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Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities?

I am interested in knowing this because I understand that Ehrhart's polynomial for a polytope will determine the number of integer points inside this polytope.

Alternatively if someone knows of an existing method to count the number of integer points inside a convex polytope (described by its vertices or a set of inequalities), it would be equally helpful.

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  • $\begingroup$ This thread looks helpful: it shows brute force ways to count lattice points within a polytope given by inequalities. They likely will fail in high dimensions because there will be too many points to inspect. $\endgroup$
    – whuber
    Commented Mar 19, 2013 at 17:56
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    $\begingroup$ Thanks whuber. You're right, its not useful in higher dimensions. For my applications, I am having to deal with inequalities having n variables and 2n constraints. Here n ~ 20 to 30 . Also, I had seen that computing the volume of a general polytope is #P-Hard. I am suspecting that computing the coefficients of its Erhart-Polynomial too is hard. But still I am in search of algorithms. I found this software called LattE which seems to be reasonably fast for n=10 . However, I do not know how to invoke commands of this software from within a mathematica notebook or a script. $\endgroup$
    – Pavithran Iyer
    Commented Mar 20, 2013 at 3:34
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    $\begingroup$ Have you seen Barvinok's papers already? $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Apr 30, 2013 at 3:40

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