sublatticeBasis -- computes a basis for the sublattice generated by integral vectors or the lattice points of a polytope

Synopsis

• Usage:

  B = sublatticeBasis M

  B = sublatticeBasis P

• Inputs:
  • M, a matrix, over ZZ with each column representing a sublattice generator
  • P, a convex polyhedron
• Outputs:
  • B, A matrix over ZZ containing a sublattice basis

Description

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 : sublatticeBasis P

o2 = | 0 1 1 |
     | 1 0 1 |
     | 0 0 3 |

              3       3
o2 : Matrix ZZ  <-- ZZ