Can sage compute the h* vector of a polytope?
We can define polytopes in sage with the command
sage: p = Polytope(A)
Here p is the convex hull of the integer matrix A.
I'm curious if we can compute the h* vector of p. Is this possible?
Roughly, the h* vector of a convex lattice polytope is constructed as follows.
The Ehrhart series can be expressed as a rational function whose numerator is a polynomial. The h* vector of a polytope is the vector of coefficients of this polynomial.
I'm aware that sage can compute the ehrhart polynomial of a polytope with
sage: p.ehrhart_polynomial() but I cant find anything about the h* vector in the documentation.
I know the command in polymake is
$p -> H_STAR_VECTOR, but I'm not sure if this vector can be constructed in sage.
Perhaps a more general question would be: can I pass a polytope defined in sage to polymake and can sage read the results of the polymake operation?