isVeryAmple -- checks if the Polyhedron is very ample

Synopsis

Usage:

b = isVeryAmple P
Inputs:
- P, a convex polyhedron, , which must be compact
Outputs:
- b, true if the Polyhedron is very ample, false otherwise

Description

A lattice polytope P in the QQ space of a lattice $M$ is very ample if for every vertex $v\in P$ the semigroup $\mathbb{N}(P\cap M - v)$ generated by $P\cap M - v = \{v'-v|v'\in P\cap M\}$ is saturated in $M$. For example, normal lattice polytopes are very ample.

Note that therefore P must be compact and a lattice polytope.

i1 : P = convexHull matrix {{0,1,0,0,1,0,1,2,0,0},{0,0,1,0,1,0,2,2,0,-1},{0,0,0,1,2,0,1,2,0,-1},{0,0,0,0,-1,1,0,-1,0,1},{0,0,0,0,0,0,-1,-1,1,1}}

o1 = {ambient dimension => 5           }
      dimension of lineality space => 0
      dimension of polyhedron => 5
      number of facets => 22
      number of rays => 0
      number of vertices => 10

o1 : Polyhedron

i2 : isVeryAmple P

o2 = true

Ways to use isVeryAmple :

isVeryAmple(Polyhedron)

For the programmer

The object isVeryAmple is a method function.