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New in Version 4
Mathematica Version 4 introduces important extensions to the Mathematica system, especially major efficiency enhancements in handling large volumes of numerical data. It also includes a range of new algorithmic, language and interface features. Except as noted in Section A.13.1, Version 4 is fully compatible with all earlier versions.
New in V4 Demo Palette.
Numerical Computation
 Internal packed array technology to make repetitive operations on large numerical datasets radically more efficient in speed and memory.
Highly optimized algorithms for doing computations on numbers with up to millions of digits.
Faster input and output of very large integers.
Complete preservation of precision on input and output of approximate real numbers.
Convolution and correlation of arrays of any dimension.
New optimized algorithms for Fourier transforms.
Faster solution of numerical polynomial equations.
New algorithms for FindMinimum.
Direct support for matrix traces.
Algebraic Computation
Support for assumptions in Simplify, FunctionExpand and related functions.
Specification of domains for variables.
Many additional transformations in FullSimplify and FunctionExpand.
Simplification of polynomial and other inequalities.
Full support of symbolic Laplace, Fourier and Z transforms.
Extensions to integration and summation.
Extensions to transcendental equation solving.
Faster multiple differentiation.
Support for subresultants.
Mathematical Functions
Dirac delta and other generalized functions.
Struve functions.
Nielsen generalized polylogarithms.
Appell F1 bivariate hypergeometric function.
Harmonic numbers.
Khinchin and Glaisher constants.
Multiplicative order and Carmichael lambda functions.
New optimized methods for evaluating  ,  and other constants to very high precision.
Full support for continued fractions.
Support for periodic digit sequences.
Direct support for bitwise operations.
Graphics and Sound
Faster generation and display of large graphics.
Export of graphics and sound in many formats.
Import of graphics and sound in many formats.
Support for discrete scaling of color levels.
Fully consistent support for absolute options.
Experimental support for real-time 3D graphics (Windows only).
Programming and Core System
NestWhile and NestWhileList, allowing generalizations of FixedPoint.
PadLeft and PadRight.
Support for padding and overhangs in Partition.
ListConvolve and ListCorrelate.
Generalization of Take, Drop and related functions to any number of dimensions and any stride.
Support for All as a specification of parts at specific levels in expressions.
Extension to Mod to support cyclic lists.
Developer` context containing advanced and algorithmic specific built-in functions.
Experimental` context providing a preview of features under development.
Input and Output
Optimized minimal-change line breaking for smooth input of expressions and programs.
Event-oriented cursor tracker for visual continuity during input.
Dynamic color cues for delimiter matching during input.
Automatic replacement of input key sequences by special characters or other objects.
 and  used by default in standard output.
New optional syntax for part extraction and function application.
Inline cells within typeset Mathematica expressions.
Much faster string-oriented output of Mathematica expressions.
Notebook Interface
Full-function spell checking including special technical dictionaries.
Dictionary-validated algorithmic hyphenation.
Additional keyboard navigation features.
Enhanced undo capabilities.
Platform-independent double buffering to eliminate flicker.
Optimized controller for smooth autoscrolling.
System Interface
Streamlined import and export of tabular data.
Extended support for conversion to HTML.
Additional support for TeX output.
Faster MathLink external program communication.
Support for additional character sets, including Chinese and Korean.
Add-ons and Experimental Features
Direct support for sparse linear algebra.
Experimental support of quantifier elimination using cylindrical algebraic decomposition.
Experimental support for symbolic optimization.
Experimental support for real-time value displays.
Experimental support for MathLink-based remote file systems.
Experimental support for pop-up palettes.
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