Mathematica 7: The World's Most Powerful Global Computing Environment 
Mathematica is a complete technical computing environment that seamlessly integrates numeric and symbolic computations, interactive document capabilities, an advanced programming language, and powerful connectivity.  

From computation to visualization, development to deployment, Mathematica 7 builds on 20 years of innovation to deliver one vision: the ultimate technical application and environment. Mathematica 7 includes over 500 new functions and 12 additional application areas, all seamlessly integrated in one system that gives you unprecedented workflow, coherence, and reliability.

Features

• Elementary mathematical function library
• Special mathematical function library
• Matrix and data manipulation tools including support for sparse arrays
• Support for complex number, arbitrary precision, interval arithmetic and symbolic computation
• 2D and 3D data and function visualization and animation tools
• Solvers for systems of equations, diophantine equations, ODEs, PDEs, DAEs, DDEs and recurrence relations
• Numeric and symbolic tools for discrete and continuous calculus
• Multivariate statistics libraries
• Constrained and unconstrained local and global optimization
• Programming language supporting procedural, functional and object oriented constructs
• Toolkit for adding user interfaces to calculations and applications
• Tools for image processing and morphological image processing
• Tools for visualizing and analysing graphs
• Tools for combinatoric problems
• Data mining tools such as cluster analysis, sequence alignment and pattern matching
• Number theory function library
• Continuous and discrete integral transforms
• Import and export filters for data, images, video, sound, CAD, GIS, document and biomedical formats
• Database collection for mathematical, scientific, and socio-economic information
• Notebook interface for review and re-use of previous inputs and outputs including graphics and text annotations
• Technical word processing including formula editing and automated report generating
• Tools for connecting to SQL, Java, .NET, C++, FORTRAN and http based systems
• Tools for parallel programing