BREAKING NEWS
FriCAS

## Summary

Developer Waldek Hebisch + independent group of people 1.3.7 / 30 June 2021; 6 months ago SPAD, Aldor, Boot, Common Lisp Cross-platform Modified BSD License .spad, .input, .as fricas.github.io

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[1] 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 compiler for Axiom and forks. FriCAS (optionally) allows running Aldor programs. Both languages share a similar syntax and a sophisticated (dependent) type system.[2][3][4]

FriCAS is comprehensively documented and available as source code and as a binary distribution for the most common platforms. Compiling the sources requires besides other prerequisites a Common Lisp environment (whereby many of the major implementations are supported and freely available as open source).

FriCAS runs on many POSIX platforms such as Linux, macOS, Unix, BSD as well as under Cygwin and Microsoft Windows (WSL).

## History

FriCAS is a descendant of Axiom [5] which itself has its origin in Scratchpad, a project that started in 1965 by James Griesmer [6] at IBM laboratories.[7] For more details see Axiom/History.

## Examples

FriCAS has a rather complete implementation of the Risch–Bronstein–Trager algorithm, but it is still incomplete.[8]

Another useful feature is stream:

)set stream calculate 5
exp_series := series(exp x, x=0)


${\displaystyle \ \ \ \ 1+x+{{\frac {1}{2}}\ {{x}^{2}}}+{{\frac {1}{6}}\ {{x}^{3}}}+{{\frac {1}{24}}\ {{x}^{4}}}+{{\frac {1}{120}}\ {{x}^{5}}}+{O\left({{x}^{6}}\right)}}$

Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)

So any coefficient may be retrieved, for instance ${\displaystyle n=40}$:

coefficient(exp_series,40)


${\displaystyle \ \ \ \ {\frac {1}{815915283247897734345611269596115894272000000000}}}$

Type: Expression(Integer)