Effective computation of singularities of parametric affine curves |
| |
Authors: | Hyungju Park |
| |
Institution: | Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA |
| |
Abstract: | Let k be a field of characteristic zero and f(t),g(t) be polynomials in kt]. For a plane curve parameterized by x=f(t),y=g(t), Abhyankar developed the notion of Taylor resultant (Mathematical Surveys and Monographs, Vol. 35, American Mathematical Society, Providence, RI, 1990) which enables one to find its singularities without knowing its defining polynomial. This concept was generalized as D-resultant by Yu and Van den Essen (Proc. Amer. Math. Soc. 125(3) (1997) 689), which works over an arbitrary field. In this paper, we extend this to a curve in affine n-space parameterized by x1=f1(t),…,xn=fn(t) over an arbitrary ground field k, where f1,…,fn∈kt]. This approach compares to the usual approach of computing the ideal of the curve first. It provides an efficient algorithm of computing the singularities of such parametric curves using Gröbner bases. Computational examples worked out by symbolic computation packages are included. |
| |
Keywords: | 13P10 14Q05 |
本文献已被 ScienceDirect 等数据库收录! |
|