The Integer Hull of a Convex Rational Polytope

Given $A\in\Z^{m\times n}$ and $b\in\Z^m$, we consider the integer program $\max \{c’x\vert Ax=b;x\in\N^n\}$ and provide an {\it equivalent} and {\it explicit} linear program $\max \{\widehat{\xcc}’q\vert \m q=r;q\geq 0\}$, where $\m,r,\widehat{c}$ 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 $\p=\{x\in\R^n\vert Ax=b;x\geq0\}$. All strong valid inequalities can be obtained from the generators of a convex cone whose definition is explicit in terms of $\m$.