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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, A matrix over ZZ containing a sublattice basis

Description

sublatticeBasis computes a basis for the sublattice generated by the columns ofM or by the lattice points ofP.

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

Ways to use `sublatticeBasis` :

sublatticeBasis(Matrix)
sublatticeBasis(Polyhedron)