Constructive proof of extended Kapranov theorem
  Kapranov Theorem is a well known generalization of Newton-Puiseux theorem for the case of several variables.   This theorem is stated mainly in the context of tropical geometry. We present a new, constructive proof, that also characterizes the possible principal terms of points in a hypersurface contained in the algebraic torus $(K^*)^n$. 
Luis Felipe Tabera