Integral Function Bases

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.