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?

1 | initial version |

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?

2 | No.2 Revision |

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.

3 | No.3 Revision |

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?

4 | No.4 Revision |

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?

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