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

## Synopsis

• Usage:
Q = toSublattice P
• Inputs:
• P, , which must be compact
• Outputs:
• Q, , 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 = P o1 : Polyhedron i2 : toSublattice P o2 = Polyhedron{...1...} o2 : Polyhedron

## Ways to use toSublattice :

• "toSublattice(Polyhedron)"

## For the programmer

The object toSublattice is .