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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 .