Ticket #9934: trac_9934_class_group_fixes.patch

sage/geometry/fan.py

@@ -1680 +1680 @@
 
         OUTPUT:
 
-        - matrix.
+        A matrix over `ZZ`.
 
         EXAMPLES::
 
@@ -1688 +1688 @@
             sage: fan.Gale_transform()
             [ 1  0  1  0 -2]
             [ 0  1  0  1 -2]
+            sage: _.base_ring()
+            Integer Ring
         """
         if "_Gale_transform" not in self.__dict__:
             m = self.ray_matrix().augment(matrix(self.lattice_dim(), 1))
             m = m.stack(matrix([1]*m.ncols()))
-            self._Gale_transform = m.transpose().integer_kernel().matrix()
+            self._Gale_transform = matrix(ZZ, m.transpose().integer_kernel().matrix())
         return self._Gale_transform
 
     def generating_cone(self, n):

sage/schemes/generic/toric_divisor.py

@@ -1801 +1801 @@
         sage: P2.rational_class_group()
         The toric rational divisor class group of a 2-d CPR-Fano 
         toric variety covered by 3 affine patches
-        sage: D = P2.divisor(1); D
-        V(y)
+        sage: D = P2.divisor(0); D
+        V(x)
         sage: Dclass = D.divisor_class(); Dclass
         Divisor class [1]
         sage: Dclass.lift()
-        V(x)
+        V(y)
         sage: Dclass.parent()
         The toric rational divisor class group of a 2-d CPR-Fano 
         toric variety covered by 3 affine patches
@@ -1823 +1823 @@
             sage: ToricRationalDivisorClassGroup(P2)
             The toric rational divisor class group of a 2-d CPR-Fano 
             toric variety covered by 3 affine patches
+
+        TESTS:
+
+        Make sure we lift integral classes to integral divisors::
+
+            sage: rays = [(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, 0, 1), (2, -1, -1)]
+            sage: cones = [(0, 2, 3), (0, 2, 4), (0, 3, 4), (1, 2, 3), (1, 2, 4), (1, 3, 4)]
+            sage: X = ToricVariety(Fan(cones=cones, rays=rays))
+            sage: Cl = X.rational_class_group()
+            sage: Cl._projection_matrix
+            [1 1 0 0 0]
+            [0 2 1 1 1]
+            sage: Cl._lift_matrix
+            [1 0]
+            [0 0]
+            [0 0]
+            [0 1]
+            [0 0]
+            sage: Cl._lift_matrix.base_ring()
+            Integer Ring
         """
         self._variety = toric_variety
         fan = toric_variety.fan()
@@ -1832 +1852 @@
                                                 dimension=rk, sparse=False)
         gale = fan.Gale_transform()
         self._projection_matrix = gale.matrix_from_columns(range(nrays))
-        self._lift_matrix = self._projection_matrix.solve_right( identity_matrix(rk) )
+        D, U, V = self._projection_matrix.transpose().smith_form()
+        assert all( D[i,i]==1 for i in range(0,D.ncols()) ), \
+            'This is a property of the Gale transform.'
+        self._lift_matrix = (V*D.transpose()*U).transpose()
 
     def _repr_(self):
         r"""

sage/schemes/generic/toric_divisor_class.pyx

@@ -286 +286 @@
             sage: D.divisor_class()
             Divisor class [29, 6, 8, 10, 0]
             sage: Dequiv = D.divisor_class().lift(); Dequiv
-            29/2*V(z0) + 6*V(z1) + 8*V(z2) + 10*V(z3)
+            6*V(z1) - 17*V(z2) - 22*V(z3) - 7*V(z4) + 25*V(z6) + 32*V(z7)
             sage: Dequiv == D
             False
             sage: Dequiv.divisor_class() == D.divisor_class()