Detecting Affine Equivalences Between Implicit Planar Algebraic Curves

Gerardo Alcazar J., GÖZÜTOK U., ÇOBAN H. A., Hermoso C.

ACTA APPLICANDAE MATHEMATICAE, vol.182, no.1, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 182 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1007/s10440-022-00539-1
  • Journal Name: ACTA APPLICANDAE MATHEMATICAE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Compendex, MathSciNet, DIALNET, Civil Engineering Abstracts
  • Keywords: Affine equivalences, Planar algebraic curves, Implicit curves, Algorithms, SYMMETRIES
  • Karadeniz Technical University Affiliated: Yes

Abstract

We present a complete algorithm for computing the affine equivalences between two implicit planar algebraic curves. We provide evidence of the efficiency of the algorithm, implemented in Maple, and compare its performance with existing algorithms. As a part of the process for developing the algorithm, we characterize planar algebraic curves, possibly singular, possibly reducible, invariant under infinitely many affine equivalences.