In mathematics, an implicit equation is a relation of the form R(x₁,..., x_n) = 0, where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is

An implicit function is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) with the others (the arguments). Thus, an implicit function for y in the context of the unit circle is defined implicitly by . This implicit equation defines f as a function of x only if -1 ≤ x ≤ 1 and one considers only non-negative (or non-positive) values for the values of the function.