Given an equation
$$f(\vec x) = 0$$
in $n$ variables (and some constraint $\vec x\in X\subseteq\mathbb R^n$), what is the hypersurface of the $n-1$ dimensional submanifold $\{\vec x\in X: f(\vec x)=0\}$?
I am not necessarily asking for a (probably non-existing) analytical formula, some integral involving $\delta(f(\vec x))$ would already do, or an algorithm.
edit If solved for one of the $x_i$, this boils down to a related question, but is there a more general formula?
