Genius is a free open source numerical computing environment and programming language, similar in some aspects to MATLAB, GNU Octave, Mathematica and Maple. Genius is aimed at mathematical experimentation rather than computation intensive tasks. It is also very useful as just a calculator. The programming language is called GEL and aims to have a mathematical friendly syntax. The software comes with a command line and a GUI interface. The graphical version supports both 2D and 3D plotting.

- Arbitrary precision integers, multiple precision floats.
- Rational numbers, stored as quotient and denominator.
- Complex numbers, stored in Cartesian coordinates as usual.
- Math-like-looking expressions, tries to be as much a what-you-mean-is-what-Genius-understands, up to a limit of course.
- Matrix calculations / Linear Algebra, with many related functions.
- Number theory.
- Calculus, numerical and even very limited symbolic calculations.
- Statistics, all the basic statistical functions.
- Numerical equation solving, polynomial roots, etc. . .
- Combinatorics.
- Most common elementary / trigonometric functions.
- Modular arithmetic, including inversions and modular arithmetic on matrices.
- A complete programming language, with automatic typing. In fact large part of Genius standard library is written in GEL.
- 2D Function line plots, standard 2D graphs of up to 10 functions at once, with possibility to export to EPS or PNG.
- Parametric plots, with possibility to export to EPS or PNG.
- 3D Function surface plots, with possibility to export to EPS or PNG
- Slopefield/Vectorfield plotting.
- GUI IDE where you can edit and run/test your programs.
- Can output matrices in LaTeX, Troff (eqn) or MathML, this is I think a very cool feature that allows you to copy stuff directly from Genius to a document in LaTeX, troff or MathML.

* Genius download link provides gnu general public license version of the software.

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