Computation of symmetries of rational surfaces
In this paper, we provided, 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., tor...
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| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024282 |
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| author | Juan Gerardo Alcázar Carlos Hermoso Hüsnü Anıl Çoban Uğur Gözütok |
| author_facet | Juan Gerardo Alcázar Carlos Hermoso Hüsnü Anıl Çoban Uğur Gözütok |
| author_sort | Juan Gerardo Alcázar |
| collection | DOAJ |
| description | In this paper, we provided, 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 provided a specific, and 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. |
| format | Article |
| id | doaj-art-3e2486fd2bbc4b0ba8c9e1c6c6829d83 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-3e2486fd2bbc4b0ba8c9e1c6c6829d832025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132116087610810.3934/era.2024282Computation of symmetries of rational surfacesJuan Gerardo Alcázar0Carlos Hermoso1Hüsnü Anıl Çoban2Uğur Gözütok3Departamento de Física y Matemáticas, Universidad de Alcalá, E-28871 Madrid, SpainDepartamento de Física y Matemáticas, Universidad de Alcalá, E-28871 Madrid, SpainDepartment of Mathematics, Karadeniz Technical University, Trabzon, TürkiyeDepartment of Natural Sciences, National Defence University, Istanbul, TürkiyeIn this paper, we provided, 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 provided a specific, and 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.https://www.aimspress.com/article/doi/10.3934/era.2024282rational surfacesruled surfacessymmetry detectionsymbolic computationdifferential invariants |
| spellingShingle | Juan Gerardo Alcázar Carlos Hermoso Hüsnü Anıl Çoban Uğur Gözütok Computation of symmetries of rational surfaces Electronic Research Archive rational surfaces ruled surfaces symmetry detection symbolic computation differential invariants |
| title | Computation of symmetries of rational surfaces |
| title_full | Computation of symmetries of rational surfaces |
| title_fullStr | Computation of symmetries of rational surfaces |
| title_full_unstemmed | Computation of symmetries of rational surfaces |
| title_short | Computation of symmetries of rational surfaces |
| title_sort | computation of symmetries of rational surfaces |
| topic | rational surfaces ruled surfaces symmetry detection symbolic computation differential invariants |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024282 |
| work_keys_str_mv | AT juangerardoalcazar computationofsymmetriesofrationalsurfaces AT carloshermoso computationofsymmetriesofrationalsurfaces AT husnuanılcoban computationofsymmetriesofrationalsurfaces AT ugurgozutok computationofsymmetriesofrationalsurfaces |