Wolfram Mathematica provides you with the world’s largest collection of algorithms in a single system each able to operate across the widest applicable scope of numeric, symbolic, or graphical input. Mathematica’s numerics support any precision or number size across all functions, in contrast to the typical fixed 16-digit limitation found in other computing systems. Without this you may be unable to produce answers accurate even to a small number of digits, as the internal workings of many calculations require much higher-precision input than they produce as output. Functions or data, discrete objects, diagrams, images, or annotations Mathematica’s visualization engine powers professional-quality static or dynamic representations, automatically optimizing the balance between computational efficiency and visual sophistication.

* Built-In Image Processing & Analysis:Introducing a new generation of industrial-strength image processing, built into Mathematica’s integrated algorithm, programming, and interface platform.
* Built-In Parallel Computing: Take advantage of the latest multicore processors with Mathematica’s new automatic parallel computing technology seamlessly parallelizing your computations.
* Visualization & Graphics
* Automated Charting Graphics: Algorithmic information visualization takes a major step forward by using Mathematica™s symbolic architecture, flexible graphics, and automatic computational aesthetics.
* New Graphics Primitives:Tubes, rounded rectangles, and 3D arrows join the powerful primitives integrated into Mathematica’s graphics system.
* Vector & Field Visualization: Create automatically optimized visualizations of vector fields and streamlines for fluids, electrodynamics, and other fields.
* Comprehensive Spline Support:The world’s most general splines, in any number of dimensions, fully integrated into computation and graphics.
* High-Impact Adaptive Visualization
* Automated Computational Aesthetics
* Fully Automated Graph Layout
* Real-Time 3D Graphics
* Automated Table Layout
* Dynamic Interactivity
* Industrial-Strength Boolean Computation
* Apply high-performance Boolean analysis, optimization, and verification to systems with thousands of variables all integrated into the Mathematica workflow.
* Discrete Calculus: Solve a new generation of discrete problems with the first-ever comprehensive system for discrete symbolic calculus.
* Delay Differential Equations: DDEs are now an integral part of Mathematica’s automatic numerical differential equation solving capabilities.
* Differential & Difference Roots: A breakthrough allows direct handling of implicit solutions of differential and difference equation dramatically generalizing the concept of special functions.
* Transcendental Roots:Introducing the first-ever systematic algorithmic treatment of roots of transcendental equations.
* Finite Group Theory: Data and algorithms on finite groups are now integrated into the Mathematica system.
* Integer Sequence Analysis:Mathematica 7 introduces a suite of new approaches to the analysis and recognition of integer sequences.
* New Number Theory Capabilities:New aspects of analytic, multiplicative, and additive number theory are now available in computational form.
* New Categories of Special Functions:q Functions, L Functions, and a range of other functions join the world’s largest collection of special functions.
* Enhanced Fourier Analysis:Explicit Fourier series are now fully integrated into Mathematica’s symbolic capabilities.
* Integrated Geometric Computing
* Combinatorial Optimization
* Constrained Nonlinear Optimization
* Equational Theorem Proving

Homepage: http://www.wolfram.com/products/mathematica/index.html