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TitleRecognizing and parametrizing curves isomorphic to a line
Author(s) Chi-Ming Lam, Vladimir Shpilrain, Jie-Tai Yu
TypeArticle in Journal
AbstractSome 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.
KeywordsPolynomial algebras, Automorphisms, Parametrization, Plane curves, Complexity
URL http://www.sciencedirect.com/science/article/pii/S0747717107000429
JournalJournal of Symbolic Computation
Pages751 - 756
Translation No
Refereed No