Bounds on the Number of Real Solutions to Polynomial Equations Academic Article uri icon

abstract

  • We use Gale duality for complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound e4 + 3/4 2(k2)nk for the number of nonzero real solutions to a system of n polynomials in n variables having n + k + 1 monomials whose exponent vectors generate a subgroup of ℤn of odd index. This bound only exceeds the bound for positive solutions by the constant factor (e4 + 3)/(e2 + 3) and it is asymptotically sharp for k fixed and n large. © The Author 2007.

author list (cited authors)

  • Bates, D. J., Bihan, F., & Sottile, F.

citation count

  • 2

publication date

  • July 2010