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

- 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 = P

    o1 : Polyhedron

    i2 : toSublattice P

    o2 = Polyhedron{...1...}

    o2 : Polyhedron

## Ways to use toSublattice:

- `toSublattice(Polyhedron)`

## For the programmer

The object toSublattice is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Polyhedra/documentation/old_documentation.m2:2865:0.