Implicitly defined in the context of "Dimensionless number"

In mathematics, an implicit equation is a relation of the form ${\displaystyle R(x_{1},\dots ,x_{n})=0,}$ where R is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is ${\displaystyle x^{2}+y^{2}-1=0.}$

An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. For example, the equation ${\displaystyle x^{2}+y^{2}-1=0}$ of the unit circle defines y as an implicit function of x, ${\displaystyle y={\sqrt {1-x^{2}}}}$, assuming −1 ≤ x ≤ 1 and y is restricted to nonnegative values. Some equations do not admit an explicit solution.