Detecting affine equivalences between certain types of parametric curves, in any dimension-Reference-Cited by-同舟云学术

Detecting affine equivalences between certain types of parametric curves, in any dimension

Published:2024 Issue:6 Volume:9 Page:13750-13769
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Alcázar Juan Gerardo¹,Çoban Hüsnü Anıl²,Gözütok Uğur³

Affiliation:

1. Departamento de Física y Matemáticas, Universidad de Alcalá, E-28871 Madrid, Spain

2. Department of Mathematics, Karadeniz Technical University, Trabzon, Türkiye

3. Department of Natural Sciences, National Defence University, İstanbul, Türkiye

Abstract

<abstract><p>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 generalized 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 nonrational but meromorphic components, it admits an also meromorphic, and in fact rational, inverse. Unlike other algorithms already known for rational curves, the algorithm completely avoids polynomial system solving, and instead uses bivariate factoring as a fundamental tool. The algorithm has been implemented in the computer algebra system ${\mathtt{Maple}}$ and can be freely downloaded and used.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference18 articles.

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