#15280: Extensions of PALP normal form, affine normal form and isomorphisms
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Reporter: jkeitel | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.0
Component: geometry | Resolution:
Keywords: toric | Merged in:
Authors: Jan Keitel | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/jkeitel/normal_form_codimension | 0828630f23bb7a8f285264f4e5a91f89e3ab6a17
Dependencies: #13525 | Stopgaps:
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Description changed by jkeitel:
Old description:
> Currently computing the normal form of a lattice polytope of non-zero
> codimension throws an exception since PALP doesn't cover it. However, the
> PALP algorithm can easily be extended to cover these cases, as suggested
> for example in Section 3.2 of
> http://magma.maths.usyd.edu.au/~kasprzyk/research/pdf/normal_form.pdf .
> The idea is to simply restrict to the sublattice spanned by vertices of
> the polytope, compute the normal form there and embed it back into the
> original ambient space.
>
> I've written a short patch doing precisely that and am attaching it.
> There is of course the long patch #13525 which overhauls all of
> normal_form(), but this point is not addressed there.
New description:
Currently computing the normal form of a lattice polytope of non-zero
codimension throws an exception since PALP doesn't cover it. However, the
PALP algorithm can easily be extended to cover these cases, as suggested
for example in Section 3.2 of
http://magma.maths.usyd.edu.au/~kasprzyk/research/pdf/normal_form.pdf .
The idea is to simply restrict to the sublattice spanned by vertices of
the polytope, compute the normal form there and embed it back into the
original ambient space.
In addition I've included affine_normal_form and find_isomorphism, which
compute the affine normal form of a lattice polytope and isomorphisms
between lattice polytopes, respectively.
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Ticket URL: <http://trac.sagemath.org/ticket/15280#comment:14>
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