Given a list of vertices of a lattice polytope, the command outputs a homogeneous ideal of $k[x_1,...,x_{n+1}]$ such that the polytope is the convex hull of the lattice points of the dehomogenization of a set of monomials that generates the ideal in $k[x_1,...,x_n]$. The following example computes the homogeneous ideal corresponding to a 2-cross polytope.
i1 : I = homIdealPolytope {(0,1),(1,0),(2,1),(1,2)} 2 2 2 2 o1 = ideal (X X , X X , X X , X X ) 1 2 1 2 1 3 2 3 o1 : Ideal of QQ[X ..X ] 1 3 |
The object homIdealPolytope is a method function with options.