Algorithms for Determining Birationality of Parametrization of Affine Curves
| dc.creator | Park, Hyungju | |
| dc.date | 1998-05-11 | |
| dc.date | 1998-05-18 | |
| dc.date.accessioned | 2026-07-07T05:24:45Z | |
| dc.date.available | 2026-07-07T05:24:45Z | |
| dc.description | Let $k$ be an arbitrary field, and C be a curve in A^n defined parametrically by x_1=f_1(t),...,x_n=f_n(t), where f_1,...,f_n\in k[t]. A necessary and sufficient condition for the two function fields k(t) and k(f_1,...,f_n) to be same is developed in terms of zero-dimensionality of a derived ideal in the bivariate polynomial ring k[s,t]. Since zero-dimensionality of such an ideal can be readily determined by a Groebner basis computation, this gives an algorithm that determines if the parametrization ψ=(f_1,...,f_n): A --> C is a birational equivalence. We also develop an algorithm that determines if k[t] and k[f_1,...,f_n] are same, by which we get an algorithm that determines if the parametrization ψ=(f_1,...,f_n): A --> C is an isomorphism. We include some computational examples showing the application of these algorithms. | |
| dc.description | Latex2e file, 12 pages. Some proofs are improved. A misuse of terminology is corrected | |
| dc.identifier | https://arxiv.org/abs/math/9805053 | |
| dc.identifier | http://arxiv.org/abs/math/9805053 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76921 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13P10 | |
| dc.title | Algorithms for Determining Birationality of Parametrization of Affine Curves | |
| dc.type | text |