 |
Number Theory Packages
(PARI/GP, Magma, Kant, NTL, ...)
Mathematica not only has broad and deep coverage of state-of-the-art number theory, but also immediately integrates number theory into the complete Mathematica computation and interface environment. Mathematica's unequaled web of symbolic, numeric and other algorithms has made possible a new generation of number theoretic functionality, with many original algorithms developed at Wolfram Research. Mathematica's number theoretic functions are fully scalable, and can immediately be used in high-performance computing, and with gridMathematica.
Number Theory Package Features Built into Mathematica:
- Efficient implementation of all standard integer and number theory functions »
- Deep handling of algebraic, analytic, multiplicative and additive number theory »
- Seamless handling of all types of exact and approximate numbers »
- Efficient handling of multimillion-digit numbers »
- Immediate scalability to high-performance computing
- Optimized on all standard and emerging computer platforms »
Key Advantages of Mathematica for Number Theory:
- Full integration of number theory with symbolic algebraic computation »
- Convenient symbolic representations of algebraic numbers, etc. »
- Flexible built-in graphics, visualization and computational geometry »
- Ability to do symbolic operations with number theoretic functions
- Broad treatment of Diophantine equations and sets »
- Powerful built-in algorithms based on interplay between symbolic computation, numerics and discrete mathematics
- Immediate access to a full range of special functions »
- Built-in number recognition functions »
- Full multiparadigm math-oriented programming language »
- Document-centered interface for complete record of investigations »
- Instant interface creation for experimentation and compelling demonstrations »
- Immediate export of publication-quality graphics, typesetting, etc. »
- Highly readable programs suitable for publishing algorithm descriptions
- Data extraction from tabular formats, web pages, etc. »
- Widespread number theory textbooks based on Mathematica
- The Wolfram Demonstrations Project with hundreds of interactive number theory examples »
Interoperability with Number Theory Packages:
- MathLink API allowing arbitrary data and function connectivity
- Ability to call Mathematica from external programs »
Interesting Tidbits:
- Many significant number theory discoveries have been made with Mathematica
- Wolfram Research has developed many original number theory algorithms
- Mathematica won the "Many Digits" Friendly Competition by a large margin
- Mathematica holds many records for number theoretic computation
See Also Analyses On:
Send a suggestion to the Mathematica analysis team