An implicit function defines a relationship between two (or more) variables differently from an explicit function. As opposed to an explicit function that can be written in the form of
\begin{equation*}
y = f(x)\text{,}
\end{equation*}
an implicit function is defined as an equation of multiple variables. It is often the case that this equation cannot be solved for one variable explicitly in terms of the other. In Maple, it is easiest to assign a name to the entire equation, including the \(=\) sign.
The elliptic curve \(y^2 = x^3 - 2*x + 1\) is a simple example. It cannot be written as a single function of the form \(y = f(x)\text{,}\) since for a given value of \(x\text{,}\) there may be two different \(y\)-values.
Although many implicit functions cannot be expressed as a single function \(y=f(x)\text{,}\) it may be possible to split up implicit functions into explicit functions by solving for \(y\text{.}\)
