Detecting Affine Equivalences Between Implicit Planar Algebraic Curves

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

ACTA APPLICANDAE MATHEMATICAE, cilt.182, sa.1, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 182 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10440-022-00539-1
  • Dergi Adı: ACTA APPLICANDAE MATHEMATICAE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Compendex, MathSciNet, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Affine equivalences, Planar algebraic curves, Implicit curves, Algorithms, SYMMETRIES
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.