Computer algebra system: Difference between revisions

Revision as of 15:51, 11 November 2020

Revision as of 23:32, 26 December 2020

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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]].

The first popular computer algebra systems were [[muMATH]], [[Reduce computer algebra system|Reduce]], [[Derive (computer algebra system)|Derive]] (based on muMATH), and [[Macsyma]]; a popular [[copyleft]] version of Macsyma called [[Maxima (software)|Maxima]] is actively being maintained. [[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|website = reduce-algebra.sourceforge.net|accessdateaccess-date = 2015-09-28}}</ref> As of today,{{when|date=October 2016}} the most popular commercial systems are [[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).

In 1987, [[Hewlett-Packard]] introduced the first hand-held calculator CAS with the [[HP-28 series]], and it was possible, for the first time in a calculator,<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> to arrange algebraic expressions, differentiation, limited symbolic integration, Taylor series construction and a ''solver'' for algebraic equations. In 1999, the independently developed CAS [[Erable]] for the [[HP&nbsp;48 series]] became an officially integrated part of the firmware of the emerging [[HP&nbsp;49/50 series]], and a year later into the [[HP 40 series]] as well, whereas the [[HP Prime]] adopted the [[Xcas]] system in 2013.

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==Use in education==

There have been many advocates for increasing the use of computer algebra systems in primary and secondary-school classrooms. The primary reason for such advocacy is that computer algebra systems represent real-world math more than do paper-and-pencil or hand calculator based mathematics.<ref>{{cite web|url=http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers?language=en|title=Teaching kids real math with computers|website=Ted.com|accessdateaccess-date=12 August 2017}}</ref>

This push for increasing computer usage in mathematics classrooms has been supported by some boards of education. It has even been mandated in the curriculum of some regions.<ref>{{cite web|url=http://www.edu.gov.mb.ca/k12/cur/math/outcomes/|title=Mathematics - Manitoba Education|website=Edu.gov.mb.ca|accessdateaccess-date=12 August 2017}}</ref>

Computer algebra systems have been extensively used in higher education.<ref>{{cite web|url=http://www.it.northwestern.edu/software/mathematica-fac/|title=Mathematica for Faculty, Staff, and Students : Information Technology - Northwestern University|website=It.northwestern.edu|accessdateaccess-date=12 August 2017}}</ref><ref>{{cite web|url=https://cuit.columbia.edu/mathematica-students|title=Mathematica for Students - Columbia University Information Technology|website=cuit.columbia.edu|accessdateaccess-date=12 August 2017}}</ref> Many universities offer either specific courses on developing their use, or they implicitly expect students to use them for their course work. The companies that develop computer algebra systems have pushed to increase their prevalence among university and college programs.<ref>{{cite web|url=https://www.wolfram.com/solutions/education/higher-education/uses-for-education.html|title=Mathematica for Higher Education: Uses for University & College Courses|website=Wolfram.com|accessdateaccess-date=12 August 2017}}</ref><ref>{{cite web|url=http://www.mathworks.com/academia/|title=MathWorks - Academia - MATLAB & Simulink|website=Mathworks.com|accessdateaccess-date=12 August 2017}}</ref>

CAS-equipped calculators are not permitted on the [[ACT (test)|ACT]], the [[PLAN (test)|PLAN]], and in some classrooms<ref>[http://www.act.org/caap/sample/calc.html ACT's CAAP Tests: Use of Calculators on the CAAP Mathematics Test<!-- Bot generated title -->] {{webarchive |url=https://web.archive.org/web/20090831032437/http://www.act.org/caap/sample/calc.html |date=August 31, 2009 }}</ref> though it may be permitted on all of [[College Board]]'s calculator-permitted tests, including the [[SAT]], some [[SAT Subject Tests]] and the [[AP Calculus]], [[AP Chemistry|Chemistry]], [[AP Physics|Physics]], and [[AP Statistics|Statistics]] exams.