sagemathgh-39349: fix bug for zero-dimension Ehrhart polynomial

make sure that the Ehrhart poly of a zero dimensional lattice polytope
is 1.

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.

URL: sagemath#39349
Reported by: Frédéric Chapoton
Reviewer(s): Dima Pasechnik

build/pkgs/configure/checksums.ini

@@ -1,3 +1,3 @@
 tarball=configure-VERSION.tar.gz
-sha1=f9c1bea6113a6a09430ee1f1aca16c75ed427d48
-sha256=c1e0826fb54dd60e78f19e6fcad0b0ef90b33e1771fbbc2165a54c9297a89557
+sha1=3cab7a94c31a21291853260a833e886cc958d794
+sha256=18b43c409535004df6117293e42809481c997fc84adc3da12a8541d166192673

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-5eb37241946a9ef9130ce36eff7e4f135d980eaf
+b8c2e4eee46c020cecb4655bf1aceb51cadecf13

src/sage/geometry/polyhedron/base_QQ.py

@@ -213,10 +213,12 @@ def integral_points_count(self, verbose=False, use_Hrepresentation=False,
 
     @cached_method(do_pickle=True)
     def ehrhart_polynomial(self, engine=None, variable='t', verbose=False,
-            dual=None, irrational_primal=None, irrational_all_primal=None,
-            maxdet=None, no_decomposition=None, compute_vertex_cones=None,
-            smith_form=None, dualization=None, triangulation=None,
-            triangulation_max_height=None, **kwds):
+                           dual=None, irrational_primal=None,
+                           irrational_all_primal=None, maxdet=None,
+                           no_decomposition=None, compute_vertex_cones=None,
+                           smith_form=None, dualization=None,
+                           triangulation=None,
+                           triangulation_max_height=None, **kwds):
         r"""
         Return the Ehrhart polynomial of this polyhedron.
 
@@ -348,23 +350,33 @@ def ehrhart_polynomial(self, engine=None, variable='t', verbose=False,
             sage: Q = loads(dumps(P))
             sage: Q.ehrhart_polynomial.is_in_cache()
             True
+
+            sage: L = Polyhedron(vertices=[[QQ(0)]])
+            sage: L.ehrhart_polynomial()
+            1
         """
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+        from sage.rings.rational_field import QQ
+        R = PolynomialRing(QQ, variable)
+
         # check if ``self`` is compact and has vertices in ZZ
         if self.is_empty():
-            from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-            from sage.rings.rational_field import QQ
-            R = PolynomialRing(QQ, variable)
             return R.zero()
 
         if not self.is_compact():
             raise ValueError("Ehrhart polynomial only defined for compact polyhedra")
 
         if any(not v.is_integral() for v in self.vertex_generator()):
             raise TypeError("the polytope has nonintegral vertices, use ehrhart_quasipolynomial with backend 'normaliz'")
+
+        if self.dimension() == 0:
+            return R.one()
+
         # Passes to specific latte or normaliz subfunction depending on engine
         if engine is None:
             # set default engine to latte
             engine = 'latte'
+
         if engine == 'latte':
             poly = self._ehrhart_polynomial_latte(verbose, dual,
             irrational_primal, irrational_all_primal, maxdet,

src/sage/geometry/polyhedron/base_ZZ.py

@@ -295,11 +295,13 @@ def _ehrhart_polynomial_normaliz(self, variable='t'):
         raise TypeError("The polyhedron's backend should be 'normaliz'")
 
     @cached_method(do_pickle=True)
-    def ehrhart_polynomial(self, engine=None, variable='t', verbose=False, dual=None,
-            irrational_primal=None, irrational_all_primal=None, maxdet=None,
-            no_decomposition=None, compute_vertex_cones=None, smith_form=None,
-            dualization=None, triangulation=None, triangulation_max_height=None,
-            **kwds):
+    def ehrhart_polynomial(self, engine=None, variable='t', verbose=False,
+                           dual=None, irrational_primal=None,
+                           irrational_all_primal=None, maxdet=None,
+                           no_decomposition=None, compute_vertex_cones=None,
+                           smith_form=None, dualization=None,
+                           triangulation=None, triangulation_max_height=None,
+                           **kwds):
         r"""
         Return the Ehrhart polynomial of this polyhedron.
 
@@ -458,12 +460,16 @@ def ehrhart_polynomial(self, engine=None, variable='t', verbose=False, dual=None
             sage: Q.ehrhart_polynomial.is_in_cache()  # optional - latte_int
             True
         """
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+        from sage.rings.rational_field import QQ
+        R = PolynomialRing(QQ, variable)
+
         if self.is_empty():
-            from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-            from sage.rings.rational_field import QQ
-            R = PolynomialRing(QQ, variable)
             return R.zero()
 
+        if self.dimension() == 0:
+            return R.one()
+
         if not self.is_compact():
             raise ValueError("Ehrhart polynomial only defined for compact polyhedra")