Dense Fewnomials

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...

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Published in:arXiv.org 2010-10
Main Authors: Rusek, Korben, Shakalli, Jeanette, Sottile, Frank
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Language:English
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Hyperspaces
Polynomials
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Shakalli, Jeanette
Sottile, Frank
description 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.
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subjects Hyperspaces
Polynomials
title Dense Fewnomials
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