Parallel algorithms for normalization

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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Detalles Bibliográficos
Autor principal:	Laplagne, Santiago Jorge
Publicado:	2013
Materias:	Grauert-Remmert criterion Integral closure Modular computation Normalization Parallel computation Test ideal
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v51_n_p99_Bohm 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	paper:paper_07477171_v51_n_p99_Bohm
record_format	dspace
spelling	paper:paper_07477171_v51_n_p99_Bohm2023-06-08T15:45:11Z Parallel algorithms for normalization Laplagne, Santiago Jorge 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v51_n_p99_Bohm 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)
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 Laplagne, Santiago Jorge 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.
author	Laplagne, Santiago Jorge
author_facet	Laplagne, Santiago Jorge
author_sort	Laplagne, Santiago Jorge
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	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v51_n_p99_Bohm http://hdl.handle.net/20.500.12110/paper_07477171_v51_n_p99_Bohm
work_keys_str_mv	AT laplagnesantiagojorge parallelalgorithmsfornormalization
_version_	1768545422889975808

Parallel algorithms for normalization

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