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.

Unlike the program distributed with PolyLib, it does not suffer from degenerate domains. (examples of such degenerate problems (tar.gz)) Note that more recent version of PolyLib do produce complete results for some of these problems.

Example runs: Philippe's simple example, Pugh's example, Example generated by Compaan, Sturmfels' vector partition function example, A3, Petr's Ehrhart series example

Try it!

The library includes PolyLib and uses NTL.

It uses Barvinok's decomposition which has also been (previously) implemented in LattE.

Since release 0.22, the barvinok distribution includes the bernstein library for computing bounds on polynomials over parametric polytopes.

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.

See the README, the paper, the technical report or the user manual for more information.
See the git repository for the latest development version.

Send bug reports to skimo@kotnet.org 

Icon  Name                    Last modified      Size  Description
[DIR] Parent Directory                             -   
[TXT] A3.txt                  04-Oct-2004 15:04  3.1K  
[   ] barvinok-0.01.tar.bz2   20-Sep-2007 14:55  127K  
[   ] barvinok-0.01.tar.gz    09-Jan-2004 10:42  172K  
[   ] barvinok-0.02.tar.bz2   20-Sep-2007 14:55  128K  
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[   ] barvinok.pdf            17-Oct-2008 00:26  878K  
[TXT] compaan.txt             04-Oct-2004 14:56  2.6K  
[   ] ehrhart_degenerate.t..> 15-May-2004 00:03  4.5K  
[TXT] petr.txt                17-Nov-2004 20:24  749   
[TXT] philippe.txt            04-Oct-2004 14:51  1.9K  
[TXT] pugh.txt                04-Oct-2004 15:00  838   
[TXT] sturmfels.txt           04-Oct-2004 15:01  9.1K
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