  Integral bases, a minimal set of solutions to $Ax\leq b, x\in\Z^n$ that
generate any other solution to $Ax\leq b, x\in\Z^n$, as a nonnegative integer
linear combination, are always finite and are at the core of the Integral Basis
Method introduced by Haus, K{\"o}ppe and Weismantel.
  In this paper we present one generalization of the notion of integral bases
to the nonlinear situation with the intention of creating an integral basis
method also for nonlinear integer programming.
