Affine solution sets of sparse polynomial systems
- Autores
- Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael
- Año de publicación
- 2013
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety. This result is applied to design an equidimensional decomposition algorithm for generic sparse systems. For arbitrary sparse systems of n polynomials in n variables with fixed supports, we obtain an upper bound for the degree of the affine variety defined and we present an algorithm which computes finite sets of points representing its equidimensional components.
Fil: Herrero, Maria Isabel. 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
Fil: Jeronimo, Gabriela Tali. 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
Fil: Sabia, Juan Vicente Rafael. 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
-
ALGORITHMS AND COMPLEXITY
DEGREE OF AFFINE VARIETIES
EQUIDIMENSIONAL DECOMPOSITION OF ALGEBRAIC VARIETIES
SPARSE POLYNOMIAL SYSTEMS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/85174
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Affine solution sets of sparse polynomial systemsHerrero, Maria IsabelJeronimo, Gabriela TaliSabia, Juan Vicente RafaelALGORITHMS AND COMPLEXITYDEGREE OF AFFINE VARIETIESEQUIDIMENSIONAL DECOMPOSITION OF ALGEBRAIC VARIETIESSPARSE POLYNOMIAL SYSTEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety. This result is applied to design an equidimensional decomposition algorithm for generic sparse systems. For arbitrary sparse systems of n polynomials in n variables with fixed supports, we obtain an upper bound for the degree of the affine variety defined and we present an algorithm which computes finite sets of points representing its equidimensional components.Fil: Herrero, Maria Isabel. 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"; ArgentinaFil: Jeronimo, Gabriela Tali. 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"; ArgentinaFil: Sabia, Juan Vicente Rafael. 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"; ArgentinaAcademic Press Ltd - Elsevier Science Ltd2013-04info: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/11336/85174Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Affine solution sets of sparse polynomial systems; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 51; 4-2013; 34-540747-7171CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2012.03.006info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717112001149info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:59:34Zoai:ri.conicet.gov.ar:11336/85174instacron: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:34982025-09-29 09:59:34.738CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Affine solution sets of sparse polynomial systems |
title |
Affine solution sets of sparse polynomial systems |
spellingShingle |
Affine solution sets of sparse polynomial systems Herrero, Maria Isabel ALGORITHMS AND COMPLEXITY DEGREE OF AFFINE VARIETIES EQUIDIMENSIONAL DECOMPOSITION OF ALGEBRAIC VARIETIES SPARSE POLYNOMIAL SYSTEMS |
title_short |
Affine solution sets of sparse polynomial systems |
title_full |
Affine solution sets of sparse polynomial systems |
title_fullStr |
Affine solution sets of sparse polynomial systems |
title_full_unstemmed |
Affine solution sets of sparse polynomial systems |
title_sort |
Affine solution sets of sparse polynomial systems |
dc.creator.none.fl_str_mv |
Herrero, Maria Isabel Jeronimo, Gabriela Tali Sabia, Juan Vicente Rafael |
author |
Herrero, Maria Isabel |
author_facet |
Herrero, Maria Isabel Jeronimo, Gabriela Tali Sabia, Juan Vicente Rafael |
author_role |
author |
author2 |
Jeronimo, Gabriela Tali Sabia, Juan Vicente Rafael |
author2_role |
author author |
dc.subject.none.fl_str_mv |
ALGORITHMS AND COMPLEXITY DEGREE OF AFFINE VARIETIES EQUIDIMENSIONAL DECOMPOSITION OF ALGEBRAIC VARIETIES SPARSE POLYNOMIAL SYSTEMS |
topic |
ALGORITHMS AND COMPLEXITY DEGREE OF AFFINE VARIETIES EQUIDIMENSIONAL DECOMPOSITION OF ALGEBRAIC VARIETIES SPARSE POLYNOMIAL SYSTEMS |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety. This result is applied to design an equidimensional decomposition algorithm for generic sparse systems. For arbitrary sparse systems of n polynomials in n variables with fixed supports, we obtain an upper bound for the degree of the affine variety defined and we present an algorithm which computes finite sets of points representing its equidimensional components. Fil: Herrero, Maria Isabel. 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 Fil: Jeronimo, Gabriela Tali. 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 Fil: Sabia, Juan Vicente Rafael. 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 |
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components which characterize the equidimensional decomposition of the associated affine variety. This result is applied to design an equidimensional decomposition algorithm for generic sparse systems. For arbitrary sparse systems of n polynomials in n variables with fixed supports, we obtain an upper bound for the degree of the affine variety defined and we present an algorithm which computes finite sets of points representing its equidimensional components. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-04 |
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/11336/85174 Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Affine solution sets of sparse polynomial systems; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 51; 4-2013; 34-54 0747-7171 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/85174 |
identifier_str_mv |
Herrero, Maria Isabel; Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Affine solution sets of sparse polynomial systems; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 51; 4-2013; 34-54 0747-7171 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2012.03.006 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717112001149 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Academic Press Ltd - Elsevier Science Ltd |
publisher.none.fl_str_mv |
Academic Press Ltd - Elsevier Science Ltd |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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 |
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1844613766576078848 |
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13.070432 |