A Sparse Effective Nullstellensatz

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 subst...

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Detalles Bibliográficos
Autor principal: Sombra, Martín
Formato: Articulo
Lenguaje:Inglés
Publicado: 1999
Materias:
Ciencias Exactas
Matemática
Cohen-Macaulay ring
effective Nullstellensatz
Newton polytope
degree of a polynomial system of equations
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/123266
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-123266
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Matemática
Cohen-Macaulay ring
effective Nullstellensatz
Newton polytope
degree of a polynomial system of equations
spellingShingle Ciencias Exactas
Matemática
Cohen-Macaulay ring
effective Nullstellensatz
Newton polytope
degree of a polynomial system of equations
Sombra, Martín
A Sparse Effective Nullstellensatz
topic_facet Ciencias Exactas
Matemática
Cohen-Macaulay ring
effective Nullstellensatz
Newton polytope
degree of a polynomial system of equations
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.
format Articulo
Articulo
author Sombra, Martín
author_facet Sombra, Martín
author_sort Sombra, Martín
title A Sparse Effective Nullstellensatz
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 sparse effective nullstellensatz
publishDate 1999
url http://sedici.unlp.edu.ar/handle/10915/123266
work_keys_str_mv AT sombramartin asparseeffectivenullstellensatz
AT sombramartin sparseeffectivenullstellensatz
bdutipo_str Repositorios
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