hstar.sage

def h_star_vector(P):
    d = P.dim()
    E = P.ehrhart_polynomial()
    return [sum([E(t)*binomial(d+1,j-t)*(-1)^(j-t) for t in (0..j)]) for j in (0..d)]

def h_star_polynomial(P):
    R.<t> = PolynomialRing(QQ)
    temp = h_star_vector(P)
    return sum([temp[i]*t^i for i in range(len(temp))])

def hypercube(d):
    return Polyhedron(vertices = list(product([0,1],repeat=d)))

def Hmatrix(P):
    pH = p.Hrepresentation()
    return (pH.b().transpose() + pH.A().transpose()).transpose()

def h_star_vector_of_hypersimplex(n,k):
    return h_star_vector(polytopes.hypersimplex(n,k))

def h_star_polynomial_of_hypersimplex(n,k):
    return h_star_polynomial(polytopes.hypersimplex(n,k))

def n_choose_2(n):
    return Subsets(list(range(n), 2))

def permutohedron(n):
    vertices = [vector(list(p)) for p in Permutations(n)]
    return Polyhedron(vertices=vertices)