Using μ-bases to reduce the degree in the computation of projective equivalences between rational curves in n-space

Abstract

We study how projective equivalences between rational curves in Rn are transferred to the elements of smallest degree of the μ-bases of the curves. We show how to compute these elements of smallest degree without computing the whole μ-basis, and prove some results on the degrees of μ-bases of curves in Rn. As a result, we provide a way to reduce the cost of computing the projective equivalences between rational curves in Rn by replacing the given curves for the curves represented by the elements of smallest degree of the μ-bases of the curves, which have a much smaller degree compared to the original degree of the curves.