# interiorLatticePoints -- computes the lattice points in the relative interior of a polytope

## Synopsis

• Usage:
L = interiorLatticePoints P
• Inputs:
• P, , which must be compact
• Outputs:
• L, a list, containing the interior lattice points as matrices over ZZ with only one column

## Description

latticePoints can only be applied to polytopes, i.e. compact polyhedra. It returns all lattice points in the relative interior of the polytope.

 i1 : P = crossPolytope(3,2) o1 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 8 number of rays => 0 number of vertices => 6 o1 : Polyhedron i2 : interiorLatticePoints P o2 = {| -1 |, | 0 |, | 0 |, 0, | 0 |, | 0 |, | 1 |} | 0 | | -1 | | 0 | | 0 | | 1 | | 0 | | 0 | | 0 | | -1 | | 1 | | 0 | | 0 | o2 : List i3 : Q = cyclicPolytope(2,4) o3 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 o3 : Polyhedron i4 : interiorLatticePoints Q o4 = {| 1 |, | 2 |} | 2 | | 5 | o4 : List

## Ways to use interiorLatticePoints :

• "interiorLatticePoints(Polyhedron)"

## For the programmer

The object interiorLatticePoints is .