Normaliz already supports half-open polyhedra, see section 3.12 ("open
facets") in the Normaliz manual
see https://github.com/Normaliz/Normaliz/blob/master/doc/Normaliz.pdf
On Wednesday, July 7, 2021 at 1:26:01 PM UTC-7 kcrisman wrote:
> Thanks to the MUCH easier install now of things like pynormaliz and latte
> (thanks to all who worked on those!), I can now do the following and
> related computations nicely.
>
> sage: n=1
>
> sage: P =
> Polyhedron(ieqs=[[-(n)/2,1,0,0],[-(n)/2,0,1,0],[(3*n)/2,-1,-1,-1],[0,1
> ....:
> ,0,0],[0,0,1,0],[0,0,0,1],[n,-1,0,0],[n,0,-1,0],[n,0,0,-1]],backend='norma
> ....: liz')
>
> sage: [p.factor() for p in P.ehrhart_quasipolynomial()]
>
> [(1/48) * (t + 2) * (t + 4) * (t + 6), (1/48) * (t - 1) * (t + 1) * (t +
> 3)]
>
> However, what I really need is an Ehrhart quasi-polynomial for some of the
> above inequalities to be *strict* inequalities, and I'm not sure how to do
> that without tedious finding of some (not all) faces and subtracting them
> off (which could be a nightmare and/or wrong in any case). Unfortunately
> changing the non-strict inequalities "by hand" to other numbers gives the
> wrong answers (really unsurprising, since it's a different polytope).
>
> Any thoughts? Thanks!
>
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