FriCAS

FriCAS (formerly known as Axiom) is a free, general-purpose computer algebra system (CAS). It can be used for symbolic and numerical computation, with a focus on abstract algebra. FriCAS distinguishes itself from many other CAS by its strong typing system based on category theory. This system allows for the creation of mathematically rigorous and well-defined objects and functions.

FriCAS is particularly strong in areas such as:

• Abstract Algebra: It provides extensive support for working with groups, rings, fields, and other algebraic structures.
• Symbolic Computation: It can perform symbolic integration, differentiation, equation solving, and simplification of algebraic expressions.
• Arbitrary Precision Arithmetic: It supports computations with numbers of arbitrary precision.

The development of FriCAS has a long history. It originated at IBM as the Axiom system in the 1970s. IBM eventually released Axiom as open-source software. The project was later forked and renamed FriCAS, continuing its development as a community-driven open-source project.

FriCAS is written in its own programming language, also named SPAD, which reflects its algebraic foundation. The system's library is implemented primarily in SPAD, providing a powerful and expressive environment for extending its capabilities.

FriCAS is used by researchers, educators, and students in mathematics, computer science, and related fields. It offers a platform for exploring and experimenting with mathematical concepts and algorithms. Its rigorous type system allows for creating robust and reliable mathematical software.