RelInt Lattice Points

[sebasguts]

Hello,

is there a possibility to compute a ( arbitrary ) lattice point in the relative interior of a polytope, if such a point exists? The property REL_INT_POINT does not return a lattice point, not even from a LatticePolytope.

Thank you very much for your help,

Sebastian

[joswig]

Right now there is no such function. However, there is a function to enumerate all lattice points in a rational polytope.

Code: Select all

polytope > print simplex(2,2)->LATTICE_POINTS; 1 0 0 1 0 1 1 0 2 1 1 0 1 1 1 1 2 0

And, there is a related function for the interior lattice points.

Code: Select all

polytope > print simplex(2,2)->INTERIOR_LATTICE_POINTS;

[sebasguts]

Thank you for the quick reply. The last method seems to do what I want, as it also computes the relative interior lattice points of an not full dimensional lattice polytope.

$p = new LatticePolytope(POINTS=>[[1,1,1,1],[1,-1,-1,1],[1,-1,1,1],[1,1,-1,1]]);
print $p->INTERIOR_LATTICE_POINTS;
1 0 0 1

Does it always compute points in the relative interior? The documentation says another thing.

Thank You,
Sebastian

[paffenholz]

INTERIOR_LATTICE_POINTS always computes points in the relative interior (in fact, it usually computes the lattice points first and then checks which do not lie on a facet, and does not care for the affine hull).

Andreas