BOUNDS ON THE NUMBER OF REAL SOLUTIONS TO
Daniel J. Bates, Frédéric Bihan, Frank Sottile · 2007
We use Gale duality for complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound e 4 + 3 4 2 ( k 2) n k 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.