toSublattice -- calculates the preimage of a polytope in the sublattice generated by its lattice points

Synopsis

• Usage:

  Q = toSublattice P

• Inputs:
  • P, a convex polyhedron, which must be compact
• Outputs:
  • Q, a convex polyhedron, preimage of P in the sublattice generated by its lattice points

Description

toSublattice can only be applied to polytopes, i.e. compact polyhedra. It calculates a basis of the sublattice generated by its lattice points, and then takes the affine preimage under the corresponding map.

i1 : P = convexHull transpose matrix {{0,0,0},{1,0,0},{0,1,0},{1,1,3}}

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o1 : Polyhedron

i2 : toSublattice P

o2 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 4
      number of rays => 0
      number of vertices => 4

o2 : Polyhedron