Dense Fewnomials
Algebraic Geometry
2010-10-15 v1
Abstract
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.
Cite
@article{arxiv.1010.2962,
title = {Dense Fewnomials},
author = {Korben Rusek and Jeanette Shakalli and Frank Sottile},
journal= {arXiv preprint arXiv:1010.2962},
year = {2010}
}
Comments
20 pages