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MixedMultiplicity :: homIdealPolytope

homIdealPolytope -- Compute the homogeneous ideal corresponding to the vertices of a lattice polytope in $\mathbb{R}^n$.

Synopsis

Description

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

Ways to use homIdealPolytope :

For the programmer

The object homIdealPolytope is a method function with options.