Details:
| Title | Recognizing and parametrizing curves isomorphic to a line | | Author(s) | Chi-Ming Lam, Vladimir Shpilrain, Jie-Tai 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 | 0747-7171 |
| 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 |
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