Detecting Affine Equivalences and Symmetries of Implicit Plane Algebraic Curves

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Atıf İçin Kopyala

Alcázar J. G., Gözütok U., Çoban H. A., Hermoso C.

9th International Congress on Fundamental and Applied Sciences 2022 (ICFAS2022) , İstanbul, Türkiye, 28 - 30 Haziran 2022, cilt.1, ss.115

• Yayın Türü: Bildiri / Özet Bildiri
• Cilt numarası: 1
• Basıldığı Şehir: İstanbul
• Basıldığı Ülke: Türkiye
• Sayfa Sayıları: ss.115
• Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

We present a computational method to detect affine equivalences of implicit plane algebraic curves. The method proceeds by first reducing the problem to the case of affine equivalences where the orgin is fixed, using the Hessian curves of the input curves. Then, the Hessian is again used to derive certain differential invariants that allow us to compute the components of the equivalences by just using resultants and polynomial factoring. In special cases, for instance curves with infinitely many self-affine equivalences, equivalences are computed using a more direct method involving polynomial system solving, but with polynomials of smaller degree. A comparison of the algorithm with other methods, including brute force, is also given.