Parallel algorithms for normalization

Autores
Böhm, J.; Decker, W.; Laplagne, S.; Pfister, G.; Steenpaß, A.; Steidel, S.
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a reduced affine algebra A over a perfect field K, we present parallel algorithms to compute the normalization Ā of A. Our starting point is the algorithm of Greuel et al. (2010), which is an improvement of de Jong's algorithm (de Jong, 1998; Decker et al., 1999). First, we propose to stratify the singular locus Sing(A) in a way which is compatible with normalization, apply a local version of the normalization algorithm at each stratum, and find Ā by putting the local results together. Second, in the case where K=Q is the field of rationals, we propose modular versions of the global and local-to-global algorithms. We have implemented our algorithms in the computer algebra system Singular and compare their performance with that of the algorithm of Greuel et al. (2010). In the case where K=Q, we also discuss the use of modular computations of Gröbner bases, radicals, and primary decompositions. We point out that in most examples, the new algorithms outperform the algorithm of Greuel et al. (2010) by far, even if we do not run them in parallel. © 2012 Elsevier B.V.
Fil:Laplagne, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Symb. Comput. 2013;51:99-114
Materia
Grauert-Remmert criterion
Integral closure
Modular computation
Normalization
Parallel computation
Test ideal
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_07477171_v51_n_p99_Bohm

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network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Parallel algorithms for normalizationBöhm, J.Decker, W.Laplagne, S.Pfister, G.Steenpaß, A.Steidel, S.Grauert-Remmert criterionIntegral closureModular computationNormalizationParallel computationTest idealGiven a reduced affine algebra A over a perfect field K, we present parallel algorithms to compute the normalization Ā of A. Our starting point is the algorithm of Greuel et al. (2010), which is an improvement of de Jong's algorithm (de Jong, 1998; Decker et al., 1999). First, we propose to stratify the singular locus Sing(A) in a way which is compatible with normalization, apply a local version of the normalization algorithm at each stratum, and find Ā by putting the local results together. Second, in the case where K=Q is the field of rationals, we propose modular versions of the global and local-to-global algorithms. We have implemented our algorithms in the computer algebra system Singular and compare their performance with that of the algorithm of Greuel et al. (2010). In the case where K=Q, we also discuss the use of modular computations of Gröbner bases, radicals, and primary decompositions. We point out that in most examples, the new algorithms outperform the algorithm of Greuel et al. (2010) by far, even if we do not run them in parallel. © 2012 Elsevier B.V.Fil:Laplagne, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2013info: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_07477171_v51_n_p99_BohmJ. Symb. Comput. 2013;51:99-114reponame: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/ar2025-09-29T13:43:06Zpaperaa:paper_07477171_v51_n_p99_BohmInstitucionalhttps://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 13:43:07.456Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Parallel algorithms for normalization
title Parallel algorithms for normalization
spellingShingle Parallel algorithms for normalization
Böhm, J.
Grauert-Remmert criterion
Integral closure
Modular computation
Normalization
Parallel computation
Test ideal
title_short Parallel algorithms for normalization
title_full Parallel algorithms for normalization
title_fullStr Parallel algorithms for normalization
title_full_unstemmed Parallel algorithms for normalization
title_sort Parallel algorithms for normalization
dc.creator.none.fl_str_mv Böhm, J.
Decker, W.
Laplagne, S.
Pfister, G.
Steenpaß, A.
Steidel, S.
author Böhm, J.
author_facet Böhm, J.
Decker, W.
Laplagne, S.
Pfister, G.
Steenpaß, A.
Steidel, S.
author_role author
author2 Decker, W.
Laplagne, S.
Pfister, G.
Steenpaß, A.
Steidel, S.
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Grauert-Remmert criterion
Integral closure
Modular computation
Normalization
Parallel computation
Test ideal
topic Grauert-Remmert criterion
Integral closure
Modular computation
Normalization
Parallel computation
Test ideal
dc.description.none.fl_txt_mv Given a reduced affine algebra A over a perfect field K, we present parallel algorithms to compute the normalization Ā of A. Our starting point is the algorithm of Greuel et al. (2010), which is an improvement of de Jong's algorithm (de Jong, 1998; Decker et al., 1999). First, we propose to stratify the singular locus Sing(A) in a way which is compatible with normalization, apply a local version of the normalization algorithm at each stratum, and find Ā by putting the local results together. Second, in the case where K=Q is the field of rationals, we propose modular versions of the global and local-to-global algorithms. We have implemented our algorithms in the computer algebra system Singular and compare their performance with that of the algorithm of Greuel et al. (2010). In the case where K=Q, we also discuss the use of modular computations of Gröbner bases, radicals, and primary decompositions. We point out that in most examples, the new algorithms outperform the algorithm of Greuel et al. (2010) by far, even if we do not run them in parallel. © 2012 Elsevier B.V.
Fil:Laplagne, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description Given a reduced affine algebra A over a perfect field K, we present parallel algorithms to compute the normalization Ā of A. Our starting point is the algorithm of Greuel et al. (2010), which is an improvement of de Jong's algorithm (de Jong, 1998; Decker et al., 1999). First, we propose to stratify the singular locus Sing(A) in a way which is compatible with normalization, apply a local version of the normalization algorithm at each stratum, and find Ā by putting the local results together. Second, in the case where K=Q is the field of rationals, we propose modular versions of the global and local-to-global algorithms. We have implemented our algorithms in the computer algebra system Singular and compare their performance with that of the algorithm of Greuel et al. (2010). In the case where K=Q, we also discuss the use of modular computations of Gröbner bases, radicals, and primary decompositions. We point out that in most examples, the new algorithms outperform the algorithm of Greuel et al. (2010) by far, even if we do not run them in parallel. © 2012 Elsevier B.V.
publishDate 2013
dc.date.none.fl_str_mv 2013
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_07477171_v51_n_p99_Bohm
url http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p99_Bohm
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 J. Symb. Comput. 2013;51:99-114
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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