2010/10/14 by Korben Rusek, Rusek, Korben, Jeanette Shakalli +3
Computer Science · Mathematics · #14P99 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1010.2962
openalex publication_date 2010/10/14 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We derive new bounds of fewnomial type for the number of real solutions to systems of polynomials that have structure intermediate between fewnomials and generic (dense) polynomials. This uses a modified version of Gale duality for polynomial systems. We also use stratified Morse theory to bound the total Betti number of a hypersurface defined by such a dense fewnomial. These bounds contain and generalize previous bounds for ordinary fewnomials obtained by Bates, Bertrand, Bihan, and Sottile.