Let \(f:\mathbb{K}^{n}\rightarrow \mathbb{K}\) be a polynomial, \(\mathbb{K}= \mathbb{R}\) or \(\mathbb{C}\). The bifurcation set of \(f\) is the smallest set \( B(f)\subset \mathbb{K}\) such that over \(\mathbb{K\diagdown }B(f)\), \(f\) is a \( C^{\infty }\)-fibration. It is known that \(B(f)\) is finite and \(B(f)\subset K_{0}(f)\cup K_{\infty }(f),\) where \(K_{0}(f)\) is the set of critical values of \(f\) and \[ K_{\infty }(f)=\{y\in \mathbb{K}:\exists x_{\nu }\in \mathbb{K}^{n},~x_{\nu }\rightarrow \infty \text{ }s.t.\text{ }f(x_{\nu })\rightarrow \nu ,~\left| \left| x_{\nu }\right| \right| \left| \left| df(x_{\nu })\right| \right| \rightarrow 0\} \] the set of asymptotic critical values of \(f\) (in other words the set where the Malgrange condition fails for \(f).\) The set \(K(f):=K_{0}(f)\cup K_{\infty }(f)\) is called the set of generalized critical values of \(f.\) The authors give an algorithm to compute the set \(K(f)\) in the real and complex case. The algorithm uses a finite dimensional space of rational arcs \(x(t)\) along which we can reach asymptotic critical values of \(f\), namely arcs with parametrizations \(x(t)=\sum_{-D_{1}\leq i\leq D_{2}}a_{i}t^{i},\) \(a_{i}\in \mathbb{K}^{n},\) for appropriate \(D_{1},D_{2}.\)