code
SymbolicC User Guide a tutorial on creating, manipulating, and optimizing C code from within Mathematica

CreateExecutable create an executable from C code
CreateLibrary create a library from C code
CCompilerDriver User Guide a tutorial on using available C compilers from within Mathematica

CUDAInformation enumerates all CUDA device information
CUDAImageConvolve convolves images with a specified kernel