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# isVeryAmple -- checks if the Polyhedron is very ample

## Synopsis

• Usage:
b = isVeryAmple P
• Inputs:
• P, , , which must be compact
• Outputs:

## 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 .