Mathematica 9 is now available
What is New in Mathematica 5.1
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Summary of New Features

Numerical Computation
See What's New in Wolfram Mathematica
  • New highly enhanced algorithms for high-precision LinearSolve.
  • Internal vectorization of high-precision vector operations.
  • New high-performance methods for MatrixExp.
  • Support for sparse singular value decomposition.
  • Support for HessenbergDecomposition.
  • Typeset notation for Conjugate.
  • Numerical integration of discontinuous piecewise functions.
  • Numerical integration over implicitly defined regions.
  • Support for event detection in NDSolve.
  • Additional convenience functions Rescale.
  • Package for cluster analysis and dendrograms.
  • Package for interactive exploration of differential equation systems.
Symbolic Computation
  • General vector derivatives, including Gradient, Hessian, and Jacobian.
  • Piecewise construct for representing general piecewise functions.
  • Simplification with piecewise and nested piecewise functions.
  • Reduction of piecewise equations and inequalities, including quantifiers.
  • D support for general piecewise functions.
  • Indefinite and definite integration of general piecewise functions.
  • Support for solving piecewise ordinary differential equations.
  • Symbolic multiple integration over regions defined by inequalities.
  • Enhanced support for solving Abel and other differential equations.
  • Support for linear differential equations with nonrational coefficients.
  • Nonlinear partial differential equation solutions based on complete integrals.
  • Support for equations with multiple moduli in Reduce.
  • Additional methods for solving Diophantine equations.
Language and Core System
  • Full support for optimized string pattern matching.
  • Integrated string and expression pattern language.
  • General support for complement patterns with Except.
  • String patterns integrated into all string operations.
  • Generalized StringCases for string analysis.
  • New functions StringCount, and StringReplaceList.
  • RegularExpression construct for compact string pattern notation.
  • English-language dictionary package.
  • Support for generalized Subsets.
  • Expression filtering function Pick.
  • Package for benchmarking of computer systems.
Data Handling and Visualization
  • ArrayPlot for flexible large-scale array visualization.
  • Package for fully automated network and tree layout in 2D and 3D.
  • Highly optimized import and export of binary data.
  • Import and export of XLS spreadsheet files.
  • Support for HDF5, MAT (v5), DIF, and PCX.
  • Export of AVI movie files.
  • Import from http and ftp URLs.
  • Automated encoding and decoding of .gz files.
  • Integrated TeX import and parsing in notebooks.
  • Symbolic names for common colors such as Red and Black.
Database Access
  • DatabaseLink for universal cross-platform database connectivity.
  • Bundled drivers for most common database systems.
  • Integrated language interface for database discovery, query, and updating.
  • Graphical interface for database connection and exploration.
  • Bundled SQL engine for creating custom databases.
GUI Tools
  • Integrated GUIKit for building standalone user interfaces.
  • Platform-independent Mathematica language GUI specification.
  • Over 100 types of controls and widgets.
  • Automatic layout for complex dialog boxes.
  • System for creating sequential wizard interfaces.
  • Large library of sample GUI applications.
Web Services
  • Transparent access to web services from within Mathematica.
  • Support for SOAP and WSDL.
  • Packages for search and lookup on Wolfram Research and other sites.
Learn More
Mathematica 9 is now available!
Over 400 new functions, including the new Wolfram Predictive Interface…