Parallel algorithms for normalization

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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 str...

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Autores principales:	Böhm, J., Decker, W., Laplagne, S., Pfister, G., Steenpaß, A., Steidel, S.
Formato:	Artículo publishedVersion
Lenguaje:	Inglés
Publicado:	2013
Materias:	Grauert-Remmert criterion Integral closure Modular computation Normalization Parallel computation Test ideal
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p99_Bohm
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paperaa:paper_07477171_v51_n_p99_Bohm
record_format	dspace
spelling	paperaa:paper_07477171_v51_n_p99_Bohm2023-06-12T16:48:15Z Parallel algorithms for normalization J. Symb. Comput. 2013;51:99-114 Böhm, J. Decker, W. Laplagne, S. Pfister, G. Steenpaß, A. Steidel, S. Grauert-Remmert criterion Integral closure Modular computation Normalization Parallel computation Test ideal 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. 2013 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p99_Bohm
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language	Inglés
orig_language_str_mv	eng
topic	Grauert-Remmert criterion Integral closure Modular computation Normalization Parallel computation Test ideal
spellingShingle	Grauert-Remmert criterion Integral closure Modular computation Normalization Parallel computation Test ideal Böhm, J. Decker, W. Laplagne, S. Pfister, G. Steenpaß, A. Steidel, S. Parallel algorithms for normalization
topic_facet	Grauert-Remmert criterion Integral closure Modular computation Normalization Parallel computation Test ideal
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.
format	Artículo Artículo publishedVersion
author	Böhm, J. Decker, W. Laplagne, S. Pfister, G. Steenpaß, A. Steidel, S.
author_facet	Böhm, J. Decker, W. Laplagne, S. Pfister, G. Steenpaß, A. Steidel, S.
author_sort	Böhm, J.
title	Parallel algorithms for normalization
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
publishDate	2013
url	http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p99_Bohm
work_keys_str_mv	AT bohmj parallelalgorithmsfornormalization AT deckerw parallelalgorithmsfornormalization AT laplagnes parallelalgorithmsfornormalization AT pfisterg parallelalgorithmsfornormalization AT steenpaßa parallelalgorithmsfornormalization AT steidels parallelalgorithmsfornormalization
_version_	1769810338927083520

Parallel algorithms for normalization

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