FriCAS

FriCAS is a general purpose computer algebra system with a strong focus on mathematical research and development of new algorithms. It comprises an interpreter, a compiler and a still-growing library
of more than 1,000 domains and categories.
FriCAS provides a strongly typed high-level programming language called SPAD and a similar interactive language
that uses type-inferencing for convenience. Aldor was intentionally developed being the
next generation compile preparation for the Axiom CAS and its forks. FriCAS optionally allows running Aldor programs. Both languages
share a similar syntax and a sophisticated type system.
FriCAS is comprehensively documented and available as source code and as a binary distribution for the most common
platforms. Compiling the Axiom lisp resources requires besides other prerequisites a Common Lisp environment, freely available as open source. A list of CL implementations are supported by fricas lisp code.
FriCAS runs on many POSIX platforms such as Linux, macOS, Unix,
BSD as well as under Cygwin and
Microsoft Windows.

History

Two computer algebra systems named Scratchpad were developed by IBM. The first one was started in 1965 by James Griesmer at the request of Ralph Gomory, and written in Fortran. The development of this software was stopped before any public release. The second Scratchpad, originally named Scratchpad II, was developed from 1977 on, at Thomas J. Watson Research Center, under the direction of Richard Dimick Jenks.
The design is principally due to Richard D. Jenks, James H. Davenport, Barry M. Trager, David Y.Y. Yun and Victor S. Miller. Early consultants on the project were David Barton and James W. Thatcher. Implementation included Robert Sutor, Scott C. Morrison, Christine J. Sundaresan, Timothy Daly, Patrizia Gianni, Albrecht Fortenbacher, Stephen M. Watt, Josh Cohen, Michael Rothstein, Manuel Bronstein, Michael Monagan, Jonathan Steinbach, William Burge, Jim Wen, William Sit, and Clifton Williamson.
Scratchpad II was renamed Axiom when IBM decided, circa 1990, to make it a commercial product. A few years later, it was sold to NAG. In 2001, it was withdrawn from the market and re-released to Tim Daly under the BSD License">Berkeley Software Distribution">BSD License. In 2007, Axiom was forked as FriCAS by Waldek Hebisch following encouragement from Tim Daly to resolve disagreements about project goals.

Examples

FriCAS has a largely complete implementation of the
Risch–Bronstein–Trager algorithm.
Another useful feature is stream:


)set stream calculate 5
exp_series := series

Type: UnivariatePuiseuxSeries

So any coefficient may be retrieved, for instance :


coefficient

Type: Expression