On sign conditions over real multivariate polynomials

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, Gabriela Tali, Perrucci, Daniel, Sabia, Juan Vicente Rafael
Publicado: 2010
Materias:
Complexity
Consistency problem
Real multivariate polynomials
Sign conditions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v44_n1_p195_Jeronimo
http://hdl.handle.net/20.500.12110/paper_01795376_v44_n1_p195_Jeronimo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01795376_v44_n1_p195_Jeronimo
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spelling paper:paper_01795376_v44_n1_p195_Jeronimo2023-06-08T15:19:28Z On sign conditions over real multivariate polynomials Jeronimo, Gabriela Tali Perrucci, Daniel Sabia, Juan Vicente Rafael Complexity Consistency problem Real multivariate polynomials Sign conditions 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v44_n1_p195_Jeronimo http://hdl.handle.net/20.500.12110/paper_01795376_v44_n1_p195_Jeronimo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Complexity
Consistency problem
Real multivariate polynomials
Sign conditions
spellingShingle Complexity
Consistency problem
Real multivariate polynomials
Sign conditions
Jeronimo, Gabriela Tali
Perrucci, Daniel
Sabia, Juan Vicente Rafael
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.
author Jeronimo, Gabriela Tali
Perrucci, Daniel
Sabia, Juan Vicente Rafael
author_facet Jeronimo, Gabriela Tali
Perrucci, Daniel
Sabia, Juan Vicente Rafael
author_sort Jeronimo, Gabriela Tali
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01795376_v44_n1_p195_Jeronimo
http://hdl.handle.net/20.500.12110/paper_01795376_v44_n1_p195_Jeronimo
work_keys_str_mv AT jeronimogabrielatali onsignconditionsoverrealmultivariatepolynomials
AT perruccidaniel onsignconditionsoverrealmultivariatepolynomials
AT sabiajuanvicenterafael onsignconditionsoverrealmultivariatepolynomials
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