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]. It can also calculate with exact integers and fractions, native floating-point, and high-precision big floats.
Maxima has user-friendly front-ends, an online manual, plotting commands, and numerical libraries. It features its own programming language, and many users have contributed useful packages in various areas over the decades. It is GPL-licensed and largely written in Common Lisp. Executables can be downloaded for Windows, Mac, Linux, and Android; source code is also available. An active community maintains and extends the system.
Website: https://maxima.sourceforge.io
Additional add-on packages for Maxima can be found at: https://github.com/maxima-project-on-github/maxima-packages