1997/10/01 by Martı́n Sombra, Mart'in Sombra, Sombra, Mart'in · 1 citation
Computer Science · Mathematics · #13P10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #alg-geom #math.AC #math.AG #msc:13P10
paper · pdf · doi:10.48550/arxiv.alg-geom/9710003
24 pages, Latex2e, available at http://www.dm.uba.ar/tera/ and http://hilbert.matesco.unican.es/tera/
arxiv created 1997/10/01 · openalex publication_date 1997/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.