Software package barvinok. 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. The library includes isl and PolyLib and uses NTL.

References in zbMATH (referenced in 11 articles )

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  1. Assarf, Benjamin; Gawrilow, Ewgenij; Herr, Katrin; Joswig, Michael; Lorenz, Benjamin; Paffenholz, Andreas; Rehn, Thomas: Computing convex hulls and counting integer points with polymake (2017)
  2. Breuer, Felix; Zafeirakopoulos, Zafeirakis: Polyhedral omega: a new algorithm for solving linear Diophantine systems (2017)
  3. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  4. Bielecki, Włodzimierz; Pałkowski, Marek: Tiling arbitrarily nested loops by means of the transitive closure of dependence graphs (2016)
  5. Fu, Norie; Shibuta, Takafumi: An algorithm for solving parametric integer program (2015)
  6. Kurz, Sascha; Tautenhahn, Nikolas: On Dedekind’s problem for complete simple games (2013)
  7. Hubler, Shane L.; Craciun, Gheorghe: Counting chemical compositions using Ehrhart quasi-polynomials (2012)
  8. Beck, Matthias; van Herick, Andrew: Enumeration of $4 \times 4$ magic squares (2011)
  9. Bianconi, Francesco; Fernández, Antonio: On the occurrence probability of local binary patterns: a theoretical study (2011)
  10. Beck, Matthias; Haase, Christian; Sottile, Frank: $\lower .95ex \hbox$\rightarrow$ \mskip-23mu \nearrow + \nwarrow \mskip-23mu \lower .95ex \hbox$\leftarrow$ + \swarrow \mskip-2mu \searrow = \hbox$\diagup\mskip-1mu\diagdown$ \lower.48ex\hbox$\mskip-31mu\hboxto 5.85mm\strut\hrulefill\strut$$ --- Formulas of Brion, Lawrence, and Varchenko on rational generating functions for cones$$ (2009)
  11. Beck, Matthias; Robins, Sinai: Computing the continuous discretely. Integer-point enumeration in polyhedra (2007)