Symmetries and similarities of planar algebraic curves using harmonic polynomials
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a similarity transformation. Both algorithms are based on the fact, we...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/58574 |
| Acceso en línea: | http://hdl.handle.net/10017/58574 https://dx.doi.org/10.1016/j.cam.2019.02.036 |
| Access Level: | acceso abierto |
| Palabra clave: | Planar algebraic curves Symmetry detection Similarity Harmonic polynomials Dihedral groups Matemáticas Mathematics |
| Sumario: | We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a similarity transformation. Both algorithms are based on the fact, well-known in Harmonic Analysis, that the Laplacian commutes with orthogonal transformations, and on efficient algorithms to find the symmetries / similarities of a harmonic algebraic curve / two given harmonic algebraic curves. In fact, we show that, except for some special cases, the problem can be reduced to the harmonic case. |
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