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

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 = {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 a method function.

The source of this document is in OldPolyhedra.m2:6316:0.