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# isLatticePolytope -- checks if a polyhedron is a lattice polytope

## Synopsis

• Usage:
b = isLatticePolytope P
• Inputs:
• P, , which must be compact
• Outputs:
• b, , 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 .