Computer algebra: Difference between revisions

Revision as of 08:16, 13 October 2021

Revision as of 05:48, 15 November 2021

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==History==

At the beginning of computer algebra, circa 1970, when the long-known [[algorithm]]s were first put on computers, they turned out to be highly inefficient.<ref>{{Citation|first1=Erich|last1=Kaltofen|chapter=Factorization of polynomials|title=Computer Algebra|publisher=Springer Verlag|year=1982|pages=95–113|editor1-first =B. |editor1-last =Buchberger|editor2-first=R. |editor2-last=Loos|editor3-first=G. |editor3-last=Collins|citeseerx = 10.1.1.39.7916 }}</ref> Therefore, a large part of the work of the researchers in the field consisted in revisiting classical [[algebra]] in order to make it [[Computable function|effective]] and to discover [[algorithmic efficiency|efficient algorithms]] to implement this effectiveness. A typical example of this kind of work is the computation of [[polynomial greatest common divisor]]s, which is required to simplify fractions. Surprisingly, the classical [[Euclid's algorithm]] turned out to be inefficient for polynomials over infinite fields, and thus new algorithms needed to be developed. The same was also true for the classical algorithms from [[linear algebra]].

== See also ==

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*{{cite book|first1=James H.|last1=Davenport|author1-link=James H. Davenport|first2=Yvon|last2=Siret|first3=Èvelyne|last3=Tournier|title=Computer algebra: systems and algorithms for algebraic computation|others=Translated from the French by A. Davenport and J.H. Davenport|year=1988|publisher=Academic Press|isbn=978-0-12-204230-0}}

*{{cite book|first1=Joachim|last1=von zur Gathen|first2=Jürgen|last2=Gerhard|title=Modern computer algebra|edition=second|publisher=Cambridge University Press|year=2003|isbn = 0-521-82646-2}}

*{{Cite journalbook | last1 = Geddes | first1 = K. O. | last2 = Czapor | first2 = S. R. | last3 = Labahn | first3 = G. | doi = 10.1007/b102438 | title = Algorithms for Computer Algebra | year = 1992 | bibcode = 1992afca.book.....G | isbn = 978-0-7923-9259-0 | url-access = registration | url = https://archive.org/details/algorithmsforcom0000gedd }}

*{{Cite journalbook | editor1-last = Buchberger | editor1-first = Bruno | editor2-first = George Edwin | editor3-first = Rüdiger | editor4-first = Rudolf | doi = 10.1007/978-3-7091-7551-4 | title = Computer Algebra | series = Computing Supplementa | volume = 4 | year = 1983 | isbn = 978-3-211-81776-6 | s2cid = 5221892 | editor2-last = Collins | editor3-last = Loos | editor4-last = Albrecht | url-access = registration | url = https://archive.org/details/computeralgebras0000unse }}

{{Computer science}}