polytopeofessential_exponents(basis::MonomialBasis)

Return the polytope of essential exponents corresponding to the monomial basis, i.e. the convex hull of exponent vectors of all occurring monomials. This is only possible if the basis was computed with compute_polytope = true.

Examples

julia> basis = basis_lie_highest_weight(:A, 3, [1,1,1]; monomial_ordering = :deglex,  compute_polytope = true)
Monomial basis of a highest weight module
  of highest weight w_1 + w_2 + w_3
  of dimension 64
  with monomial ordering deglex([x1, x2, x3, x4, x5, x6])
over abstract Lie algebra of type A3 over QQ
where the used birational sequence consists of the following roots:
  [a_1, a_2, a_3, a_1 + a_2, a_2 + a_3, a_1 + a_2 + a_3]

julia> polytope_of_essential_exponents(basis)
Polyhedron in ambient dimension 6