On Wednesday, July 7, 2021 at 2:36:27 PM UTC-7 kcrisman wrote:
> 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
>>
>
> Thank you! But, based on the tickets I've just been cc:ed on, probably
> there is no current easy Sage interface for these?
>
That's right. You would have to use PyNormaliz directly.
Also, it's only certain of the inequalities I would want to be strict - is
> that too much to ask? Maybe "Semiopen polyhedra" is more like what I'm
> looking for - I do not know the facets, only the inequalities, which in
> more complicated examples than the one I provided tend to have nontrivial
> interactions.
>
I think Normaliz only supports the special case of polyhedra with some
facets removed, not the more general situation in which you would remove
some lower-dimensional faces. This case would still have to be handled
using a combination of techniques, including inclusion-exclusion and
reciprocity (including the technique of "inside out polytopes").
sage.geometry.polyhedron.modules.FormalPolyhedraModule is a step toward
expressing such decomposition and transformation techniques,
see https://trac.sagemath.org/ticket/29799
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