2024/10/24 by Juan Juan Gerardo Alcázar, Carlos Hermoso, Alcázar, Juan Juan Gerardo +5
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry (math.AG) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2410.18609
openalex publication_date 2024/10/24 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/31
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the algorithm works well for sparse parametrizations (e.g. toric surfaces) and PN surfaces. Additionally, we provide a specific, also symbolic algorithm for computing the symmetries of ruled surfaces; this algorithm works extremely well in practice, since the problem is reduced to that of rational space curves, which can be efficiently solved by using existing methods. The algorithm for ruled surfaces is based on the fact, proven in the paper, that every symmetry of a rational surface must also be a symmetry of its line of striction, which is a rational space curve. The algorithms have been implemented in the computer algebra system Maple, and the implementations have been made public; evidence of their performance is given in the paper.