Bounds on the number of real solutions to polynomial equations

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dc.creatorBates, Daniel J.
dc.creatorBihan, Frédéric
dc.creatorSottile, Frank
dc.date2007-06-28
dc.date2007-10-03
dc.date.accessioned2026-07-07T08:33:26Z
dc.date.available2026-07-07T08:33:26Z
dc.descriptionWe use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the number of non-zero real solutions to a system of n polynomials in n variables having n+k+1 monomials whose exponent vectors generate a subgroup of Z^n of odd index. This bound exceeds the bound for positive solutions only by the constant factor (e^4+3)/(e^2+3) and it is asymptotically sharp for k fixed and n large.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/0706.4134
dc.identifierhttp://arxiv.org/abs/0706.4134
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139132
dc.subjectAlgebraic Geometry
dc.subject14M25, 14P25, 52C35
dc.titleBounds on the number of real solutions to polynomial equations
dc.typetext

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