RelInt Lattice Points
Posted: 23 Jan 2012, 10:26
by 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
Re: RelInt Lattice Points
Posted: 23 Jan 2012, 10:36
by 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;
Re: RelInt Lattice Points
Posted: 23 Jan 2012, 10:57
by 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
Re: RelInt Lattice Points
Posted: 23 Jan 2012, 13:45
by 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