\begin{definition}[Definition:Parametric Equation]
Let $\map \RR {x_1, x_2, \ldots, x_n}$ be a relation on the variables $x_1, x_2, \ldots, x_n$.
Let the truth set of $\RR$ be definable as:
:$\forall k \in \N: 1 \le k \le n: x_k = \map {\phi_k} t$
where:
:$t$ is a variable whose domain is to be defined
:each of $\phi_k$ is a mapping whose domain is the domain of $t$ and whose codomain is the domain of $x_k$.
Then each of:
:$x_k = \map {\phi_k} t$
is a '''parametric equation'''.
The set:
:$\set {\phi_k: 1 \le k \le n}$
is a '''set of parametric equations specifying $\RR$'''.
\end{definition}