Effective computation of singularities of parametric affine curves (Q1612159)

Given a parametric affine curve \(\phi:C\to {\mathbb A}^n_K\), defined by polynomials \(f_1(t),\dots,f_n(t)\), the author introduces a new method for determining if the parametrization is birational or an immersion. The proof is based on the observation that \(\phi\) is birational (respectively, an immersion) when the locus of the polynomials: \[ g_i(t,s)={{f_i(t)-f_i(s)}\over {(t-s)}} \] is finite (respectively, empty). With respect to previously known methods, this one has the advantage of using Gröbner basis computations with just two variables.