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 = P

o1 : Polyhedron

i2 : isVeryAmple P

o2 = true