Fast computation of a rational point of a variety over a finite field

Autores
Cafure, A.; Matera, G.
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety. © 2006 American Mathematical Society.
Fil:Cafure, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Math. Comput. 2006;75(256):2049-2085
Materia
First Bertini theorem
Geometric solutions
Probabilistic algorithms
Rational points
Straight-line programs
Varieties over finite fields
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_00255718_v75_n256_p2049_Cafure
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network_name_str Biblioteca Digital (UBA-FCEN)
spelling Fast computation of a rational point of a variety over a finite fieldCafure, A.Matera, G.First Bertini theoremGeometric solutionsProbabilistic algorithmsRational pointsStraight-line programsVarieties over finite fieldsWe exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety. © 2006 American Mathematical Society.Fil:Cafure, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2006info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00255718_v75_n256_p2049_CafureMath. Comput. 2006;75(256):2049-2085reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-09-29T13:42:54Zpaperaa:paper_00255718_v75_n256_p2049_CafureInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-09-29 13:42:56.193Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Fast computation of a rational point of a variety over a finite field
title Fast computation of a rational point of a variety over a finite field
spellingShingle Fast computation of a rational point of a variety over a finite field
Cafure, A.
First Bertini theorem
Geometric solutions
Probabilistic algorithms
Rational points
Straight-line programs
Varieties over finite fields
title_short Fast computation of a rational point of a variety over a finite field
title_full Fast computation of a rational point of a variety over a finite field
title_fullStr Fast computation of a rational point of a variety over a finite field
title_full_unstemmed Fast computation of a rational point of a variety over a finite field
title_sort Fast computation of a rational point of a variety over a finite field
dc.creator.none.fl_str_mv Cafure, A.
Matera, G.
author Cafure, A.
author_facet Cafure, A.
Matera, G.
author_role author
author2 Matera, G.
author2_role author
dc.subject.none.fl_str_mv First Bertini theorem
Geometric solutions
Probabilistic algorithms
Rational points
Straight-line programs
Varieties over finite fields
topic First Bertini theorem
Geometric solutions
Probabilistic algorithms
Rational points
Straight-line programs
Varieties over finite fields
dc.description.none.fl_txt_mv We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety. © 2006 American Mathematical Society.
Fil:Cafure, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety. © 2006 American Mathematical Society.
publishDate 2006
dc.date.none.fl_str_mv 2006
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/20.500.12110/paper_00255718_v75_n256_p2049_Cafure
url http://hdl.handle.net/20.500.12110/paper_00255718_v75_n256_p2049_Cafure
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Math. Comput. 2006;75(256):2049-2085
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 13.070432

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