Detecting affine equivalences between certain types of parametric curves, in any dimension
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914729247637504 |
|---|---|
| author | Alcázar, Juan Gerardo Çoban, Hüsnü Anıl Gözütok, Uğur |
| author_facet | Alcázar, Juan Gerardo Çoban, Hüsnü Anıl Gözütok, Uğur |
| contents | Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In this paper we generalize previous results by the authors to provide an algorithm for computing the affine equivalences between two parametric curves of certain types, in any dimension. In more detail, the algorithm is valid for rational curves, and for parametric curves with non-rational but meromorphic components admitting a rational inverse. Unlike other algorithms already known for rational curves, the algorithm completely avoids polynomial system solving, and uses bivariate factoring, instead, as a fundamental tool. The algorithm has been implemented in the computer algebra system {\tt Maple}, and can be freely downloaded and used. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detecting affine equivalences between certain types of parametric curves, in any dimension Alcázar, Juan Gerardo Çoban, Hüsnü Anıl Gözütok, Uğur Algebraic Geometry Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In this paper we generalize previous results by the authors to provide an algorithm for computing the affine equivalences between two parametric curves of certain types, in any dimension. In more detail, the algorithm is valid for rational curves, and for parametric curves with non-rational but meromorphic components admitting a rational inverse. Unlike other algorithms already known for rational curves, the algorithm completely avoids polynomial system solving, and uses bivariate factoring, instead, as a fundamental tool. The algorithm has been implemented in the computer algebra system {\tt Maple}, and can be freely downloaded and used. |
| title | Detecting affine equivalences between certain types of parametric curves, in any dimension |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.16636 |