barvinok is a library for counting the number of integer points in parametric and non-parametric polytopes. For parametric polytopes an explicit function in the shape of a piece-wise step-polynomial is constructed. This is a generalization of both Ehrhart quasi-polynomials and vector partition functions. Alternatively, a generalized Ehrhart series can be constructed as well.
Try it! (tutorial) For an introduction to the underlying concepts of this interactive environment, see Presburger Formulas and Polyhedral Compilation.
The library includes isl and PolyLib and uses NTL.
It uses Barvinok's decomposition which has also been (previously) implemented in LattE.
From release 0.22 until release 0.30, the barvinok distribution included the bernstein library for computing bounds on polynomials over parametric polytopes. This functionality has now been taken over by the isl library.
Since release 0.25, the library can also compute the sum of a polynomial over the integer points in a parametric polygon using local Euler-Maclaurin formulae. The original implementation of this algorithm in Maple can be found here.
Since release 0.30, the barvinok distribution includes the isl library.
or the user manual for more information.
See the git repository for the latest development version.
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See http://polyhedral.info/software for related software.