A Sparse Effective Nullstellensatz
- Autores
- Sombra, Martín
- Año de publicación
- 1999
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We present bounds for the sparseness in the Nullstellensatz. These bounds can give a much sharper characterization than degree bounds of the monomial structure of the polynomials in the Nullstellensatz in case that the input system is sparse. As a consequence we derive a degree bound which can substantially improve the known ones in case of a sparse system.In addition we introduce the notion of algebraic degree associated to a polynomial system of equations. We obtain a new degree bound which is sharper than the known ones when this parameter is small. We also improve the previous effective Nullstellensatze in case the input polynomials are quadratic.Our approach is completely algebraic, and the obtained results are independent of the characteristic of the base field.
Facultad de Ciencias Exactas - Materia
-
Ciencias Exactas
Matemática
Cohen-Macaulay ring
effective Nullstellensatz
Newton polytope
degree of a polynomial system of equations - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/123266
Ver los metadatos del registro completo
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A Sparse Effective NullstellensatzSombra, MartínCiencias ExactasMatemáticaCohen-Macaulay ringeffective NullstellensatzNewton polytopedegree of a polynomial system of equationsWe present bounds for the sparseness in the Nullstellensatz. These bounds can give a much sharper characterization than degree bounds of the monomial structure of the polynomials in the Nullstellensatz in case that the input system is sparse. As a consequence we derive a degree bound which can substantially improve the known ones in case of a sparse system.In addition we introduce the notion of algebraic degree associated to a polynomial system of equations. We obtain a new degree bound which is sharper than the known ones when this parameter is small. We also improve the previous effective Nullstellensatze in case the input polynomials are quadratic.Our approach is completely algebraic, and the obtained results are independent of the characteristic of the base field.Facultad de Ciencias Exactas1999-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf271-295http://sedici.unlp.edu.ar/handle/10915/123266enginfo:eu-repo/semantics/altIdentifier/issn/0196-8858info:eu-repo/semantics/altIdentifier/doi/10.1006/aama.1998.0633info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:29:18Zoai:sedici.unlp.edu.ar:10915/123266Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:29:18.951SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
A Sparse Effective Nullstellensatz |
| title |
A Sparse Effective Nullstellensatz |
| spellingShingle |
A Sparse Effective Nullstellensatz Sombra, Martín Ciencias Exactas Matemática Cohen-Macaulay ring effective Nullstellensatz Newton polytope degree of a polynomial system of equations |
| title_short |
A Sparse Effective Nullstellensatz |
| title_full |
A Sparse Effective Nullstellensatz |
| title_fullStr |
A Sparse Effective Nullstellensatz |
| title_full_unstemmed |
A Sparse Effective Nullstellensatz |
| title_sort |
A Sparse Effective Nullstellensatz |
| dc.creator.none.fl_str_mv |
Sombra, Martín |
| author |
Sombra, Martín |
| author_facet |
Sombra, Martín |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Matemática Cohen-Macaulay ring effective Nullstellensatz Newton polytope degree of a polynomial system of equations |
| topic |
Ciencias Exactas Matemática Cohen-Macaulay ring effective Nullstellensatz Newton polytope degree of a polynomial system of equations |
| dc.description.none.fl_txt_mv |
We present bounds for the sparseness in the Nullstellensatz. These bounds can give a much sharper characterization than degree bounds of the monomial structure of the polynomials in the Nullstellensatz in case that the input system is sparse. As a consequence we derive a degree bound which can substantially improve the known ones in case of a sparse system.In addition we introduce the notion of algebraic degree associated to a polynomial system of equations. We obtain a new degree bound which is sharper than the known ones when this parameter is small. We also improve the previous effective Nullstellensatze in case the input polynomials are quadratic.Our approach is completely algebraic, and the obtained results are independent of the characteristic of the base field. Facultad de Ciencias Exactas |
| description |
We present bounds for the sparseness in the Nullstellensatz. These bounds can give a much sharper characterization than degree bounds of the monomial structure of the polynomials in the Nullstellensatz in case that the input system is sparse. As a consequence we derive a degree bound which can substantially improve the known ones in case of a sparse system.In addition we introduce the notion of algebraic degree associated to a polynomial system of equations. We obtain a new degree bound which is sharper than the known ones when this parameter is small. We also improve the previous effective Nullstellensatze in case the input polynomials are quadratic.Our approach is completely algebraic, and the obtained results are independent of the characteristic of the base field. |
| publishDate |
1999 |
| dc.date.none.fl_str_mv |
1999-02 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://sedici.unlp.edu.ar/handle/10915/123266 |
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http://sedici.unlp.edu.ar/handle/10915/123266 |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/issn/0196-8858 info:eu-repo/semantics/altIdentifier/doi/10.1006/aama.1998.0633 |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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