sage.geometry: Use even more block tags

Author: Matthias Koeppe

src/sage/geometry/cone.py

@@ -2518,22 +2518,23 @@ def face_lattice(self):
         Note that if ``cone`` is a face of ``supercone``, then the face
         lattice of ``cone`` consists of (appropriate) faces of ``supercone``::
 
+            sage: # needs sage.combinat sage.graphs
             sage: supercone = Cone([(1,2,3,4), (5,6,7,8),
             ....:                   (1,2,4,8), (1,3,9,7)])
-            sage: supercone.face_lattice()                                              # needs sage.combinat sage.graphs
+            sage: supercone.face_lattice()
             Finite lattice containing 16 elements with distinguished linear extension
-            sage: supercone.face_lattice().top()                                        # needs sage.combinat sage.graphs
+            sage: supercone.face_lattice().top()
             4-d cone in 4-d lattice N
-            sage: cone = supercone.facets()[0]                                          # needs sage.combinat sage.graphs
-            sage: cone                                                                  # needs sage.combinat sage.graphs
+            sage: cone = supercone.facets()[0]
+            sage: cone
             3-d face of 4-d cone in 4-d lattice N
-            sage: cone.face_lattice()                                                   # needs sage.combinat sage.graphs
+            sage: cone.face_lattice()
             Finite poset containing 8 elements with distinguished linear extension
-            sage: cone.face_lattice().bottom()                                          # needs sage.combinat sage.graphs
+            sage: cone.face_lattice().bottom()
             0-d face of 4-d cone in 4-d lattice N
-            sage: cone.face_lattice().top()                                             # needs sage.combinat sage.graphs
+            sage: cone.face_lattice().top()
             3-d face of 4-d cone in 4-d lattice N
-            sage: cone.face_lattice().top() == cone                                     # needs sage.combinat sage.graphs
+            sage: cone.face_lattice().top() == cone
             True
 
         TESTS::
@@ -2721,16 +2722,17 @@ def faces(self, dim=None, codim=None):
         In the case of non-strictly convex cones even faces of small
         non-negative dimension may be missing::
 
+            sage: # needs sage.graphs
             sage: halfplane = Cone([(1,0), (0,1), (-1,0)])
-            sage: halfplane.faces(0)                                                    # needs sage.graphs
+            sage: halfplane.faces(0)
             ()
-            sage: halfplane.faces()                                                     # needs sage.graphs
+            sage: halfplane.faces()
             ((1-d face of 2-d cone in 2-d lattice N,),
              (2-d cone in 2-d lattice N,))
             sage: plane = Cone([(1,0), (0,1), (-1,-1)])
-            sage: plane.faces(1)                                                        # needs sage.graphs
+            sage: plane.faces(1)
             ()
-            sage: plane.faces()                                                         # needs sage.graphs
+            sage: plane.faces()
             ((2-d cone in 2-d lattice N,),)
 
         TESTS:
@@ -2908,19 +2910,20 @@ def facet_of(self):
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: octant = Cone([(1,0,0), (0,1,0), (0,0,1)])
-            sage: octant.facet_of()                                                     # needs sage.graphs
+            sage: octant.facet_of()
             ()
-            sage: one_face = octant.faces(1)[0]                                         # needs sage.graphs
-            sage: len(one_face.facet_of())                                              # needs sage.graphs
+            sage: one_face = octant.faces(1)[0]
+            sage: len(one_face.facet_of())
             2
-            sage: one_face.facet_of()[1]                                                # needs sage.graphs
+            sage: one_face.facet_of()[1]
             2-d face of 3-d cone in 3-d lattice N
 
         While fan is the top element of its own cone lattice, which is a
         variant of a face lattice, we do not refer to cones as its facets::
 
-            sage: fan = Fan([octant])
+            sage: fan = Fan([octant])                                                   # needs sage.graphs
             sage: fan.generating_cone(0).facet_of()                                     # needs sage.graphs
             ()
 
@@ -3923,17 +3926,18 @@ def sublattice_quotient(self, *args, **kwds):
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: C2_Z2 = Cone([(1,0), (1,2)])     # C^2/Z_2
-            sage: c1, c2 = C2_Z2.facets()                                               # needs sage.graphs
-            sage: c2.sublattice_quotient()                                              # needs sage.graphs
+            sage: c1, c2 = C2_Z2.facets()
+            sage: c2.sublattice_quotient()
             1-d lattice, quotient of 2-d lattice N by Sublattice <N(1, 2)>
             sage: N = C2_Z2.lattice()
             sage: n = N(1,1)
-            sage: n_bar = c2.sublattice_quotient(n); n_bar                              # needs sage.graphs
+            sage: n_bar = c2.sublattice_quotient(n); n_bar
             N[1, 1]
-            sage: n_bar.lift()                                                          # needs sage.graphs
+            sage: n_bar.lift()
             N(1, 1)
-            sage: vector(n_bar)                                                         # needs sage.graphs
+            sage: vector(n_bar)
             (-1)
         """
         if "_sublattice_quotient" not in self.__dict__:
@@ -4205,30 +4209,32 @@ def relative_orthogonal_quotient(self, supercone):
 
         EXAMPLES::
 
+            sage: # needs sage.graphs
             sage: rho = Cone([(1,1,1,3), (1,-1,1,3), (-1,-1,1,3), (-1,1,1,3)])
             sage: rho.orthogonal_sublattice()
             Sublattice <M(0, 0, 3, -1)>
-            sage: sigma = rho.facets()[1]                                               # needs sage.graphs
-            sage: sigma.orthogonal_sublattice()                                         # needs sage.graphs
+            sage: sigma = rho.facets()[1]
+            sage: sigma.orthogonal_sublattice()
             Sublattice <M(0, 1, 1, 0), M(0, 0, 3, -1)>
-            sage: sigma.is_face_of(rho)                                                 # needs sage.graphs
+            sage: sigma.is_face_of(rho)
             True
-            sage: Q = sigma.relative_orthogonal_quotient(rho); Q                        # needs sage.graphs
+            sage: Q = sigma.relative_orthogonal_quotient(rho); Q
             1-d lattice, quotient
             of Sublattice <M(0, 1, 1, 0), M(0, 0, 3, -1)>
             by Sublattice <M(0, 0, 3, -1)>
-            sage: Q.gens()                                                              # needs sage.graphs
+            sage: Q.gens()
             (M[0, 1, 1, 0],)
 
         Different codimension::
 
+            sage: # needs sage.graphs
             sage: rho = Cone([[1,-1,1,3],[-1,-1,1,3]])
-            sage: sigma = rho.facets()[0]                                               # needs sage.graphs
-            sage: sigma.orthogonal_sublattice()                                         # needs sage.graphs
+            sage: sigma = rho.facets()[0]
+            sage: sigma.orthogonal_sublattice()
             Sublattice <M(1, 0, 2, -1), M(0, 1, 1, 0), M(0, 0, 3, -1)>
-            sage: rho.orthogonal_sublattice()                                           # needs sage.graphs
+            sage: rho.orthogonal_sublattice()
             Sublattice <M(0, 1, 1, 0), M(0, 0, 3, -1)>
-            sage: sigma.relative_orthogonal_quotient(rho).gens()                        # needs sage.graphs
+            sage: sigma.relative_orthogonal_quotient(rho).gens()
             (M[-1, 0, -2, 1],)
 
         Sign choice in the codimension one case::
@@ -5741,19 +5747,20 @@ def positive_operators_gens(self, K2=None):
         The positive operators on a permuted cone can be obtained by
         conjugation::
 
+            sage: # needs sage.groups
             sage: K = random_cone(max_ambient_dim=3)
             sage: L = ToricLattice(K.lattice_dim()**2)
-            sage: p = SymmetricGroup(K.lattice_dim()).random_element().matrix()         # needs sage.groups
-            sage: pK = Cone((p*k for k in K), K.lattice(), check=False)                 # needs sage.groups
-            sage: pi_gens = pK.positive_operators_gens()                                # needs sage.groups
-            sage: actual = Cone((g.list() for g in pi_gens),                            # needs sage.groups
+            sage: p = SymmetricGroup(K.lattice_dim()).random_element().matrix()
+            sage: pK = Cone((p*k for k in K), K.lattice(), check=False)
+            sage: pi_gens = pK.positive_operators_gens()
+            sage: actual = Cone((g.list() for g in pi_gens),
             ....:               lattice=L,
             ....:               check=False)
             sage: pi_gens = K.positive_operators_gens()
-            sage: expected = Cone(((p*g*p.inverse()).list() for g in pi_gens),          # needs sage.groups
+            sage: expected = Cone(((p*g*p.inverse()).list() for g in pi_gens),
             ....:                 lattice=L,
             ....:                 check=False)
-            sage: actual.is_equivalent(expected)                                        # needs sage.groups
+            sage: actual.is_equivalent(expected)
             True
 
         An operator is positive from one cone to another if and only if

src/sage/geometry/cone_catalog.py

@@ -527,13 +527,14 @@ def schur(ambient_dim=None, lattice=None):
     generators of the Schur cone and the nonnegative orthant in
     dimension five is `\left(3/4\right)\pi`::
 
+        sage: # needs sage.rings.number_fields
         sage: P = cones.schur(5)
         sage: Q = cones.nonnegative_orthant(5)
         sage: G = ( g.change_ring(QQbar).normalized() for g in P )
         sage: H = ( h.change_ring(QQbar).normalized() for h in Q )
-        sage: actual = max(arccos(u.inner_product(v)) for u in G for v in H)            # needs sage.rings.number_fields
-        sage: expected = 3*pi/4                                                         # needs sage.rings.number_fields
-        sage: abs(actual - expected).n() < 1e-12                                        # needs sage.rings.number_fields
+        sage: actual = max(arccos(u.inner_product(v)) for u in G for v in H)
+        sage: expected = 3*pi/4
+        sage: abs(actual - expected).n() < 1e-12
         True
 
     The dual of the Schur cone is the "downward monotonic cone"

src/sage/geometry/fan.py

@@ -196,11 +196,12 @@
 
 We can also make ``fan3`` smooth, but it will take a bit more work::
 
+    sage: # needs palp
     sage: cube = lattice_polytope.cross_polytope(3).polar()
-    sage: sk = cube.skeleton_points(2)                                                  # needs palp
-    sage: rays = [cube.point(p) for p in sk]                                            # needs palp
-    sage: fan4 = fan3.subdivide(new_rays=rays)                                          # needs palp
-    sage: fan4.is_smooth()                                                              # needs palp
+    sage: sk = cube.skeleton_points(2)
+    sage: rays = [cube.point(p) for p in sk]
+    sage: fan4 = fan3.subdivide(new_rays=rays)
+    sage: fan4.is_smooth()
     True
 
 Let's see how "different" are ``fan2`` and ``fan4``::