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→Mathematics used in computer algebra systems: Tarski method is too inefficient for having ever been implemented |
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== History ==
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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.
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]].
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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>
==Symbolic manipulations==
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*[[Application programming interface|APIs]] for linking it on an external program such as a database, or using in a programming language to use the computer algebra system
*[[string manipulation]] such as [[string matching|matching]] and [[string searching|searching]]
*add-ons for use in [[applied mathematics]] such as physics, [[bioinformatics]], [[computational chemistry]] and packages for [[computational physics|physical computation]]<ref>{{Cite
*solvers for [[differential equation]]s<ref>{{Cite web|title=dsolve - Maple Programming Help|url=https://www.maplesoft.com/support/help/Maple/view.aspx?path=dsolve|website=www.maplesoft.com|access-date=2020-05-09}}</ref><ref>{{Cite web|title=DSolve - Wolfram Language Documentation|url=https://reference.wolfram.com/language/ref/DSolve.html|website=www.wolfram.com|access-date=2020-06-28}}</ref><ref>{{Cite web|title=Basic Algebra and Calculus — Sage Tutorial v9.0|url=http://doc.sagemath.org/html/en/tutorial/tour_algebra.html|website=doc.sagemath.org|access-date=2020-05-09}}</ref><ref>{{Cite web|title=Symbolic algebra and Mathematics with Xcas|url=http://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf}}</ref>
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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|date=15 November 2010 |access-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|access-date=12 August 2017}}</ref>
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* Derivatives of [[elementary function]]s and [[special functions]]. (e.g. See [[derivatives of the incomplete gamma function]].)
* [[Cylindrical algebraic decomposition]]
* [[Quantifier elimination]] over real numbers via
==See also==
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