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Some New Features of Mathematica 3.0

The first major new version of Mathematica in several years, 3.0 strengthens the core computational capabilities of Mathematica, and adds some revolutionary new features. Throughout this book, items that are new are indicated by

  • ; those that are changed are indicated by
  • . Except as noted in Section A.13, 3.0 is fully compatible with earlier versions.

    Numerical Computation

  • Adaptive precision control to generate results with guaranteed precision.
  • High-performance compilation of list-oriented, procedural and functional numerical operations.
  • Optimized algorithms for one- and higher-dimensional interpolation.
  • Optimized algorithms for solution of differential equations.
  • Solution of boundary value ordinary differential equations, and initial value partial differential equations.
  • High-dimensional numerical integration.
  • Optimized minimization algorithms.
  • LU and Jordan decomposition of matrices.
  • Numerical differentiation.
  • Automatic comparison and manipulation of exact numeric quantities.
  • Support for exact implicitly-defined algebraic numbers.
  • Support for interval arithmetic.
  • Fully adjustable global numerical precision control model.
  • New capabilities for extracting segments of digits in exact and inexact numbers.
  • Machine-independent mechanisms for input and output of numbers without loss of precision.

    Algebraic Computation

  • Enhanced and optimized simplification of algebraic expressions.
  • Simplification of expressions involving special functions.
  • Built-in functions for transformations on trigonometric expressions.
  • Greatly extended indefinite and definite symbolic integration.

  • Support for principal values and assumptions on parameters in integrals.
  • Greatly extended symbolic sums and products.
  • Greatly extended symbolic solution of ordinary and partial differential equations.
  • Optimized symbolic linear algebra.
  • Enhanced handling of exact numerical quantities.
  • Generation and system-wide support for algebraic numbers.
  • Highly optimized Gröbner basis reduction.

    Mathematical Functions

  • Faster evaluation of many special functions.
  • Fresnel integrals and hyperbolic sine and cosine integrals.
  • Inverse error function, gamma function and beta function.
  • Product log function.
  • generalized hypergeometric functions and Meijer G functions.
  • Additional Weierstrass, elliptic and related functions.
  • Mathieu functions.
  • Stieltjes constants.
  • Built-in Fibonacci numbers and polynomials.


  • Full typesetting capabilities for labels and text in plots.
  • Automatic conversions to EPS, TIFF, GIF and other formats.
  • Kernel control of animation in notebooks.
  • Absolute offset specifications in graphics primitives.
  • Direct control of final graphics size, resolution, etc.
  • Direct generation of text strings for graphics in various formats.

    Programming and Core System

  • Faster execution speed and lower memory usage for typical kernel operations.
  • Dumping of function definitions for optimized loading.

  • Powerful new general symbolic programming functions, including ReplaceList and Split.
  • Pattern-based non-local control flow with Throw and Catch.
  • Separate support for verbatim and held patterns.
  • Enhanced control of basic evaluation.
  • New functions and enhancements for string manipulation.
  • Extensive support for manipulation of non-ASCII characters.

    Input and Output

  • Support for WYSIWYG fully editable two-dimensional typeset input and output.
  • Extended Mathematica language incorporating special characters and two-dimensional notation.
  • Over 700 special characters for mathematical and other notation.
  • Support for traditional math textbook notation for output and heuristic input.
  • Top-quality typeset output with advanced adjustable layout rules.
  • Complete symbolic language for specifying two-dimensional typeset structures.
  • Two-dimensional input and manipulation of arrays and matrices.
  • Complete support for international character sets and Unicode.
  • TeX conversion with line-breaking information.
  • Optimized textual import and export of typeset structures.

    Notebook Interface

  • Programmable documents based on underlying symbolic representation.
  • Symbolic language for specifying user interface operations.
  • Customizable palettes that can execute any kernel or front end operation.
  • Integrated active elements and hyperlinks in notebooks.
  • Separate style environments for screen and printing.
  • New style sheets for varied document types.
  • Language-based control of all features of text, graphics, cells and notebooks.
  • In-line typesetting and graphics embedded in text.
  • Enhanced text formatting capabilities including full text justification.

  • Integrated customizable notebook-based on-line help with hyperlinks and the full text of this book.
  • Fully platform-independent notebook file format.
  • Notebook conversion to TeX, HTML and other external formats.
  • Option inspector for interactive control of all notebooks and front end properties.
  • Keyboard commands for editing and notebook navigation; drag and drop.

    System Interface

  • Additional kernel directory and file manipulation functions.
  • Support for multi-platform external program clusters.
  • Optimized MathLink external program interface.
  • Loopback links for storing expressions in external programs.
  • Direct support for arrays in external programs.
  • Shared libraries for MathLink.
  • Uniform layout of system files across all platforms.
  • Automatic initialization of kernel and front end functionality as well as documentation for add-ons.
  • Support for multi-lingual versions and all standard keyboard character encodings.
  • Direct CD-ROM executability.
  • TCP-based network license server.
  • OLE support under Microsoft Windows.

    Standard Add-on Packages

  • Manipulating and solving algebraic inequalities.
  • Symmetric polynomials.
  • Manipulating quaternions and elements of Galois fields.
  • Complete integrals and differential invariants of nonlinear PDEs.
  • Z transforms.
  • Primitive roots for arbitrary algebraic extensions.
  • Numerical residue and series computations.
  • Data smoothing and filtering.
  • Classical and robust multivariate descriptive statistics.
  • Linear and nonlinear regression with diagnostics.
  • Simplified arithmetic and algebra without complex numbers.
  • Full on-line documentation of all packages.