Degeneracy Loci and Polynomial Equation Solving

Autores
Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Lecerf, Grégoire; Matera, Guillermo; Solernó, Pablo Luis
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let (Formula presented.) be a smooth, equidimensional, quasi-affine variety of dimension (Formula presented.) over (Formula presented.), and let (Formula presented.) be a (Formula presented.) matrix of coordinate functions of (Formula presented.), where (Formula presented.). The pair (Formula presented.) determines a vector bundle (Formula presented.) of rank (Formula presented.) over (Formula presented.). We associate with (Formula presented.) a descending chain of degeneracy loci of (Formula presented.) (the generic polar varieties of (Formula presented.) represent a typical example of this situation). The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded-error probabilistic pseudo-polynomial-time algorithm that we will design and that solves a series of computational elimination problems that can be formulated in this framework. We describe applications to polynomial equation solving over the reals and to the computation of a generic fiber of a dominant endomorphism of an affine space.
Fil: Bank, Bernd. Universität zu Berlin; Alemania
Fil: Giusti, Marc. Laboratoire D'informatique de L'ecole Polytechnique; Francia
Fil: Heintz, Joos Ulrich. Universidad de Cantabria; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lecerf, Grégoire. Laboratoire D'informatique de L'ecole Polytechnique; Francia
Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Solernó, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Degeneracy Locus
Degree of Varieties
Polynomial Equation Solving
Pseudo-Polynomial Complexity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/38112
Acceder
id CONICETDig_ce51df0b567e86ce7938ecf47f84c51c
oai_identifier_str oai:ri.conicet.gov.ar:11336/38112
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Degeneracy Loci and Polynomial Equation SolvingBank, BerndGiusti, MarcHeintz, Joos UlrichLecerf, GrégoireMatera, GuillermoSolernó, Pablo LuisDegeneracy LocusDegree of VarietiesPolynomial Equation SolvingPseudo-Polynomial Complexityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let (Formula presented.) be a smooth, equidimensional, quasi-affine variety of dimension (Formula presented.) over (Formula presented.), and let (Formula presented.) be a (Formula presented.) matrix of coordinate functions of (Formula presented.), where (Formula presented.). The pair (Formula presented.) determines a vector bundle (Formula presented.) of rank (Formula presented.) over (Formula presented.). We associate with (Formula presented.) a descending chain of degeneracy loci of (Formula presented.) (the generic polar varieties of (Formula presented.) represent a typical example of this situation). The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded-error probabilistic pseudo-polynomial-time algorithm that we will design and that solves a series of computational elimination problems that can be formulated in this framework. We describe applications to polynomial equation solving over the reals and to the computation of a generic fiber of a dominant endomorphism of an affine space.Fil: Bank, Bernd. Universität zu Berlin; AlemaniaFil: Giusti, Marc. Laboratoire D'informatique de L'ecole Polytechnique; FranciaFil: Heintz, Joos Ulrich. Universidad de Cantabria; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lecerf, Grégoire. Laboratoire D'informatique de L'ecole Polytechnique; FranciaFil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Solernó, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaSpringer2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/38112Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Lecerf, Grégoire; Matera, Guillermo; et al.; Degeneracy Loci and Polynomial Equation Solving; Springer; Foundations Of Computational Mathematics; 15; 1; 1-2015; 159-1841615-33751615-3383CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-014-9214-zinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10208-014-9214-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:11:57Zoai:ri.conicet.gov.ar:11336/38112instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:11:57.652CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Degeneracy Loci and Polynomial Equation Solving
title Degeneracy Loci and Polynomial Equation Solving
spellingShingle Degeneracy Loci and Polynomial Equation Solving
Bank, Bernd
Degeneracy Locus
Degree of Varieties
Polynomial Equation Solving
Pseudo-Polynomial Complexity
title_short Degeneracy Loci and Polynomial Equation Solving
title_full Degeneracy Loci and Polynomial Equation Solving
title_fullStr Degeneracy Loci and Polynomial Equation Solving
title_full_unstemmed Degeneracy Loci and Polynomial Equation Solving
title_sort Degeneracy Loci and Polynomial Equation Solving
dc.creator.none.fl_str_mv Bank, Bernd
Giusti, Marc
Heintz, Joos Ulrich
Lecerf, Grégoire
Matera, Guillermo
Solernó, Pablo Luis
author Bank, Bernd
author_facet Bank, Bernd
Giusti, Marc
Heintz, Joos Ulrich
Lecerf, Grégoire
Matera, Guillermo
Solernó, Pablo Luis
author_role author
author2 Giusti, Marc
Heintz, Joos Ulrich
Lecerf, Grégoire
Matera, Guillermo
Solernó, Pablo Luis
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Degeneracy Locus
Degree of Varieties
Polynomial Equation Solving
Pseudo-Polynomial Complexity
topic Degeneracy Locus
Degree of Varieties
Polynomial Equation Solving
Pseudo-Polynomial Complexity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let (Formula presented.) be a smooth, equidimensional, quasi-affine variety of dimension (Formula presented.) over (Formula presented.), and let (Formula presented.) be a (Formula presented.) matrix of coordinate functions of (Formula presented.), where (Formula presented.). The pair (Formula presented.) determines a vector bundle (Formula presented.) of rank (Formula presented.) over (Formula presented.). We associate with (Formula presented.) a descending chain of degeneracy loci of (Formula presented.) (the generic polar varieties of (Formula presented.) represent a typical example of this situation). The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded-error probabilistic pseudo-polynomial-time algorithm that we will design and that solves a series of computational elimination problems that can be formulated in this framework. We describe applications to polynomial equation solving over the reals and to the computation of a generic fiber of a dominant endomorphism of an affine space.
Fil: Bank, Bernd. Universität zu Berlin; Alemania
Fil: Giusti, Marc. Laboratoire D'informatique de L'ecole Polytechnique; Francia
Fil: Heintz, Joos Ulrich. Universidad de Cantabria; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lecerf, Grégoire. Laboratoire D'informatique de L'ecole Polytechnique; Francia
Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Solernó, Pablo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Let (Formula presented.) be a smooth, equidimensional, quasi-affine variety of dimension (Formula presented.) over (Formula presented.), and let (Formula presented.) be a (Formula presented.) matrix of coordinate functions of (Formula presented.), where (Formula presented.). The pair (Formula presented.) determines a vector bundle (Formula presented.) of rank (Formula presented.) over (Formula presented.). We associate with (Formula presented.) a descending chain of degeneracy loci of (Formula presented.) (the generic polar varieties of (Formula presented.) represent a typical example of this situation). The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded-error probabilistic pseudo-polynomial-time algorithm that we will design and that solves a series of computational elimination problems that can be formulated in this framework. We describe applications to polynomial equation solving over the reals and to the computation of a generic fiber of a dominant endomorphism of an affine space.
publishDate 2015
dc.date.none.fl_str_mv 2015-01
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/11336/38112
Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Lecerf, Grégoire; Matera, Guillermo; et al.; Degeneracy Loci and Polynomial Equation Solving; Springer; Foundations Of Computational Mathematics; 15; 1; 1-2015; 159-184
1615-3375
1615-3383
CONICET Digital
CONICET
url http://hdl.handle.net/11336/38112
identifier_str_mv Bank, Bernd; Giusti, Marc; Heintz, Joos Ulrich; Lecerf, Grégoire; Matera, Guillermo; et al.; Degeneracy Loci and Polynomial Equation Solving; Springer; Foundations Of Computational Mathematics; 15; 1; 1-2015; 159-184
1615-3375
1615-3383
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-014-9214-z
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10208-014-9214-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842270178970173440
score 13.13397

Publicaciones similares