In this paper, we use Tarski-Seidenberg algorithm (for deciding the first order theory of real numbers) to design an algorithm that, given a polynomial mapping φ: C^{k} --> C^{n} which is known to be rectifiable, returns a polynomial mapping α: C^{n} --> C^{n} that rectifies φ.

The above general algorithm is not practical for large n, since its computation time grows faster than 2^{(2n)}. To make computations more practically useful, for several important case, we have also designed a much faster alternative algorithm.