Entire Algebraic Function

An entire algebraic function of n variables is a function that satisfies an equation of the form

y^k + p₁y^k–1 + · · · + p_k = 0

where p₁, . . ., p_k are polynomials in n variables. For example,

is an entire algebraic function, since y² + 2x₁x₂y + 4 = 0.