Optimal Reparametrization of polynomial algebraic curves

摘要

In this paper, we present an algorithm for optimally parametrizing polynomial algebraic curves. Let C be a polynomial plane algebraic curve given by a polynomial parametrization P(t) ∈ L[≈]~≠, where L is a finite field extension of a field K of characteristic zero. We prove that if C is polynomial over K, then Weil's descente variety associated with P(t) is surprisingly simple; it is, in fact, a line. Applying this result we are able to derive an effective algorithm to algebraically optimal reparametrize polynomial algebraic curves.