New in Version 5.1Numerical computation• 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 Transpose and Conjugate. • Numerical integration of discontinuous piecewise functions. • Numerical integration over implicitly defined regions. • Support for event detection in NDSolve. • Additional convenience functions Boole, Clip and 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. • Limit, Series and 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 non-rational 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 StringSplit, StringCount and StringReplaceList. • RegularExpression construct for compact string pattern notation. • English-language dictionary package. • Support for generalized Tuples and 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.
| 
