Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors. Maxima yields high precision numerical results by using exact fractions, arbitrary-precision integers and variable-precision floating-point numbers. Maxima can plot functions and data in two and three dimensions.

Maxima is a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology. It is the only system based on that effort still publicly available and with an active user community, thanks to its open source nature. Macsyma was revolutionary in its day, and many later systems, such as Maple and Mathematica, were inspired by it.

Maxima is a computer algebra system comparable to commercial systems like Mathematica and Maple. It emphasizes symbolic mathematical computation: algebra, trigonometry, calculus, and much more.

For example, Maxima solves x^2-r*x-s^2-r*s=0 giving the symbolic results [x=r+s, x=-s].

Maxima can calculate with exact integers and fractions, native floating-point and high-precision big floats.

Maxima has user-friendly front-ends, an on-line manual, plotting commands, and numerical libraries. Users can write programs in its native programming language, and many have contributed useful packages in a variety of areas over the decades.

Maxima is largely written in Common Lisp. An active community maintains and extends the system.

The Maxima branch of Macsyma was maintained by William Schelter from 1982 until he passed away in 2001.

It was his efforts and skill which have made the survival of Maxima possible, and we are very grateful to him for volunteering his time and expert knowledge to keep the original DOE Macsyma code alive and well. Since his death, a group of users and developers has formed to bring Maxima to a wider audience.

Maxima is updated very frequently, to fix bugs and improve the code and the documentation.

• Specialized in symbolic operations but offering numerical capabilities too.

• Can be accessed programmatically and extended, as the underlying Lisp can be called from it.

• Complete programming language with ALGOL-like syntax but Lisp-like semantics.

• Arbitrary-precision integers.

• Rational numbers of sizes limited only by machine memory.

• Arbitrarily large floating-point numbers ("bfloats").