Detecting isometries and symmetries of implicit algebraic surfaces

Gözütok U., Çoban H. A.

AIMS Mathematics, cilt.9, sa.2, ss.4294-4308, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3934/math.2024212
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.4294-4308
  • Anahtar Kelimeler: computer algebra, equivalences, implicit surfaces, isometries, symmetries
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

We presented a new and complete algorithm for detecting isometries and symmetries of implicit algebraic surfaces. First, our method reduced the problem to the case of isometries fixing the origin. Second, using tools from elimination theory and polynomial factoring, we determined the desired isometries between the surfaces. We have implemented the algorithm in Maple to provide evidences of the efficiency of the method.