Editing Computer algebra system (section)

== Mathematics used in computer algebra systems ==
* [[Knuth–Bendix completion algorithm]]<ref name="BuchbergerCollins2013"/>
* [[Root-finding algorithm]]s<ref name="BuchbergerCollins2013">{{cite book|author1=B. Buchberger|author2=G.E. Collins|author3=R. Loos|title=Computer Algebra: Symbolic and Algebraic Computation|url=https://books.google.com/books?id=yUmqCAAAQBAJ&q=%22algorithm%22|date=29 June 2013|publisher=Springer Science & Business Media|isbn=978-3-7091-3406-1}}</ref>
* [[Symbolic integration]] via e.g. [[Risch algorithm]] or [[Risch–Norman algorithm]]
* [[Hypergeometric summation]] via e.g. [[Gosper's algorithm]]
* [[Limit (mathematics)|Limit computation]] via e.g. Gruntz's algorithm
* [[Polynomial factorization]] via e.g., over finite fields,<ref name="GathenGerhard2013">{{cite book|author1=Joachim von zur Gathen|author2=Jürgen Gerhard|title=Modern Computer Algebra|url=https://books.google.com/books?id=7fE9baKyqSEC&q=%22polynomial+factorization%22+%22finite+field%22|date=25 April 2013|publisher=Cambridge University Press|isbn=978-1-107-03903-2}}</ref> [[Berlekamp's algorithm]] or [[Cantor–Zassenhaus algorithm]].
* [[Greatest common divisor]] via e.g. [[Euclidean algorithm]]
* [[Gaussian elimination]]<ref name="GeddesCzapor2007">{{cite book|author1=Keith O. Geddes|author2=Stephen R. Czapor|author3=George Labahn|title=Algorithms for Computer Algebra|url=https://books.google.com/books?id=9fOUwkkRxT4C|date=30 June 2007|publisher=Springer Science & Business Media|isbn=978-0-585-33247-5}}</ref>
* [[Gröbner basis]] via e.g. [[Buchberger's algorithm]]; generalization of Euclidean algorithm and Gaussian elimination
* [[Padé approximant]]
* [[Schwartz–Zippel lemma]] and testing polynomial identities
* [[Chinese remainder theorem]]
* [[Diophantine equation]]s
* [[Landau's algorithm]] (nested radicals)
* 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 cylindrical algebraic decomposition