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- W2220230152 abstract "Abstract 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." @default.
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- W2220230152 date "2015-12-01" @default.
- W2220230152 modified "2023-09-29" @default.
- W2220230152 title "An algebraic-perturbation variant of Barvinok's algorithm" @default.
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- W2220230152 doi "https://doi.org/10.1016/j.endm.2015.07.004" @default.
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