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In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Examples of such functions are: * * * Some algebraic functions, however, cannot be expressed by such finite expressions (this is the Abel–Ruffini theorem). This is the case, for example, for the Bring radical, which is the function implicitly defined by .

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