Trac #33847: Bug in h_star_vector for polytopes with the normaliz bac…

…kend

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()`.

URL: https://trac.sagemath.org/33847
Reported by: yzh
Ticket author(s): Yuan Zhou
Reviewer(s): Matthias Koeppe

src/sage/geometry/polyhedron/backend_normaliz.py

@@ -1433,8 +1433,18 @@ def _h_star_vector_normaliz(self):
             sage: cube = polytopes.cube(intervals='zero_one', backend='normaliz') # optional - pynormaliz
             sage: cube.h_star_vector()   # optional - pynormaliz
             [1, 4, 1]
+
+        TESTS:
+
+        Check that :trac:`33847` is fixed::
+
+            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')  # optional - pynormaliz
+            sage: P.h_star_vector()                              # optional - pynormaliz
+            [1, 0, 2]
         """
-        return self.ehrhart_series().numerator().coefficients()
+        return self.ehrhart_series().numerator().list()
 
     def _volume_normaliz(self, measure='euclidean'):
         r"""