Bounds on the number of real solutions to polynomial equations

Daniel J. Bates, Frédéric Bihan and Frank Sottile.

    We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e4+3)/4 2k(k-1)/2nk for the number of non-zero real solutions to a system of n polynomials in n variables having n+k1 monomials whose exponent vectors generate a subgroup of Zn of odd index. This bound exceeds the bound for positive solutions only by the constant factor (e4+3)/(e2+3) and it is asymptotically sharp for k fixed and n large.



The manuscript in postscript, and in pdf.
Previous