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A large part of the work of researchers in the field consisted of revisiting classical [[algebra]] to increase its [[Computable function|effectiveness]] while developing [[Algorithmic efficiency|efficient algorithms]] for use in computer algebra. An example of this type of work is the computation of [[Polynomial greatest common divisor|polynomial greatest common divisors]], a task required to simplify fractions and an essential component of computer algebra. Classical algorithms for this computation, such as [[Euclidean algorithm|Euclid's algorithm]], provided inefficient over infinite fields; algorithms from [[linear algebra]] faced similar struggles.<ref>{{Citation |last=Kaltofen |first=E. |title=Factorization of Polynomials |date=1983 |url=http://link.springer.com/10.1007/978-3-7091-7551-4_8 |work=Computer Algebra |volume=4 |pages=95–113 |editor-last=Buchberger |editor-first=Bruno |access-date=2023-11-29 |place=Vienna |publisher=Springer Vienna |doi=10.1007/978-3-7091-7551-4_8 |isbn=978-3-211-81776-6 |editor2-last=Collins |editor2-first=George Edwin |editor3-last=Loos |editor3-first=Rüdiger |editor4-last=Albrecht |editor4-first=Rudolf}}</ref> Thus, researchers turned to discovering methods of reducing polynomials (such as those over a [[ring of integers]] or a [[unique factorization ___domain]]) to a variant efficiently computable via a Euclidian algorithm.
== Algorithms used in computer algebra ==
{{excerpt|List of algorithms|Computer algebra}}
== See also ==
* [[Automated theorem prover]]
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