Symmetries and similarities of planar algebraic curves using harmonic polynomials
| dc.contributor.author | Alcazar, Juan Gerardo | |
| dc.contributor.author | Lávička, Miroslav | |
| dc.contributor.author | Vršek, Jan | |
| dc.date.accessioned | 2019-06-24T10:00:10Z | |
| dc.date.available | 2019-06-24T10:00:10Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract-translated | 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. | en |
| dc.format | 17 s. | cs |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | ALCAZAR, J. G., LÁVIČKA, M., VRŠEK, J. Symmetries and similarities of planar algebraic curves using harmonic polynomials. Journal of computational and applied mathematics, 2019, roč. 357, č. September 2019, s. 302-318. ISSN 0377-0427. | en |
| dc.identifier.document-number | 465168400019 | |
| dc.identifier.doi | 10.1016/j.cam.2019.02.036 | |
| dc.identifier.issn | 0377-0427 | |
| dc.identifier.obd | 43926030 | |
| dc.identifier.uri | 2-s2.0-85062972111 | |
| dc.identifier.uri | http://hdl.handle.net/11025/34823 | |
| dc.language.iso | en | en |
| dc.project.ID | LO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnost | cs |
| dc.publisher | Elsevier | en |
| dc.relation.ispartofseries | Journal Of Computational And Applied Mathematics | en |
| dc.rights | Plný text je přístupný v rámci univerzity přihlášeným uživatelům. | cs |
| dc.rights | © Elsevier | en |
| dc.rights.access | restrictedAccess | en |
| dc.subject.translated | Planar algebraic curves | en |
| dc.subject.translated | Symmetry detection | en |
| dc.subject.translated | Similarity | en |
| dc.subject.translated | Harmonic polynomials | en |
| dc.subject.translated | Dihedral groups | en |
| dc.title | Symmetries and similarities of planar algebraic curves using harmonic polynomials | en |
| dc.type | preprint | cs |
| dc.type | preprint | en |
| dc.type.version | draft | en |