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Article Dans Une Revue international mathematical research notices Année : 2007

Bounds on the number of real solutions to polynomial equations

Résumé

We use Gale duality for complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain a new bound 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 only exceeds the bound for positive solutions by the constant factor (e^4+3)/(e^2+3) and it is asymptotically sharp for k fixed and n large.
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Dates et versions

hal-00379898 , version 1 (29-04-2009)

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  • HAL Id : hal-00379898 , version 1

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Dan Bates, Frederic Bihan, Frank Sottile. Bounds on the number of real solutions to polynomial equations. international mathematical research notices, 2007, 2007, pp.article ID rnm114. ⟨hal-00379898⟩
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