On sign conditions over real multivariate polynomials

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We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that intersect transversally. This enables us to show a probabilist...

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Autores principales: Jeronimo, G., Perrucci, D., Sabia, J.
Formato: Artículo publishedVersion
Publicado: 2010
Materias:
Complexity
Consistency problem
Real multivariate polynomials
Sign conditions
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01795376_v44_n1_p195_Jeronimo
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_01795376_v44_n1_p195_Jeronimo_oai
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Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
id I28-R145-paper_01795376_v44_n1_p195_Jeronimo_oai
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spelling I28-R145-paper_01795376_v44_n1_p195_Jeronimo_oai2024-08-16 Jeronimo, G. Perrucci, D. Sabia, J. 2010 We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that intersect transversally. This enables us to show a probabilistic procedure to list all feasible sign conditions over the polynomials. In addition, we extend these results to the case of closed sign conditions over an arbitrary family of real multivariate polynomials. The complexity bounds for these procedures improve the known ones. © Springer Science+Business Media, LLC 2009. Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Perrucci, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_01795376_v44_n1_p195_Jeronimo info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Discrete Comput. Geom. 2010;44(1):195-222 Complexity Consistency problem Real multivariate polynomials Sign conditions On sign conditions over real multivariate polynomials info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_01795376_v44_n1_p195_Jeronimo_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic Complexity
Consistency problem
Real multivariate polynomials
Sign conditions
spellingShingle Complexity
Consistency problem
Real multivariate polynomials
Sign conditions
Jeronimo, G.
Perrucci, D.
Sabia, J.
On sign conditions over real multivariate polynomials
topic_facet Complexity
Consistency problem
Real multivariate polynomials
Sign conditions
description We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that intersect transversally. This enables us to show a probabilistic procedure to list all feasible sign conditions over the polynomials. In addition, we extend these results to the case of closed sign conditions over an arbitrary family of real multivariate polynomials. The complexity bounds for these procedures improve the known ones. © Springer Science+Business Media, LLC 2009.
format Artículo
Artículo
publishedVersion
author Jeronimo, G.
Perrucci, D.
Sabia, J.
author_facet Jeronimo, G.
Perrucci, D.
Sabia, J.
author_sort Jeronimo, G.
title On sign conditions over real multivariate polynomials
title_short On sign conditions over real multivariate polynomials
title_full On sign conditions over real multivariate polynomials
title_fullStr On sign conditions over real multivariate polynomials
title_full_unstemmed On sign conditions over real multivariate polynomials
title_sort on sign conditions over real multivariate polynomials
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_01795376_v44_n1_p195_Jeronimo
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_01795376_v44_n1_p195_Jeronimo_oai
work_keys_str_mv AT jeronimog onsignconditionsoverrealmultivariatepolynomials
AT perruccid onsignconditionsoverrealmultivariatepolynomials
AT sabiaj onsignconditionsoverrealmultivariatepolynomials
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