View source for FriCAS

{{Short description|Computer algebra system}}
{{Infobox programming language
 |name = FriCAS
 |developer = Waldek Hebisch + independent [https://fricas.github.io/contributors.html group] of people
 |latest release version = 1.3.11
 |latest release date  = {{start date and age|df=yes|2024|07|01}}
 |status = Active
 |operating system = [[Cross-platform]]
 |genre = [[Computer algebra system]], [[Mathematical software]]
 |license = [[BSD licenses|Modified BSD License]]
 |programming language = SPAD, [[Aldor]], Boot, [[Common Lisp]]
 |file ext = <code>.spad</code>, <code>.input</code>, <code>.as</code>
 |website = {{URL|https://fricas.github.io/}}
}}

'''FriCAS''' is a general purpose [[computer algebra system]] with a strong focus on mathematical research and development of new [[algorithm]]s. It comprises an [[Interpreter (computing)|interpreter]], a [[compiler]] and a still-growing [[Library (computing)|library]]<ref>[https://fricas.github.io/api/ FriCAS API]</ref>
of more than 1,000 domains and categories.

FriCAS provides a [[Strong and weak typing|strongly typed]] [[high-level programming language]] called SPAD and a similar interactive language
that uses [[Type inference|type-inferencing]] for convenience. [[Aldor]] was intentionally developed being the 
next generation compiler for the Axiom CAS and its [[Fork (software development)|forks]]. FriCAS (optionally) allows running Aldor programs. Both languages
share a similar syntax and a sophisticated ([[Dependent type|dependent]]) [[type system]].<ref>
{{Cite web| last1 = Poll| first1 = Erik| last2 = Thompson| first2 = Simon| title = Adding the axioms to Axiom: Towards a system of automated reasoning in Aldor| date = May 1998| format = Monograph| access-date = 2017-01-27| url = https://kar.kent.ac.uk/21662/}}
</ref><ref>
{{Cite web| last1 = Poll| first1 = Erik| last2 = Thompson| first2 = Simon| title = The Type System of Aldor| format = Monograph| access-date = 2017-01-27| url = http://www.cs.kent.ac.uk/pubs/1999/874}}
</ref><ref>
{{Cite conference| publisher = Springer-Verlag Berlin| isbn = 978-3-540-67281-4| conference = 3rd International Workshop on Frontiers of Combining Systems (FroCoS 2000)| volume = 1794| pages = 136–150|editor1= Hélène Kirchner |editor2=Christophe Ringeissen | last1 = Poll| first1 = Erik| last2 = Thompson| first2 = Simon| title = Integrating Computer Algebra and Reasoning through the Type System of Aldor| book-title = Frontiers of Combining Systems| location = Nancy, France| access-date = 2017-01-27| url = https://kar.kent.ac.uk/22041/}}
</ref>

FriCAS is comprehensively documented and available as [[source code]] and as a binary [[Software distribution|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 software|open source]]).

FriCAS runs on many [[POSIX]] platforms such as [[Linux]], [[macOS]], [[Unix]],
[[Berkeley Software Distribution|BSD]] as well as under [[Cygwin]] and
[[Microsoft Windows]] ([[Windows_Subsystem_for_Linux|WSL]]).

== History ==

Two computer algebra systems named '''Scratchpad''' were developed by [[IBM]]. The first one was started in 1965 by James Griesmer<ref>{{Cite journal|title=James Griesmer 1929--2011|first=John|last=Fitch|date=July 23, 2012|journal=ACM Communications in Computer Algebra|volume=46|issue=1/2|pages=10–11|doi=10.1145/2338496.2338499|s2cid=36788754 |doi-access=free}}</ref> at the request of [[Ralph E. Gomory|Ralph Gomory]], and written in [[Fortran]].<ref>{{Cite web|url=http://axiom-developer.org/|title=Axiom Computer Algebra System|website=axiom-developer.org}}</ref> 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.<ref>{{Cite web|url=https://www.eecis.udel.edu/~caviness/jenks/jenksbio/|title=Richard D. Jenks Biographical Information|website=www.eecis.udel.edu}}</ref>

The design is principally due to Richard D. Jenks (IBM Research), [[James H. Davenport]] (University of Bath), Barry M. Trager (IBM Research), David Y.Y. Yun (Southern Methodist University) and [[Victor S. Miller]] (IBM Research). Early consultants on the project were David Barton (University of California, Berkeley) and [[James W. Thatcher]] (IBM Research). Implementation included Robert Sutor (IBM Research), Scott C. Morrison (University of California, Berkeley), Christine J. Sundaresan (IBM Research), Timothy Daly (IBM Research), [[Patrizia Gianni]] (University of Pisa), Albrecht Fortenbacher (Universitaet Karlsruhe), [[Stephen M. Watt]] (IBM Research and University of Waterloo), Josh Cohen (Yale University), Michael Rothstein (Kent State University), Manuel Bronstein (IBM Research), Michael Monagan (Simon Fraser University), Jonathan Steinbach (IBM Research), William Burge (IBM Research), Jim Wen (IBM Research), William Sit (City College of New York), and Clifton Williamson (IBM Research)<ref>{{Cite journal|url=https://www.springer.com/gp/book/9783540159841|title=EUROCAL '85 &#124; SpringerLink|website=www.springer.com}}</ref>

Scratchpad II was renamed '''Axiom''' when IBM decided, circa 1990, to make it a commercial product. A few years later, it was sold to [[Numerical Algorithms Group|NAG]]. In 2001, it was withdrawn from the market and re-released to Tim Daly under the [[Modified BSD License]]. In 2007, Axiom was [[fork (software development)|forked]] as '''FriCAS''' by Waldek Hebisch following encouragement from Tim Daly<ref>{{Cite web|url=https://lists.nongnu.org/archive/html/axiom-developer/2007-06/msg00627.html|title=[Axiom-developer] A modest proposal|website=lists.nongnu.org}}</ref> to resolve disagreements about project goals.<ref>{{Cite web|url=https://fricas.github.io/history.html|title=History — FriCAS|website=fricas.github.io}}</ref>

== Examples ==

FriCAS has a largely complete implementation of the 
[[Risch algorithm|Risch–Bronstein–Trager algorithm]].<ref>{{Cite web|title=MathAction RischImplementationStatus|url=http://wiki.fricas.org/RischImplementationStatus|access-date=2021-10-03|website=wiki.fricas.org}}</ref>

Another useful feature is [[Stream (computer science)|stream]]:

<pre>
)set stream calculate 5
exp_series := series(exp x, x=0)
</pre>

<math>
\ \ \ \ 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)}
</math>
<pre>Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)</pre>

So any coefficient may be retrieved, for instance <math>n=40</math>:

<pre>
coefficient(exp_series,40)
</pre>
<math>
\ \ \ \ \frac{1}{81591528324789773434 56112695961158942720 00000000} 
</math>

<pre>Type: Expression(Integer)</pre>


==See also==
{{Portal|Free and open-source software}}
*[[List of computer algebra systems]]

==References==
{{reflist|
refs=
}}

== External links ==
* [https://fricas.github.io/ FriCAS Homepage]
* [https://wiki.fricas.org FriCAS Wiki]
* [https://wiki.fricas.org/SandBox SandBox: Try FriCAS online]
* [https://fricas.github.io/ Documentation at fricas.github.io]
* [https://fricas.github.io/api/index.html FriCAS API (sphinx)]
* Source code repositories: [https://sourceforge.net/p/fricas/code/HEAD/tree/ SourceForge], [https://github.com/fricas/fricas GitHub]
* [https://wiki.fricas.org/images/Rosetta.pdf Rosetta stone (pdf)]
* [https://wiki.fricas.org/Rosetta Rosetta stone (some other formats)]
* [https://wiki.fricas.org/RosettaStone Rosetta Stone (html)]
* [http://rosettacode.org/wiki/Category:SPAD rosettacode.org, Category:SPAD]
* [https://groups.google.com/forum/#!forum/fricas-devel Forum: fricas-devel]
* [https://github.com/fricas/jfricas FriCAS Jupyter Kernel (jfricas/src)]
* [https://pypi.org/project/jfricas/ FriCAS Jupyter (pypi)] 
Related:
* [http://www.axiom-developer.org/ Axiom]
* [http://www.open-axiom.org OpenAxiom]
* [[A Sharp (Axiom)|A# programming language]]
* [[Aldor]] programming language

{{Computer algebra systems}}

{{DEFAULTSORT:FriCAS (Computer Algebra System)}}
[[Category:Common Lisp (programming language) software]]
[[Category:Computer algebra system software for Linux]]
[[Category:Free computer algebra systems]]
[[Category:Free software programmed in Lisp]]
[[Category:Software using the BSD license]]