Detecting isometries and symmetries of implicit algebraic surfaces

Gözütok U., Çoban H. A.

AIMS Mathematics, vol.9, no.2, pp.4294-4308, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.3934/math.2024212
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.4294-4308
  • Keywords: computer algebra, equivalences, implicit surfaces, isometries, symmetries
  • Karadeniz Technical University Affiliated: Yes


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.