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- Algebraic_function abstract "In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions can be expressed using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power: are typical examples. However, some algebraic functions cannot be expressed by such finite expressions (as proven by Galois and Niels Abel), as it is for example the case of the function defined by .In more precise terms, an algebraic function of degree n in one variable x is a function that satisfies a polynomial equation where the coefficients ai(x) are polynomial functions of x, with coefficients belonging to a set S.Quite often, , and one then talks about "function algebraic over ", andthe evaluation at a given rational value of such an algebraic function gives an algebraic number.A function which is not algebraic is called a transcendental function, as it is for example the case of . A composition of transcendental functions can give an algebraic function: .As an equation of degree n has n roots, a polynomial equation does not implicitly define a single function, but nfunctions, sometimes also called branches. Consider for example the equation of the unit circle:This determines y, except only up to an overall sign; accordingly, it has two branches:An algebraic function in m variables is similarly defined as a function y which solves a polynomial equation in m + 1 variables:It is normally assumed that p should be an irreducible polynomial. The existence of an algebraic function is then guaranteed by the implicit function theorem.Formally, an algebraic function in m variables over the field K is an element of the algebraic closure of the field of rational functions K(x1,...,xm).".
- Algebraic_function wikiPageExternalLink algebraic_function.html.
- Algebraic_function wikiPageExternalLink Algebraic_function.
- Algebraic_function wikiPageID "974169".
- Algebraic_function wikiPageRevisionID "597119962".
- Algebraic_function hasPhotoCollection Algebraic_function.
- Algebraic_function id "AlgebraicFunction".
- Algebraic_function title "Algebraic Function".
- Algebraic_function urlname "AlgebraicFunction".
- Algebraic_function subject Category:Analytic_functions.
- Algebraic_function subject Category:Functions_and_mappings.
- Algebraic_function subject Category:Meromorphic_functions.
- Algebraic_function subject Category:Special_functions.
- Algebraic_function subject Category:Types_of_functions.
- Algebraic_function comment "In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions can be expressed using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power: are typical examples.".
- Algebraic_function label "Algebraic function".
- Algebraic_function label "Algebraische Funktion".
- Algebraic_function label "Algebraïsche functie".
- Algebraic_function label "Fonction algébrique".
- Algebraic_function label "Función algebraica".
- Algebraic_function label "Funkcja algebraiczna".
- Algebraic_function label "Funzione algebrica".
- Algebraic_function label "Função algébrica".
- Algebraic_function label "Алгебраическая функция".
- Algebraic_function label "دالة جبرية".
- Algebraic_function label "代數函數".
- Algebraic_function sameAs Algebraische_Funktion.
- Algebraic_function sameAs Función_algebraica.
- Algebraic_function sameAs Fonction_algébrique.
- Algebraic_function sameAs Funzione_algebrica.
- Algebraic_function sameAs Algebraïsche_functie.
- Algebraic_function sameAs Funkcja_algebraiczna.
- Algebraic_function sameAs Função_algébrica.
- Algebraic_function sameAs m.03vs3w.
- Algebraic_function sameAs Q746863.
- Algebraic_function sameAs Q746863.
- Algebraic_function wasDerivedFrom Algebraic_function?oldid=597119962.
- Algebraic_function isPrimaryTopicOf Algebraic_function.