Bug in h_star_vector for polytopes with the normaliz backend

[yuan-zhou]

Dr. Ben Braun reported the following error.

The h-star-vector records the coefficients of the polynomial in the
numerator of the Ehrhart series of a lattice polytope.
The method h_star_vector() for polytopes with the normaliz backend was implemented in #28413.
The implementation seems to have an error, namely that it drops internal zeros from the vector.

Example:

sage: L = [[1, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [1, 0, 0,
....:  1, 0, 0], [1, 0, 0, 0, 1, 0], [1, 0, 0, 1, 2, 3]]
sage: P = Polyhedron(vertices=L,backend='normaliz')
sage: P.ehrhart_series().numerator()
2*t^2 + 1
sage: P.h_star_vector()
[1, 2]

Actually, the correct return should be [1, 0, 2].

This bug is caused by the line 1437 of src/sage/geometry/polyhedron/backend_normaliz.py, which forgets to pass sparse=False into self.ehrhart_series().numerator().coefficients().

We fix the bug by changing this line to
return self.ehrhart_series().numerator().list().

CC: @braunmath @sophiasage @jplab @fchapoton @w-bruns @videlec @mkoeppe

Component: geometry

Keywords: polytopes, normaliz

Author: Yuan Zhou

Branch/Commit: 6027fb1

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/33847

[yuan-zhou]

Branch: u/yzh/bug_in_h_star_vector_for_polytopes_with_the_normaliz_backend

[yuan-zhou]

New commits:

0a08dfb

return all coefficients, including the zero coefficients of P.ehrhart_series().numerator()

[yuan-zhou]

Commit: 0a08dfb

[mkoeppe]

comment:4

Output is missing in the new doctest

[sagetrac-git]

Changed commit from 0a08dfb to 6027fb1

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

6027fb1

new doctest

[fchapoton]

comment:7

please fill the "Authors" box

[yuan-zhou]

Author: Yuan Zhou

[yuan-zhou]

comment:9

Patchbot reports one doctest failure, as follows. I'm not sure if it is related.

File "sage/parallel/map_reduce.py", line 1151, in sage.parallel.map_reduce.RESetMapReduce.start_workers
Failed example:
    all(not w.is_alive() for w in S._workers)
Expected:
    True
Got:
    False

[mkoeppe]

comment:10

unrelated, that's #33834

[mkoeppe]

Reviewer: Matthias Koeppe

[vbraun]

Changed branch from u/yzh/bug_in_h_star_vector_for_polytopes_with_the_normaliz_backend to 6027fb1