A Sparse Effective Nullstellensatz : Notas de Matemática, 62

We present bounds for the sparseness and for the degrees of the polynomials in the Nullstellensatz. Our bounds depend mainly on the unmixed volume of the input polynomial system. The degree bounds can substantially improve the known ones when this polynomial system is sparse, and they are, in the wo...

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Detalles Bibliográficos
Autor principal: Sombra, Martín
Formato: Publicacion seriada
Lenguaje:Español
Publicado: 1997
Materias:
Matemática
Cohen-Macaulay ring
Effective Nullstellensatz
Newton polytope
Degree of a polynomial system of equations
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/171050
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-171050
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spelling I19-R120-10915-1710502024-10-02T20:11:24Z http://sedici.unlp.edu.ar/handle/10915/171050 A Sparse Effective Nullstellensatz : Notas de Matemática, 62 Sombra, Martín 1997 2024-10-02T16:58:10Z es Matemática Cohen-Macaulay ring Effective Nullstellensatz Newton polytope Degree of a polynomial system of equations We present bounds for the sparseness and for the degrees of the polynomials in the Nullstellensatz. Our bounds depend mainly on the unmixed volume of the input polynomial system. The degree bounds can substantially improve the known ones when this polynomial system is sparse, and they are, in the worst case, simply exponential in terms of the number of variables and the maximum degree of the input polynomials. Material digitalizado en SEDICI gracias a la colaboración de la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP). Facultad de Ciencias Exactas Publicacion seriada Publicacion seriada http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Español
topic Matemática
Cohen-Macaulay ring
Effective Nullstellensatz
Newton polytope
Degree of a polynomial system of equations
spellingShingle Matemática
Cohen-Macaulay ring
Effective Nullstellensatz
Newton polytope
Degree of a polynomial system of equations
Sombra, Martín
A Sparse Effective Nullstellensatz : Notas de Matemática, 62
topic_facet Matemática
Cohen-Macaulay ring
Effective Nullstellensatz
Newton polytope
Degree of a polynomial system of equations
description We present bounds for the sparseness and for the degrees of the polynomials in the Nullstellensatz. Our bounds depend mainly on the unmixed volume of the input polynomial system. The degree bounds can substantially improve the known ones when this polynomial system is sparse, and they are, in the worst case, simply exponential in terms of the number of variables and the maximum degree of the input polynomials.
format Publicacion seriada
Publicacion seriada
author Sombra, Martín
author_facet Sombra, Martín
author_sort Sombra, Martín
title A Sparse Effective Nullstellensatz : Notas de Matemática, 62
title_short A Sparse Effective Nullstellensatz : Notas de Matemática, 62
title_full A Sparse Effective Nullstellensatz : Notas de Matemática, 62
title_fullStr A Sparse Effective Nullstellensatz : Notas de Matemática, 62
title_full_unstemmed A Sparse Effective Nullstellensatz : Notas de Matemática, 62
title_sort sparse effective nullstellensatz : notas de matemática, 62
publishDate 1997
url http://sedici.unlp.edu.ar/handle/10915/171050
work_keys_str_mv AT sombramartin asparseeffectivenullstellensatznotasdematematica62
AT sombramartin sparseeffectivenullstellensatznotasdematematica62
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