Computing the topology of a planar or space hyperelliptic curve

We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of t...

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Autores: Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710, Caravantes Tortajada, Jorge|||0000-0001-9550-2481, Díaz Toca, Gema María, Tsigaridas, Elias
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/58588
Acceso en línea:http://hdl.handle.net/10017/58588
https://dx.doi.org/10.1016/j.cagd.2020.101830
Access Level:acceso abierto
Palabra clave:Hyperelliptic curves
Topology
Birational mappings
Complexity
Algebraic curves
Matemáticas
Mathematics
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spelling Computing the topology of a planar or space hyperelliptic curveAlcázar Arribas, Juan Gerardo|||0000-0002-1665-9710Caravantes Tortajada, Jorge|||0000-0001-9550-2481Díaz Toca, Gema MaríaTsigaridas, EliasHyperelliptic curvesTopologyBirational mappingsComplexityAlgebraic curvesMatemáticasMathematicsWe present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the space. We report on a Mapleimplementation of these algorithms, and present several examples. Complexity and certification issues are also discussed.Agencia Estatal de InvestigaciónAgence Nationale de la RechercheElsevier20202020-03-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/58588https://dx.doi.org/10.1016/j.cagd.2020.101830reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-88796-P COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/585882026-06-18T11:13:07Z
dc.title.none.fl_str_mv Computing the topology of a planar or space hyperelliptic curve
title Computing the topology of a planar or space hyperelliptic curve
spellingShingle Computing the topology of a planar or space hyperelliptic curve
Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Hyperelliptic curves
Topology
Birational mappings
Complexity
Algebraic curves
Matemáticas
Mathematics
title_short Computing the topology of a planar or space hyperelliptic curve
title_full Computing the topology of a planar or space hyperelliptic curve
title_fullStr Computing the topology of a planar or space hyperelliptic curve
title_full_unstemmed Computing the topology of a planar or space hyperelliptic curve
title_sort Computing the topology of a planar or space hyperelliptic curve
dc.creator.none.fl_str_mv Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Caravantes Tortajada, Jorge|||0000-0001-9550-2481
Díaz Toca, Gema María
Tsigaridas, Elias
author Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
author_facet Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Caravantes Tortajada, Jorge|||0000-0001-9550-2481
Díaz Toca, Gema María
Tsigaridas, Elias
author_role author
author2 Caravantes Tortajada, Jorge|||0000-0001-9550-2481
Díaz Toca, Gema María
Tsigaridas, Elias
author2_role author
author
author
dc.subject.none.fl_str_mv Hyperelliptic curves
Topology
Birational mappings
Complexity
Algebraic curves
Matemáticas
Mathematics
topic Hyperelliptic curves
Topology
Birational mappings
Complexity
Algebraic curves
Matemáticas
Mathematics
description We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the space. We report on a Mapleimplementation of these algorithms, and present several examples. Complexity and certification issues are also discussed.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/58588
https://dx.doi.org/10.1016/j.cagd.2020.101830
url http://hdl.handle.net/10017/58588
https://dx.doi.org/10.1016/j.cagd.2020.101830
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-88796-P COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
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