The Integer Hull of a Convex Rational Polytope

Given A ∈ Zm×n and b ∈ Z, we consider the integer program max{c′x|Ax = b;x ∈ N} and provide an equivalent and explicit linear program max{ĉ′q|Mq = r; q ≥ 0}, where M, r, ĉ are easily obtained from A, b, c with no calculation. We also provide an explicit algebraic characterization of the integer hull of the convex polytope P = {x ∈ R|Ax = b;x ≥ 0}. All strong valid inequalities can be obtained from the generators of a convex cone whose definition is explicit in terms of M.