Details:
Title  Recognizing and parametrizing curves isomorphic to a line  Author(s)  ChiMing Lam, Vladimir Shpilrain, JieTai Yu  Type  Article in Journal  Abstract  Some time ago, Shpilrain and Yu reported an algorithm for deciding whether or not a polynomial p ∈ K [ x , y ] is a coordinate, or, equivalently, whether or not a plane curve p ( x , y ) = 0 is isomorphic to a line. Here K is any constructible field of characteristic 0. In this paper, we show that their algorithm requires O ( n^2 ) field operations, where n is the degree of a given polynomial. We also show how their algorithm can be used to find a polynomial parametrization of a plane curve p ( x , y ) = 0 which is isomorphic to a line. This requires O ( n^2 log^2 n ) field operations.  Keywords  Polynomial algebras, Automorphisms, Parametrization, Plane curves, Complexity  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717107000429 
Language  English  Journal  Journal of Symbolic Computation  Volume  42  Number  7  Pages  751  756  Year  2007  Edition  0  Translation 
No  Refereed 
No 
