isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice

Synopsis

Function: isNormal
Usage:

b = isNormal P
Inputs:
- P, a convex polyhedron, which must be compact
Outputs:
- b, a Boolean value, true if P is normal in the ambient lattice

Description

isNormal can only be applied to polytopes, i.e. compact polyhedra. It embeds the polytope on height 1 in a space of dimension plus 1 and takes the Cone over this polytope. Then it checks if all elements of the Hilbert basis lie in height 1.

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 : isNormal P

o2 = false

Ways to use this method: