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

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 pr...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 6; pp. 13750 - 13769
Main Authors Alcázar, Juan Gerardo, Çoban, Hüsnü Anıl, Gözütok, Uğur
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
affine equivalence
algorithm
rational parametrization
symbolic computation
symmetry
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024670