# 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, , over ZZ with each column representing a sublattice generator
• Outputs:
• B, 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)"

## For the programmer

The object sublatticeBasis is .