

Computer Algebra Systems
(Maple, Reduce, MuPAD, Magma, Axiom, Maxima, ...)
Computer algebra has been a central component of Mathematica's overall vision since its inception, and indeed Mathematica's original release in 1988 was what first brought computer algebra into the mainstream. For over 20 years, Wolfram Research has been a consistent leader in computer algebra research, implementing and inventing an unsurpassed number of new methods and algorithms—and indeed shaping the very concept of computer algebra.
While a variety of systems have been developed to provide basic computer algebra functionality, Mathematica is unique not only in delivering far greater depth and quality of coverage, but also in tightly integrating computer algebra into a unified overall framework. This integration is what has allowed Mathematica to bring computer algebra into industrial applications. And in education, it makes computer algebra an increasingly compelling educational tool, by linking it not only to the best in static visualization, but also now to a new generation of dynamic exploratory visualization and instant interactive interface creation technology. In addition, the Wolfram Demonstrations Project provides thousands of prebuilt resources for applying computer algebra in education.
In recent years, Mathematica's integration of efficient arbitraryprecision numerics, special functions, number theory, discrete mathematics, computational geometry and other areas has allowed Mathematica to drive the development of major new classes of computer algebra algorithms that could not realistically be implemented in narrowly defined computer algebra systems.
 Computer algebra seamlessly integrated with numerics, graphics, programming, etc.

Integrated document interface with full 2D traditional math input »
 Realtime interactive computer algebra using GUI controls
 Professionally supported system, available on all standard computer platforms

Unified system design, maximizing interoperability of all system functions »

Consistent language and interface, optimized for rapid learning »

Full automation of superfunctions
such as Solve,
with automatic
algorithm selection »
 Many original mathematical algorithms developed specifically for Mathematica

Consistent handling of mathematical subtleties such as function branch cuts »

Complete handling of real, complex, integer domains for equations, inequalities, etc. »

Full symbolic and numeric support for 250+ special functions »

Fully integrated highperformance numerics, linear algebra, etc. »

Arbitraryprecision numerics for all functions, with automatic precision control »

Fully editable and interpretable 2D traditional math notation »
 Worldclass software quality assurance, with millions of computer algebra tests

Extensive builtin mathematical data collections »
 Integration with MathWorld's encyclopedic website of mathematical information

Thousands of readybuilt interactive demonstrations of mathematical concepts »
 Wolfram Research has the world's most active computer algebra research organization
 Mathematica has been the basis for many thousands of mathematical papers
 Algorithms for Mathematica are increasingly discovered using NKS algorithm search methodology
 Mathematica has been a key element of calculus reform for nearly 20 years
 Mathematica was the first commercially successful system with computer algebra capabilities






