Maxima
A system for the manipulation of symbolic and numerical expressions
Maxima is a computer algebra system written in Lisp for manipulating symbolic and numerical expressions. It handles differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices, and tensors, and produces high-precision numerical results using exact fractions, arbitrary-precision integers, and variable-precision floating-point numbers. It can plot functions and data in two and three dimensions.
The core maxima program runs in a terminal window, while the included wxMaxima and XMaxima systems provide a notebook interface with formatted mathematical output. Maxima runs on Windows, Linux, and Mac, with source code available via GIT. It is distributed under the GNU General Public License and can be tried online or installed locally.
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