Detecting affine equivalences between implicit planar algebraic curves
type: Item
instance of: scholarly article
title: Detecting affine equivalences between implicit planar algebraic curves
zbMATH Open document ID: 1504.14102
author: Juan Gerardo Alcazar
author: Uğur Gözütok
author: Hüsnü Anıl Çoban
author: Carlos Hermoso
published in: Acta Applicandae Mathematicae
publication date: 2022-12-08T00:00:00Z
review text: The authors present an algorithm that computes the affine equivalences between two planar algebraic curves defined implicitly. It is shown the efficiency of the algorithm which is implemented in Maple. Furthermore, they compare its performance with existing algorithms. As a consequence of the method and techniques used in this paper, additionally the authors provide a detailed proof of the characterization of curves invariant under infinitely many affine equivalences.
reviewed by: Sonia Pérez Díaz
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 14H50
zbMATH DE Number: 7629801
zbMATH Keywords: affine equivalences
zbMATH Keywords: planar algebraic curves
zbMATH Keywords: implicit curves
zbMATH Keywords: algorithms
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: s10440-022-00539-1
OpenAlex ID: W4308410961
cites work: Efficient detection of symmetries of polynomially parametrized curves
cites work: Detecting similarity of rational plane curves
cites work: Symmetry detection of rational space curves from their curvature and torsion
cites work: Symmetries and similarities of planar algebraic curves using harmonic polynomials
cites work: Affine equivalences of trigonometric curves
cites work: Computing projective equivalences of planar curves birationally equivalent to elliptic and hyperelliptic curves
cites work: Automorphism Groups of Nonsingular Plane Curves of Degree 5
cites work: Computing projective equivalences of special algebraic varieties
cites work: Symmetries of discrete curves and point clouds via trigonometric interpolation
cites work: Approximate symmetries of planar algebraic curves with inexact input
cites work: Q4502840
cites work: On automorphisms of algebraic curves
cites work: Q4190739
cites work: Plane algebraic curves. Transl. from the German by Leslie Kay
cites work: Mathematics of public key cryptography.
cites work: A new method to detect projective equivalences and symmetries of rational \(3 D\) curves
cites work: Automorphism groups of smooth plane curves
cites work: Projective and affine symmetries and equivalences of rational curves in arbitrary dimension
cites work: Projective and affine symmetries and equivalences of rational and polynomial surfaces
cites work: Projective isomorphisms between rational surfaces
cites work: Rotations, translations and symmetry detection for complexified curves
cites work: Rational algebraic curves. A computer algebra approach
DOI: 10.1007/S10440-022-00539-1
description: scientific article; zbMATH DE number 7629801