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### 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?

### 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 know the command in polymake is $p -> H_STAR_VECTOR, but I'm not sure if this vector can be constructed in sage. ### 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 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?

### 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?