Editing Computer algebra system (section)

== History ==
[[File:TI-Nspire.jpg|thumb|A Texas Instruments [[TI-Nspire]] calculator that contains a computer algebra system]]
In the 1950s, while computers were mainly used for numerical computations, there were some research projects into using them for symbolic manipulation. Computer algebra systems began to appear in the 1960s and evolved out of two quite different sources—the requirements of theoretical physicists and research into [[artificial intelligence]].

A prime example for the first development was the pioneering work conducted by the later Nobel Prize laureate in physics [[Martinus Veltman]], who designed a program for symbolic mathematics, especially high-energy physics, called [[Schoonschip]] (Dutch for "clean ship") in 1963. Other early systems include [[FORMAC (programming language)|FORMAC]].

Using [[Lisp (programming_language)|Lisp]] as the programming basis, [[Carl Engelman]] created [[MATHLAB]] in 1964 at [[MITRE]] within an artificial-intelligence research environment. Later MATHLAB was made available to users on PDP-6 and PDP-10 systems running TOPS-10 or TENEX in universities. Today it can still be used on [[SIMH]] emulations of the PDP-10. MATHLAB ("'''math'''ematical '''lab'''oratory") should not be confused with [[MATLAB]] ("'''mat'''rix '''lab'''oratory"), which is a system for numerical computation built 15 years later at the [[University of New Mexico]].

In 1987, [[Hewlett-Packard]] introduced the first hand-held calculator CAS with the [[HP-28 series]].<ref name="Nelson">{{cite web | title=Hewlett-Packard Calculator Firsts | first=Richard | last=Nelson | publisher=Hewlett-Packard | url=http://h20331.www2.hp.com/Hpsub/cache/392617-0-0-225-121.html | archive-url=https://web.archive.org/web/20100703031935/http://h20331.www2.hp.com/Hpsub/cache/392617-0-0-225-121.html | archive-date=2010-07-03}}</ref> Other early handheld calculators with symbolic algebra capabilities included the [[Texas Instruments]] [[TI-89 series]] and [[TI-92]] calculator, and the [[Casio]] [[CFX-9970G]].<ref>{{citation
 | last = Coons | first = Albert
 | date = October 1999
 | department = Technology Tips
 | doi = 10.5951/mt.92.7.0620
 | issue = 7
 | journal = The Mathematics Teacher
 | jstor = 27971125
 | pages = 620–622
 | title = Getting started with symbolic mathematics systems: a productivity tool
 | volume = 92}}</ref>

The first popular computer algebra systems were [[muMATH]], [[Reduce computer algebra system|Reduce]], [[Derive (computer algebra system)|Derive]] (based on muMATH), and [[Macsyma]]; a [[copyleft]] version of Macsyma is called [[Maxima (software)|Maxima]]. [[Reduce (computer algebra system)|Reduce]] became free software in 2008.<ref>{{Cite web |title=REDUCE Computer Algebra System at SourceForge |url=http://reduce-algebra.sourceforge.net |access-date=2015-09-28 |website=reduce-algebra.sourceforge.net}}</ref> Commercial systems include [[Mathematica]]<ref>[http://history.siam.org/oralhistories/gonnet.htm Interview with Gaston Gonnet, co-creator of Maple] {{webarchive|url=https://web.archive.org/web/20071229044836/http://history.siam.org/oralhistories/gonnet.htm|date=2007-12-29}}, SIAM History of Numerical Analysis and Computing, March 16, 2005.</ref> and [[Maple (software)|Maple]], which are commonly used by research mathematicians, scientists, and engineers. Freely available alternatives include [[SageMath]] (which can act as a [[Front and back ends|front-end]] to several other free and nonfree CAS). Other significant systems include [[Axiom (computer algebra system)|Axiom]], [[GAP_(computer_algebra_system)|GAP]], [[Maxima (software)|Maxima]] and [[Magma (computer algebra system)|Magma]].

The movement to web-based applications in the early 2000s saw the release of [[WolframAlpha]], an online search engine and CAS which includes the capabilities of [[Mathematica]].<ref>{{Cite news |last=Bhattacharya |first=Jyotirmoy |date=2022-05-12 |title=Wolfram{{!}}Alpha: a free online computer algebra system |language=en-IN |work=The Hindu |url=https://www.thehindu.com/sci-tech/technology/wolframalpha-a-free-online-computer-algebra-system/article65401003.ece |access-date=2023-04-26 |issn=0971-751X}}</ref>

More recently, computer algebra systems have been implemented using [[artificial neural networks]], though as of 2020 they are not commercially available.<ref>{{Cite web |last=Ornes |first=Stephen |title=Symbolic Mathematics Finally Yields to Neural Networks |url=https://www.quantamagazine.org/symbolic-mathematics-finally-yields-to-neural-networks-20200520/ |access-date=2020-11-04 |website=Quanta Magazine |date=20 May 2020 |language=en}}</ref>