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You can use the normaliz backend (requires Normaliz 3.5.4) and its python interface pynormaliz (requires PyNormaliz 1.16).

You can install them by typing:

sage -i normaliz
sage -i pynormaliz

in a terminal once this ticket has been merged. Then you can type in sage:

sage: C = polytopes.hypercube(3, backend="normaliz")
sage: C.hilbert_series().numerator().coefficients()
[1, 3, 6, 7, 6, 3, 1]

Note that this requires the latest features of this ticket.

You can use the normaliz backend (requires Normaliz 3.5.4) and its python interface pynormaliz (requires PyNormaliz 1.16).

You can install them by typing:

sage -i normaliz
sage -i pynormaliz

Then, in a terminal once this ticket has been merged. Then with Sage 8.9 or more recent, you can type in sage:get the h^*-vector by typing:

sage: C = polytopes.hypercube(3, backend="normaliz")
sage: C.hilbert_series().numerator().coefficients()
C.ehrhart_series().numerator().coefficients()
[1, 3, 6, 7, 6, 3, 23, 23, 1]

Note that this requires This hypercube is the latest features of ±1 cube, so its volume is 8*factorial(3)=48, which is 1+23+23+1.

Eventually, once this ticket. is merged, it will be possible to call it directly on the polytope like so:

sage: C.h_star_vector()
[1, 23, 23, 1]