Maxima is a free and open-source computer algebra system (CAS) for symbolic and numerical mathematics, developed and maintained by an active global community. It handles symbolic differentiation and integration, Taylor series expansions, Laplace transforms, systems of equations, and ordinary differential equations, while supporting arbitrary-precision arithmetic, matrices, and tensors.

The system emphasizes symbolic computation across algebra, trigonometry, and calculus, while also providing numerical capabilities for high-precision calculations. With its long development history and extensible design, Maxima serves as a mature, no-cost alternative to commercial computer algebra systems for students, educators, researchers, and engineers.

Core mathematical capabilities

Maxima descends from the historic Macsyma project and provides a symbolic computation engine for algebraic manipulation, calculus operations, integral transforms, and differential equations.

It supports arbitrary-precision integers, rational numbers, native floating-point arithmetic, and arbitrarily large floating-point numbers known as big floats. The system also handles matrix and tensor operations and includes numerical capabilities for computational tasks.

Mathematical expressions can be exported to LaTeX, and integration with Gnuplot enables two- and three-dimensional plotting. In addition to its core functionality, Maxima includes numerous user-contributed packages covering areas such as statistics, combinatorics, and other specialized domains, supporting both research and teaching applications.

Interactive workflows and interfaces

Maxima supports multiple user interfaces, including command-line use and graphical front-ends such as wxMaxima, which provides a notebook-style environment for interactive sessions. This interface allows users to combine input, output, and formatted mathematical expressions within a single document, making the system practical for classroom demonstrations, assignments, research exploration, and technical documentation.

When installed locally, Maxima performs computations on the user’s machine without requiring an internet connection. The project provides documentation, including an online manual, along with community-contributed resources to assist users in learning its syntax and capabilities. As with many symbolic computation systems, new users may encounter a learning curve when becoming familiar with its command structure and programming model.

Open-source CAS for academic and research use

Maxima is a mature, free computer algebra system with strong symbolic capabilities, arbitrary-precision arithmetic, and built-in support for plotting and LaTeX export. Its open-source development model and long-standing package ecosystem make it well suited for students, educators, and researchers seeking a capable CAS without commercial licensing requirements.