This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Wolfram Research, Inc.

New in Version 4The Role of This Book

New in Version 3

Released at the end of 1996, Mathematica Version 3 was the first new version of Mathematica in several years. It substantially strengthened the core computational capabilities of Mathematica, and introduced some revolutionary new features. Except as noted in Section A.13.1, Version 3 was fully compatible with earlier versions.

Numerical Computation

FilledSmallSquare Adaptive precision control to generate results with guaranteed precision.

FilledSmallSquare High-performance compilation of list-oriented, procedural and functional numerical operations.

FilledSmallSquare Optimized algorithms for one- and higher-dimensional interpolation.

FilledSmallSquare Optimized algorithms for solution of differential equations.

FilledSmallSquare Solution of boundary value ordinary differential equations, and initial value partial differential equations.

FilledSmallSquare High-dimensional numerical integration.

FilledSmallSquare Optimized minimization algorithms.

FilledSmallSquare LU and Jordan decomposition of matrices.

FilledSmallSquare Numerical differentiation.

FilledSmallSquare Automatic comparison and manipulation of exact numeric quantities.

FilledSmallSquare Support for exact implicitly-defined algebraic numbers.

FilledSmallSquare Support for interval arithmetic.

FilledSmallSquare Fully adjustable global numerical precision control model.

FilledSmallSquare New capabilities for extracting segments of digits in exact and inexact numbers.

FilledSmallSquare Machine-independent mechanisms for input and output of numbers without loss of precision.

Algebraic Computation

FilledSmallSquare Enhanced and optimized simplification of algebraic expressions.

FilledSmallSquare Simplification of expressions involving special functions.

FilledSmallSquare Built-in functions for transformations on trigonometric expressions.

FilledSmallSquare Greatly extended indefinite and definite symbolic integration.

FilledSmallSquare Support for principal values and assumptions on parameters in integrals.

FilledSmallSquare Greatly extended symbolic sums and products.

FilledSmallSquare Greatly extended symbolic solution of ordinary and partial differential equations.

FilledSmallSquare Optimized symbolic linear algebra.

FilledSmallSquare Enhanced handling of exact numerical quantities.

FilledSmallSquare Generation and system-wide support for algebraic numbers.

FilledSmallSquare Highly optimized Gröbner basis reduction.

Mathematical Functions

FilledSmallSquare Faster evaluation of many special functions.

FilledSmallSquare Fresnel integrals and hyperbolic sine and cosine integrals.

FilledSmallSquare Inverse error function, gamma function and beta function.

FilledSmallSquare Product log function.

FilledSmallSquare generalized hypergeometric functions and Meijer G functions.

FilledSmallSquare Additional Weierstrass, elliptic and related functions.

FilledSmallSquare Mathieu functions.

FilledSmallSquare Stieltjes constants.

FilledSmallSquare Built-in Fibonacci numbers and polynomials.


FilledSmallSquare Full typesetting capabilities for labels and text in plots.

FilledSmallSquare Automatic conversions to EPS, TIFF, GIF and other formats.

FilledSmallSquare Kernel control of animation in notebooks.

FilledSmallSquare Absolute offset specifications in graphics primitives.

FilledSmallSquare Direct control of final graphics size, resolution, etc.

FilledSmallSquare Direct generation of text strings for graphics in various formats.

Programming and Core System

FilledSmallSquare Faster execution speed and lower memory usage for typical kernel operations.

FilledSmallSquare Dumping of function definitions for optimized loading.

FilledSmallSquare Powerful new general symbolic programming functions, including ReplaceList and Split.

FilledSmallSquare Pattern-based non-local control flow with Throw and Catch.

FilledSmallSquare Separate support for verbatim and held patterns.

FilledSmallSquare Enhanced control of basic evaluation.

FilledSmallSquare New functions and enhancements for string manipulation.

FilledSmallSquare Extensive support for manipulation of non-ASCII characters.

Input and Output

FilledSmallSquare Support for WYSIWYG fully editable two-dimensional typeset input and output.

FilledSmallSquare Extended Mathematica language incorporating special characters and two-dimensional notation.

FilledSmallSquare Over 700 special characters for mathematical and other notation.

FilledSmallSquare Support for traditional math textbook notation for output and heuristic input.

FilledSmallSquare Top-quality typeset output with advanced adjustable layout rules.

FilledSmallSquare Complete symbolic language for specifying two-dimensional typeset structures.

FilledSmallSquare Two-dimensional input and manipulation of arrays and matrices.

FilledSmallSquare Complete support for international character sets and Unicode.

FilledSmallSquare TeX conversion with line-breaking information.

FilledSmallSquare Optimized textual import and export of typeset structures.

Notebook Interface

FilledSmallSquare Programmable documents based on underlying symbolic representation.

FilledSmallSquare Symbolic language for specifying user interface operations.

FilledSmallSquare Customizable palettes that can execute any kernel or front end operation.

FilledSmallSquare Integrated active elements and hyperlinks in notebooks.

FilledSmallSquare Separate style environments for screen and printing.

FilledSmallSquare New style sheets for varied document types.

FilledSmallSquare Language-based control of all features of text, graphics, cells and notebooks.

FilledSmallSquare Inline typesetting and graphics embedded in text.

FilledSmallSquare Enhanced text formatting capabilities including full text justification.

FilledSmallSquare Integrated customizable notebook-based online help with hyperlinks and the full text of this book.

FilledSmallSquare Fully platform-independent notebook file format.

FilledSmallSquare Notebook conversion to TeX, HTML and other external formats.

FilledSmallSquare Option inspector for interactive control of all notebooks and front end properties.

FilledSmallSquare Keyboard commands for editing and notebook navigation; drag and drop.

System Interface

FilledSmallSquare Additional kernel directory and file manipulation functions.

FilledSmallSquare Support for multi-platform external program clusters.

FilledSmallSquare Optimized MathLink external program interface.

FilledSmallSquare Loopback links for storing expressions in external programs.

FilledSmallSquare Direct support for arrays in external programs.

FilledSmallSquare Shared libraries for MathLink.

FilledSmallSquare Uniform layout of system files across all platforms.

FilledSmallSquare Automatic initialization of kernel and front end functionality as well as documentation for add-ons.

FilledSmallSquare Support for multi-lingual versions and all standard keyboard character encodings.

FilledSmallSquare TCP-based network license server.

FilledSmallSquare OLE support under Microsoft Windows.

Standard Add-on Packages

FilledSmallSquare Manipulating and solving algebraic inequalities.

FilledSmallSquare Symmetric polynomials.

FilledSmallSquare Manipulating quaternions and elements of Galois fields.

FilledSmallSquare Complete integrals and differential invariants of nonlinear PDEs.

FilledSmallSquare Primitive roots for arbitrary algebraic extensions.

FilledSmallSquare Numerical residue and series computations.

FilledSmallSquare Data smoothing and filtering.

FilledSmallSquare Classical and robust multivariate descriptive statistics.

FilledSmallSquare Linear and nonlinear regression with diagnostics.

FilledSmallSquare Simplified arithmetic and algebra without complex numbers.

FilledSmallSquare Full online documentation of all packages.

New in Version 4The Role of This Book