An algebraic-perturbation variant of Barvinok's algorithm.

We give a variant of Barvinok's algorithm for computing a short rational generating function for the integer points in P : = { x ∈ R n : A x ≤ b } ; a use of which is to count the number of integer points in P . We use an algebraic perturbation, replacing each b i with b i + τ i , where τ > 0 is an arbitrarily small indeterminate . Hence, our new right-hand vector has components in the ordered ring Q [ τ ] of polynomials in τ . Denoting the perturbed polyhedron by P ( τ ) ⊂ R [ τ ] n , we use the facts that: P ( τ ) is full dimensional, simple, and contains the same integer points as P . [ABSTRACT FROM AUTHOR]