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A Sparse Effective Nullstellensatz
Author: Sombra M.
Source: Advances in Applied Mathematics, Volume 22, Number 1, February 1999 , pp. 271-295(25)
Publisher: Academic Press
Abstract:
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 Nullstellensätze 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. Copyright 1999 Academic Press.
Language: English
Document Type: Research article
Affiliations: Departamento de Matemática, Universidad Nacional de La Plata, Calle 50 y 115, La Plata, 1900, Argentina
Publication date: 1999-02-01
- In this: publication
- By this: publisher
- In this Subject: Mathematics and Statistics
- By this author: Sombra M.
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