Bipolar varieties and real solving of a singular polynomial equation

Autores
Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Pardo, Luis Miguel
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of the given hypersurface and in this sense intrinsic.
Fil: Bank, Bernd. Universität zu Berlin; Alemania
Fil: Giusti, Marc. Centre National de la Recherche Scientifique; Francia
Fil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pardo, Luis Miguel. Universidad de Cantabria; España
Materia
Real Polynomial Equation Solving
Singular Hypersurface
Polar Variety
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/16377
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/16377
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Bipolar varieties and real solving of a singular polynomial equationBank, BerndGiusti, MarcHeintz, Joos UlrichPardo, Luis MiguelReal Polynomial Equation SolvingSingular HypersurfacePolar Varietyhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of the given hypersurface and in this sense intrinsic.Fil: Bank, Bernd. Universität zu Berlin; AlemaniaFil: Giusti, Marc. Centre National de la Recherche Scientifique; FranciaFil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pardo, Luis Miguel. Universidad de Cantabria; EspañaUniversidad de Jaén2010-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16377Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Pardo, Luis Miguel; Bipolar varieties and real solving of a singular polynomial equation; Universidad de Jaén; Jaen Journal of Approximation; 2; 1; 3-2010; 79-911889-30661989-7251enginfo:eu-repo/semantics/altIdentifier/url/http://www.ujaen.es/revista/jja/volumes-papers-0002-01.phpinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:45:33Zoai:ri.conicet.gov.ar:11336/16377instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:45:33.459CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Bipolar varieties and real solving of a singular polynomial equation
title Bipolar varieties and real solving of a singular polynomial equation
spellingShingle Bipolar varieties and real solving of a singular polynomial equation
Bank, Bernd
Real Polynomial Equation Solving
Singular Hypersurface
Polar Variety
title_short Bipolar varieties and real solving of a singular polynomial equation
title_full Bipolar varieties and real solving of a singular polynomial equation
title_fullStr Bipolar varieties and real solving of a singular polynomial equation
title_full_unstemmed Bipolar varieties and real solving of a singular polynomial equation
title_sort Bipolar varieties and real solving of a singular polynomial equation
dc.creator.none.fl_str_mv Bank, Bernd
Giusti, Marc
Heintz, Joos Ulrich
Pardo, Luis Miguel
author Bank, Bernd
author_facet Bank, Bernd
Giusti, Marc
Heintz, Joos Ulrich
Pardo, Luis Miguel
author_role author
author2 Giusti, Marc
Heintz, Joos Ulrich
Pardo, Luis Miguel
author2_role author
author
author
dc.subject.none.fl_str_mv Real Polynomial Equation Solving
Singular Hypersurface
Polar Variety
topic Real Polynomial Equation Solving
Singular Hypersurface
Polar Variety
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of the given hypersurface and in this sense intrinsic.
Fil: Bank, Bernd. Universität zu Berlin; Alemania
Fil: Giusti, Marc. Centre National de la Recherche Scientifique; Francia
Fil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pardo, Luis Miguel. Universidad de Cantabria; España
description We introduce the concept of a bipolar variety of a real algebraic hypersurface. This notion is then used for the design and complexity estimations of a novel type of algorithms that finds algebraic sample points for the connected components of a singular real hypersurface. The complexity of these algorithms is polynomial in the maximal geometric degree of the bipolar varieties of the given hypersurface and in this sense intrinsic.
publishDate 2010
dc.date.none.fl_str_mv 2010-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/16377
Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Pardo, Luis Miguel; Bipolar varieties and real solving of a singular polynomial equation; Universidad de Jaén; Jaen Journal of Approximation; 2; 1; 3-2010; 79-91
1889-3066
1989-7251
url http://hdl.handle.net/11336/16377
identifier_str_mv Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Pardo, Luis Miguel; Bipolar varieties and real solving of a singular polynomial equation; Universidad de Jaén; Jaen Journal of Approximation; 2; 1; 3-2010; 79-91
1889-3066
1989-7251
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ujaen.es/revista/jja/volumes-papers-0002-01.php
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universidad de Jaén
publisher.none.fl_str_mv Universidad de Jaén
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842268738973335552
score 13.13397

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