On the complexity of some birational transformations
| Autor: | Jean Christian Angles D'Auriac, Claude M. Viallet, J.-M. Maillard |
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| Přispěvatelé: | Centre de Recherches sur les Très Basses Températures (CRTBT), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique des Liquides (LPTL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2006 |
| Předmět: |
Polynomial
Pure mathematics math-ph [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences General Physics and Astronomy 01 natural sciences Square matrix Domain (mathematical analysis) Matrix (mathematics) math.MP Integer Simple (abstract algebra) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0103 physical sciences Physical Sciences and Mathematics 0101 mathematics 010306 general physics Mathematical Physics Mathematics Conjecture nlin.CD 010102 general mathematics Univariate Statistical and Nonlinear Physics Mathematical Physics (math-ph) Nonlinear Sciences - Chaotic Dynamics [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] Chaotic Dynamics (nlin.CD) |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical Journal of Physics A: Mathematical and Theoretical, 2006, 39, pp.3641. ⟨10.1088/0305-4470/39/14/009⟩ Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2006, 39, pp.3641. ⟨10.1088/0305-4470/39/14/009⟩ D'Auriac, Jean Christian Angles; Maillard, Jean-Marie; & Viallet, Claude. (2005). On the complexity of some birational transformations. Journal of Physics A Mathematical and Theoretical 39 (2006) 3641. doi: 10.1088/0305-4470/39/14/009. UC Davis: Retrieved from: http://www.escholarship.org/uc/item/7bg0k2m0 |
| ISSN: | 1361-6447 0305-4470 1751-8113 1751-8121 |
| DOI: | 10.1088/0305-4470/39/14/009 |
| Popis: | Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions. |
| Databáze: | OpenAIRE |
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