Rational certificates of non-negativity on semialgebraic subsets of cylinders
- Autores
- Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto
- Año de publicación
- 2024
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let g1, . . . , gs ∈ R[X1, . . . , Xn, Y ] and S = {(¯x, y) ∈ R n+1 | g1(¯x, y) ≥ 0, . . . , gs(¯x, y) ≥ 0} be a non-empty, possibly unbounded, subset of a cylinder in R n+1. Let f ∈ R[X1, . . . , Xn, Y ] be a polynomial which is positive on S. We prove that, under certain additional assumptions, for any non-constant polynomial q ∈ R[Y ] which is positive on R, there is a certificate of the non-negativity of f on S given by a rational function having as numerator a polynomial in the quadratic module generated by g1, . . . , gs and as denominator a power of q.
Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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. Departamento de Ciencias Exactas; Argentina
Fil: Perrucci, Daniel Roberto. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina - Materia
-
POSITIVSTELLENSATZ
POSITIVE POLYNOMIALS
SUMS OF SQUARES
QUADRATIC MODULES - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/234782
Ver los metadatos del registro completo
| id |
CONICETDig_cdc829d6cc2a012fe2bdb1bf5e73945f |
|---|---|
| oai_identifier_str |
oai:ri.conicet.gov.ar:11336/234782 |
| network_acronym_str |
CONICETDig |
| repository_id_str |
3498 |
| network_name_str |
CONICET Digital (CONICET) |
| spelling |
Rational certificates of non-negativity on semialgebraic subsets of cylindersJeronimo, Gabriela TaliPerrucci, Daniel RobertoPOSITIVSTELLENSATZPOSITIVE POLYNOMIALSSUMS OF SQUARESQUADRATIC MODULEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let g1, . . . , gs ∈ R[X1, . . . , Xn, Y ] and S = {(¯x, y) ∈ R n+1 | g1(¯x, y) ≥ 0, . . . , gs(¯x, y) ≥ 0} be a non-empty, possibly unbounded, subset of a cylinder in R n+1. Let f ∈ R[X1, . . . , Xn, Y ] be a polynomial which is positive on S. We prove that, under certain additional assumptions, for any non-constant polynomial q ∈ R[Y ] which is positive on R, there is a certificate of the non-negativity of f on S given by a rational function having as numerator a polynomial in the quadratic module generated by g1, . . . , gs and as denominator a power of q.Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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. Departamento de Ciencias Exactas; ArgentinaFil: Perrucci, Daniel Roberto. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaElsevier Science2024-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/234782Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Rational certificates of non-negativity on semialgebraic subsets of cylinders; Elsevier Science; Journal Of Pure And Applied Algebra; 228; 6; 6-2024; 1-120022-4049CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jpaa.2023.107596info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022404923002785info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T11:59:26Zoai:ri.conicet.gov.ar:11336/234782instacron: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:34982025-10-29 11:59:26.608CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Rational certificates of non-negativity on semialgebraic subsets of cylinders |
| title |
Rational certificates of non-negativity on semialgebraic subsets of cylinders |
| spellingShingle |
Rational certificates of non-negativity on semialgebraic subsets of cylinders Jeronimo, Gabriela Tali POSITIVSTELLENSATZ POSITIVE POLYNOMIALS SUMS OF SQUARES QUADRATIC MODULES |
| title_short |
Rational certificates of non-negativity on semialgebraic subsets of cylinders |
| title_full |
Rational certificates of non-negativity on semialgebraic subsets of cylinders |
| title_fullStr |
Rational certificates of non-negativity on semialgebraic subsets of cylinders |
| title_full_unstemmed |
Rational certificates of non-negativity on semialgebraic subsets of cylinders |
| title_sort |
Rational certificates of non-negativity on semialgebraic subsets of cylinders |
| dc.creator.none.fl_str_mv |
Jeronimo, Gabriela Tali Perrucci, Daniel Roberto |
| author |
Jeronimo, Gabriela Tali |
| author_facet |
Jeronimo, Gabriela Tali Perrucci, Daniel Roberto |
| author_role |
author |
| author2 |
Perrucci, Daniel Roberto |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
POSITIVSTELLENSATZ POSITIVE POLYNOMIALS SUMS OF SQUARES QUADRATIC MODULES |
| topic |
POSITIVSTELLENSATZ POSITIVE POLYNOMIALS SUMS OF SQUARES QUADRATIC MODULES |
| 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 g1, . . . , gs ∈ R[X1, . . . , Xn, Y ] and S = {(¯x, y) ∈ R n+1 | g1(¯x, y) ≥ 0, . . . , gs(¯x, y) ≥ 0} be a non-empty, possibly unbounded, subset of a cylinder in R n+1. Let f ∈ R[X1, . . . , Xn, Y ] be a polynomial which is positive on S. We prove that, under certain additional assumptions, for any non-constant polynomial q ∈ R[Y ] which is positive on R, there is a certificate of the non-negativity of f on S given by a rational function having as numerator a polynomial in the quadratic module generated by g1, . . . , gs and as denominator a power of q. Fil: Jeronimo, Gabriela Tali. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. 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. Departamento de Ciencias Exactas; Argentina Fil: Perrucci, Daniel Roberto. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina |
| description |
Let g1, . . . , gs ∈ R[X1, . . . , Xn, Y ] and S = {(¯x, y) ∈ R n+1 | g1(¯x, y) ≥ 0, . . . , gs(¯x, y) ≥ 0} be a non-empty, possibly unbounded, subset of a cylinder in R n+1. Let f ∈ R[X1, . . . , Xn, Y ] be a polynomial which is positive on S. We prove that, under certain additional assumptions, for any non-constant polynomial q ∈ R[Y ] which is positive on R, there is a certificate of the non-negativity of f on S given by a rational function having as numerator a polynomial in the quadratic module generated by g1, . . . , gs and as denominator a power of q. |
| publishDate |
2024 |
| dc.date.none.fl_str_mv |
2024-06 |
| 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/11336/234782 Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Rational certificates of non-negativity on semialgebraic subsets of cylinders; Elsevier Science; Journal Of Pure And Applied Algebra; 228; 6; 6-2024; 1-12 0022-4049 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/234782 |
| identifier_str_mv |
Jeronimo, Gabriela Tali; Perrucci, Daniel Roberto; Rational certificates of non-negativity on semialgebraic subsets of cylinders; Elsevier Science; Journal Of Pure And Applied Algebra; 228; 6; 6-2024; 1-12 0022-4049 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.jpaa.2023.107596 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022404923002785 |
| 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 |
| dc.publisher.none.fl_str_mv |
Elsevier Science |
| publisher.none.fl_str_mv |
Elsevier Science |
| 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_ |
1847426731793711104 |
| score |
13.10058 |