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Maxima is a GPL computer algebra system based on DOE-MACSYMA. It
is 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 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. Maxima is widely used.