New Complexity Bounds for Certain Real Fewnomial Zero Sets

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dc.creatorGomez, Joel
dc.creatorNiles, Andrew
dc.creatorRojas, J. Maurice
dc.date2007-09-15
dc.date.accessioned2026-07-07T08:29:50Z
dc.date.available2026-07-07T08:29:50Z
dc.descriptionConsider real bivariate polynomials f and g, respectively having 3 and m monomial terms. We prove that for all m>=3, there are systems of the form (f,g) having exactly 2m-1 roots in the positive quadrant. Even examples with m=4 having 7 positive roots were unknown before this paper, so we detail an explicit example of this form. We also present an O(n^{11}) upper bound for the number of diffeotopy types of the real zero set of an n-variate polynomial with n+4 monomial terms.
dc.description8 pages, no figures. Extended abstract accepted and presented at MEGA (Effective Methods in Algebraic Geometry) 2007
dc.identifierhttps://arxiv.org/abs/0709.2405
dc.identifierhttp://arxiv.org/abs/0709.2405
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138078
dc.subjectAlgebraic Geometry
dc.subjectComputational Geometry
dc.titleNew Complexity Bounds for Certain Real Fewnomial Zero Sets
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