#15240: Switch lattice polytopes to point collections
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Reporter: novoselt | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.0
Component: geometry | Resolution:
Keywords: toric sd53 | Merged in:
Authors: Andrey | Reviewers:
Novoseltsev | Work issues:
Report Upstream: N/A | Commit:
Branch: u/novoselt/lp2pc | 9e2512e40f2f3428b63e7dc46170a207bcf36ccc
Dependencies: | Stopgaps:
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Comment (by novoselt):
Replying to [comment:6 vbraun]:
> Replying to [comment:4 novoselt]:
> > Also, I am not sure what the output of "normal_form" should be -
keeping it as a matrix does not seem a good choice.
>
> A matrix isn't totally strange, after all the normal form is a version
of hermite normal form together with permutation of vertices.
>
> If you want to return it as another `LatticePolytope` then the
constructor should keep the vertices in the specified order. The ambient
lattice should be the same as the lattice of the original polytope, imho.
I always want to preserve order, especially when the input consists of
vertices rather than spanning points ;-) The issue with the same lattice
as the original one is that normal forms of equivalent polytopes in
different lattices will compare as different, which seems a bit
counterintuitive with respect to index, i.e. with my default lattice
choice we would have for any 2- or 3-d reflexive polytope
{{{
sage: p.normal_form() == ReflexivePolytope(p.dim(), p.index())
True
}}}
On the other hand starting with a polytope in N and getting as its normal
form something in M isn't great either... So maybe a matrix is the way to
go. Perhaps with vertices as rows rather than columns?
Speaking of `index` - are you OK with the name or something like
`db_index` would be better? I definitely find it very useful, but the
meaning of `index` for morphisms and cones is completely different and
there are "more mathematical" indices associated to polytopes, like
Gorenstein one.
--
Ticket URL: <http://trac.sagemath.org/ticket/15240#comment:7>
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