Algebraic function

In mathematics, an algebraic function of indeterminates

: X 1, X 2, ..., X n ,

is a function F that satisfies some non-trivial equation

: P ( F , X 1, X 2, ..., X n ) = 0,

with P a polynomial in n + 1 variables over a given field (mathematics) K . That is, F is an implicit function that solves an algebraic equation. A simple example would be

: F ( X ) = √( X 2 + 1).

The class of algebraic functions contains all it is inaccurate to equate polynomials with functions, rather than symbolic expressions; however the term algebraic function is used nonetheless).