isLatticePolytope -- checks if a polyhedron is a lattice polytope

Usage:

b = isLatticePolytope P
Inputs:
- P, a convex polyhedron, which must be compact
Outputs:
- b, a Boolean value, true if P is a lattice polytope

Description

isLatticePolytope can only be applied to polytopes, i.e. compact polyhedra. It simply checks if it is compact and all vertices are lattice points.

i1 : P = intersection(matrix{{2,0},{0,-3},{-3,0},{0,2}},matrix{{1},{1},{1},{1}})

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o1 : Polyhedron

i2 : isLatticePolytope P

o2 = false

i3 : P = intersection(matrix{{2,0},{0,-3},{-3,0},{0,2}},matrix{{4},{6},{3},{6}})

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 : isLatticePolytope P

o4 = true

Ways to use isLatticePolytope:

isLatticePolytope(Polyhedron)

For the programmer

The object isLatticePolytope is a method function.

The source of this document is in OldPolyhedra.m2:5674:0.