gh-36033: sage.geometry: Update # needs, use block-scoped tags

    
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Cherry-picked from
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URL: #36033
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe

src/sage/geometry/abc.pyx

@@ -13,13 +13,13 @@ class LatticePolytope:
     EXAMPLES::
 
         sage: import sage.geometry.abc
-        sage: P = LatticePolytope([(1,2,3), (4,5,6)])                         # optional - sage.geometry.polyhedron
-        sage: isinstance(P, sage.geometry.abc.LatticePolytope)                # optional - sage.geometry.polyhedron
+        sage: P = LatticePolytope([(1,2,3), (4,5,6)])                                   # needs sage.geometry.polyhedron
+        sage: isinstance(P, sage.geometry.abc.LatticePolytope)                          # needs sage.geometry.polyhedron
         True
 
     By design, there is a unique direct subclass::
 
-        sage: sage.geometry.abc.LatticePolytope.__subclasses__()              # optional - sage.geometry.polyhedron
+        sage: sage.geometry.abc.LatticePolytope.__subclasses__()                        # needs sage.geometry.polyhedron
         [<class 'sage.geometry.lattice_polytope.LatticePolytopeClass'>]
 
         sage: len(sage.geometry.abc.Polyhedron.__subclasses__()) <= 1
@@ -39,13 +39,13 @@ class ConvexRationalPolyhedralCone:
     EXAMPLES::
 
         sage: import sage.geometry.abc
-        sage: C = cones.nonnegative_orthant(2)                                # optional - sage.geometry.polyhedron
-        sage: isinstance(C, sage.geometry.abc.ConvexRationalPolyhedralCone)   # optional - sage.geometry.polyhedron
+        sage: C = cones.nonnegative_orthant(2)                                          # needs sage.geometry.polyhedron
+        sage: isinstance(C, sage.geometry.abc.ConvexRationalPolyhedralCone)             # needs sage.geometry.polyhedron
         True
 
     By design, there is a unique direct subclass::
 
-        sage: sage.geometry.abc.ConvexRationalPolyhedralCone.__subclasses__() # optional - sage.geometry.polyhedron
+        sage: sage.geometry.abc.ConvexRationalPolyhedralCone.__subclasses__()           # needs sage.geometry.polyhedron
         [<class 'sage.geometry.cone.ConvexRationalPolyhedralCone'>]
 
         sage: len(sage.geometry.abc.Polyhedron.__subclasses__()) <= 1
@@ -65,13 +65,13 @@ class Polyhedron:
     EXAMPLES::
 
         sage: import sage.geometry.abc
-        sage: P = polytopes.cube()                                            # optional - sage.geometry.polyhedron
-        sage: isinstance(P, sage.geometry.abc.Polyhedron)                     # optional - sage.geometry.polyhedron
+        sage: P = polytopes.cube()                                                      # needs sage.geometry.polyhedron
+        sage: isinstance(P, sage.geometry.abc.Polyhedron)                               # needs sage.geometry.polyhedron
         True
 
     By design, there is a unique direct subclass::
 
-        sage: sage.geometry.abc.Polyhedron.__subclasses__()                   # optional - sage.geometry.polyhedron
+        sage: sage.geometry.abc.Polyhedron.__subclasses__()                             # needs sage.geometry.polyhedron
         [<class 'sage.geometry.polyhedron.base0.Polyhedron_base0'>]
 
         sage: len(sage.geometry.abc.Polyhedron.__subclasses__()) <= 1

src/sage/geometry/cone_catalog.py

@@ -374,8 +374,8 @@ def rearrangement(p, ambient_dim=None, lattice=None):
         sage: ambient_dim = ZZ.random_element(2,10).abs()
         sage: p = ZZ.random_element(1, ambient_dim)
         sage: K = cones.rearrangement(p, ambient_dim)
-        sage: P = SymmetricGroup(ambient_dim).random_element().matrix()     # optional - sage.groups
-        sage: all(K.contains(P*r) for r in K)                               # optional - sage.groups
+        sage: P = SymmetricGroup(ambient_dim).random_element().matrix()                 # needs sage.groups
+        sage: all(K.contains(P*r) for r in K)                                           # needs sage.groups
         True
 
     The smallest ``p`` components of every element of the rearrangement
@@ -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 )              # optional - sage.rings.number_fields
-        sage: H = ( h.change_ring(QQbar).normalized() for h in Q )              # optional - sage.rings.number_fields
-        sage: actual = max(arccos(u.inner_product(v)) for u in G for v in H)    # optional - sage.rings.number_fields
-        sage: expected = 3*pi/4                                                 # optional - sage.rings.number_fields
-        sage: abs(actual - expected).n() < 1e-12                                # optional - sage.rings.number_fields
+        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)
+        sage: expected = 3*pi/4
+        sage: abs(actual - expected).n() < 1e-12
         True
 
     The dual of the Schur cone is the "downward monotonic cone"
@@ -566,7 +567,7 @@ def schur(ambient_dim=None, lattice=None):
         True
         sage: x = V.random_element()
         sage: y = V.random_element()
-        sage: majorized_by(x,y) == ( (y-x) in S )                               # optional - sage.rings.number_fields
+        sage: majorized_by(x,y) == ( (y-x) in S )
         True
 
     If a ``lattice`` was given, it is actually used::