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

Synopsis

• Usage:

  L = interiorLatticePoints P

• Inputs:
  • P, a convex polyhedron, 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 = P

o1 : Polyhedron

i2 : interiorLatticePoints P

o2 = {| 0 |, | 1 |, | 0 |, | -1 |, 0, | 0  |, | 0  |}
      | 0 |  | 0 |  | 1 |  | 0  |     | -1 |  | 0  |
      | 1 |  | 0 |  | 0 |  | 0  |     | 0  |  | -1 |

o2 : List

i3 : Q = cyclicPolytope(2,4)

o3 = Q

o3 : Polyhedron

i4 : interiorLatticePoints Q

o4 = {| 1 |, | 2 |}
      | 2 |  | 5 |

o4 : List