src/sage/topology: remove all "needs sage.foo" tags

These are unmaintained, and do nothing in upstream SageMath.

Author: orlitzky

src/sage/topology/all.py

@@ -1,4 +1,3 @@
-# sage.doctest: needs sage.graphs
 from sage.topology.simplicial_complex import SimplicialComplex, Simplex
 
 from sage.topology.simplicial_complex_morphism import SimplicialComplexMorphism

src/sage/topology/cell_complex.py

@@ -1,4 +1,3 @@
-# sage.doctest: needs sage.graphs
 r"""
 Generic cell complexes
 
@@ -228,7 +227,6 @@ def _n_cells_sorted(self, n, subcomplex=None):
             sage: Z._n_cells_sorted(2, subcomplex=K)
             [(1, 2, 4), (1, 3, 4)]
 
-            sage: # needs sage.symbolic
             sage: S = SimplicialComplex([[complex(i), complex(1)]])
             sage: S._n_cells_sorted(0)
             [((1+0j),), (1j,)]
@@ -508,7 +506,6 @@ def homology(self, dim=None, base_ring=ZZ, subcomplex=None,
 
         EXAMPLES::
 
-            sage: # needs sage.modules
             sage: P = delta_complexes.RealProjectivePlane()
             sage: P.homology()
             {0: 0, 1: C2, 2: 0}
@@ -527,7 +524,7 @@ def homology(self, dim=None, base_ring=ZZ, subcomplex=None,
         Sage can compute generators of homology groups::
 
             sage: S2 = simplicial_complexes.Sphere(2)
-            sage: S2.homology(dim=2, generators=True, base_ring=GF(2))                  # needs sage.modules
+            sage: S2.homology(dim=2, generators=True, base_ring=GF(2))
             [(Vector space of dimension 1 over Finite Field of size 2,
               (0, 1, 2) + (0, 1, 3) + (0, 2, 3) + (1, 2, 3))]
 
@@ -538,15 +535,15 @@ def homology(self, dim=None, base_ring=ZZ, subcomplex=None,
         complexes, each generator is a linear combination of cubes::
 
             sage: S2_cub = cubical_complexes.Sphere(2)
-            sage: S2_cub.homology(dim=2, generators=True)                               # needs sage.modules
+            sage: S2_cub.homology(dim=2, generators=True)
             [(Z,
              [0,0] x [0,1] x [0,1] - [0,1] x [0,0] x [0,1] + [0,1] x [0,1] x [0,0]
              - [0,1] x [0,1] x [1,1] + [0,1] x [1,1] x [0,1] - [1,1] x [0,1] x [0,1])]
 
         Similarly for simplicial sets::
 
             sage: S = simplicial_sets.Sphere(2)
-            sage: S.homology(generators=True)                                           # needs sage.modules
+            sage: S.homology(generators=True)
             {0: [], 1: 0, 2: [(Z, sigma_2)]}
         """
         from sage.homology.homology_group import HomologyGroup
@@ -625,14 +622,13 @@ def cohomology(self, dim=None, base_ring=ZZ, subcomplex=None,
         EXAMPLES::
 
             sage: circle = SimplicialComplex([[0,1], [1,2], [0, 2]])
-            sage: circle.cohomology(0)                                                  # needs sage.modules
+            sage: circle.cohomology(0)
             0
-            sage: circle.cohomology(1)                                                  # needs sage.modules
+            sage: circle.cohomology(1)
             Z
 
         Projective plane::
 
-            sage: # needs sage.modules
             sage: P2 = SimplicialComplex([[0,1,2], [0,2,3], [0,1,5], [0,4,5], [0,3,4],
             ....:                         [1,2,4], [1,3,4], [1,3,5], [2,3,5], [2,4,5]])
             sage: P2.cohomology(2)
@@ -642,20 +638,20 @@ def cohomology(self, dim=None, base_ring=ZZ, subcomplex=None,
             sage: P2.cohomology(2, base_ring=GF(3))
             Vector space of dimension 0 over Finite Field of size 3
 
-            sage: cubical_complexes.KleinBottle().cohomology(2)                         # needs sage.modules
+            sage: cubical_complexes.KleinBottle().cohomology(2)
             C2
 
         Relative cohomology::
 
             sage: T = SimplicialComplex([[0,1]])
             sage: U = SimplicialComplex([[0], [1]])
-            sage: T.cohomology(1, subcomplex=U)                                         # needs sage.modules
+            sage: T.cohomology(1, subcomplex=U)
             Z
 
         A `\Delta`-complex example::
 
             sage: s5 = delta_complexes.Sphere(5)
-            sage: s5.cohomology(base_ring=GF(7))[5]                                     # needs sage.modules
+            sage: s5.cohomology(base_ring=GF(7))[5]
             Vector space of dimension 1 over Finite Field of size 7
         """
         return self.homology(dim=dim, cohomology=True, base_ring=base_ring,
@@ -689,23 +685,23 @@ def betti(self, dim=None, subcomplex=None):
         two-point space with itself::
 
             sage: S = SimplicialComplex([[0], [1]])
-            sage: (S*S*S).betti()                                                       # needs sage.modules
+            sage: (S*S*S).betti()
             {0: 1, 1: 0, 2: 1}
-            sage: (S*S*S).betti([1,2])                                                  # needs sage.modules
+            sage: (S*S*S).betti([1,2])
             {1: 0, 2: 1}
-            sage: (S*S*S).betti(2)                                                      # needs sage.modules
+            sage: (S*S*S).betti(2)
             1
 
         Or build the two-sphere as a `\Delta`-complex::
 
             sage: S2 = delta_complexes.Sphere(2)
-            sage: S2.betti([1,2])                                                       # needs sage.modules
+            sage: S2.betti([1,2])
             {1: 0, 2: 1}
 
         Or as a cubical complex::
 
             sage: S2c = cubical_complexes.Sphere(2)
-            sage: S2c.betti(2)                                                          # needs sage.modules
+            sage: S2c.betti(2)
             1
         """
         dic = {}
@@ -733,9 +729,9 @@ def is_acyclic(self, base_ring=ZZ) -> bool:
         EXAMPLES::
 
             sage: RP2 = simplicial_complexes.RealProjectivePlane()
-            sage: RP2.is_acyclic()                                                      # needs sage.modules
+            sage: RP2.is_acyclic()
             False
-            sage: RP2.is_acyclic(QQ)                                                    # needs sage.modules
+            sage: RP2.is_acyclic(QQ)
             True
 
         This first computes the Euler characteristic: if it is not 1,
@@ -779,12 +775,12 @@ def n_chains(self, n, base_ring=ZZ, cochains=False):
         EXAMPLES::
 
             sage: S2 = simplicial_complexes.Sphere(2)
-            sage: S2.n_chains(1, QQ)                                                    # needs sage.modules
+            sage: S2.n_chains(1, QQ)
             Free module generated by {(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)}
              over Rational Field
-            sage: list(S2.n_chains(1, QQ, cochains=False).basis())                      # needs sage.modules
+            sage: list(S2.n_chains(1, QQ, cochains=False).basis())
             [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]
-            sage: list(S2.n_chains(1, QQ, cochains=True).basis())                       # needs sage.modules
+            sage: list(S2.n_chains(1, QQ, cochains=True).basis())
             [\chi_(0, 1), \chi_(0, 2), \chi_(0, 3), \chi_(1, 2), \chi_(1, 3), \chi_(2, 3)]
         """
         from sage.homology.chains import Chains, Cochains
@@ -847,7 +843,6 @@ def homology_with_basis(self, base_ring=QQ, cohomology=False):
 
         EXAMPLES::
 
-            sage: # needs sage.modules
             sage: K = simplicial_complexes.KleinBottle()
             sage: H = K.homology_with_basis(QQ); H
             Homology module of Minimal triangulation of the Klein bottle
@@ -863,12 +858,12 @@ def homology_with_basis(self, base_ring=QQ, cohomology=False):
         The homology is constructed as a graded object, so for
         example, you can ask for the basis in a single degree::
 
-            sage: H.basis(1)                                                            # needs sage.modules
+            sage: H.basis(1)
             Finite family {(1, 0): h_{1,0}, (1, 1): h_{1,1}}
 
             sage: S3 = delta_complexes.Sphere(3)
-            sage: H = S3.homology_with_basis(QQ, cohomology=True)                       # needs sage.modules
-            sage: list(H.basis(3))                                                      # needs sage.modules
+            sage: H = S3.homology_with_basis(QQ, cohomology=True)
+            sage: list(H.basis(3))
             [h^{3,0}]
         """
         from sage.homology.homology_vector_space_with_basis import \
@@ -914,7 +909,6 @@ def cohomology_ring(self, base_ring=QQ):
 
         EXAMPLES::
 
-            sage: # needs sage.modules
             sage: K = simplicial_complexes.KleinBottle()
             sage: H = K.cohomology_ring(QQ); H
             Cohomology ring of Minimal triangulation of the Klein bottle
@@ -928,23 +922,22 @@ def cohomology_ring(self, base_ring=QQ):
             [h^{0,0}, h^{1,0}, h^{1,1}, h^{2,0}]
 
             sage: X = delta_complexes.SurfaceOfGenus(2)
-            sage: H = X.cohomology_ring(QQ); H                                          # needs sage.modules
+            sage: H = X.cohomology_ring(QQ); H
             Cohomology ring of Delta complex with 3 vertices and 29 simplices
              over Rational Field
-            sage: sorted(H.basis(1), key=str)                                           # needs sage.modules
+            sage: sorted(H.basis(1), key=str)
             [h^{1,0}, h^{1,1}, h^{1,2}, h^{1,3}]
 
-            sage: H = simplicial_complexes.Torus().cohomology_ring(QQ); H               # needs sage.modules
+            sage: H = simplicial_complexes.Torus().cohomology_ring(QQ); H
             Cohomology ring of Minimal triangulation of the torus
              over Rational Field
-            sage: x = H.basis()[1,0]; x                                                 # needs sage.modules
+            sage: x = H.basis()[1,0]; x
             h^{1,0}
-            sage: y = H.basis()[1,1]; y                                                 # needs sage.modules
+            sage: y = H.basis()[1,1]; y
             h^{1,1}
 
         You can compute cup products of cohomology classes::
 
-            sage: # needs sage.modules
             sage: x.cup_product(y)
             -h^{2,0}
             sage: x * y # alternate notation
@@ -956,13 +949,12 @@ def cohomology_ring(self, base_ring=QQ):
 
         Cohomology operations::
 
-            sage: # needs sage.groups
             sage: RP2 = simplicial_complexes.RealProjectivePlane()
             sage: K = RP2.suspension()
             sage: K.set_immutable()
-            sage: y = K.cohomology_ring(GF(2)).basis()[2,0]; y                          # needs sage.modules
+            sage: y = K.cohomology_ring(GF(2)).basis()[2,0]; y
             h^{2,0}
-            sage: y.Sq(1)                                                               # needs sage.modules
+            sage: y.Sq(1)
             h^{3,0}
 
         To compute the cohomology ring, the complex must be
@@ -976,12 +968,12 @@ def cohomology_ring(self, base_ring=QQ):
             sage: T = S1.product(S1)
             sage: T.is_immutable()
             False
-            sage: T.cohomology_ring()                                                   # needs sage.modules
+            sage: T.cohomology_ring()
             Traceback (most recent call last):
             ...
             ValueError: this simplicial complex must be immutable; call set_immutable()
             sage: T.set_immutable()
-            sage: T.cohomology_ring()                                                   # needs sage.modules
+            sage: T.cohomology_ring()
             Cohomology ring of Simplicial complex with 9 vertices and
              18 facets over Rational Field
         """

src/sage/topology/cubical_complex.py

@@ -1,4 +1,3 @@
-# sage.doctest: needs sage.graphs
 r"""
 Finite cubical complexes
 
@@ -46,11 +45,11 @@
 segment in the plane from `(0,2)` to `(0,3)`.  We could form a
 topologically equivalent space by inserting some degenerate simplices::
 
-    sage: S1.homology()                                                                 # needs sage.modules
+    sage: S1.homology()
     {0: 0, 1: Z}
     sage: X = CubicalComplex([([0,0], [2,3], [2]), ([0,1], [3,3], [2]),
     ....:                     ([0,1], [2,2], [2]), ([1,1], [2,3], [2])])
-    sage: X.homology()                                                                  # needs sage.modules
+    sage: X.homology()
     {0: 0, 1: Z}
 
 Topologically, the cubical complex ``X`` consists of four edges of a
@@ -797,26 +796,26 @@ class :class:`Cube`, or lists or tuples suitable for conversion to
         sage: S1 = CubicalComplex([([0,0], [2,3]), ([0,1], [3,3]),
         ....:                      ([0,1], [2,2]), ([1,1], [2,3])]); S1
         Cubical complex with 4 vertices and 8 cubes
-        sage: S1.homology()                                                             # needs sage.modules
+        sage: S1.homology()
         {0: 0, 1: Z}
 
     A set of five points and its product with ``S1``::
 
         sage: pts = CubicalComplex([([0],), ([3],), ([6],), ([-12],), ([5],)])
         sage: pts
         Cubical complex with 5 vertices and 5 cubes
-        sage: pts.homology()                                                            # needs sage.modules
+        sage: pts.homology()
         {0: Z x Z x Z x Z}
         sage: X = S1.product(pts); X
         Cubical complex with 20 vertices and 40 cubes
-        sage: X.homology()                                                              # needs sage.modules
+        sage: X.homology()
         {0: Z x Z x Z x Z, 1: Z^5}
 
     Converting a simplicial complex to a cubical complex::
 
         sage: S2 = simplicial_complexes.Sphere(2)
         sage: C2 = CubicalComplex(S2)
-        sage: all(C2.homology(n) == S2.homology(n) for n in range(3))                   # needs sage.modules
+        sage: all(C2.homology(n) == S2.homology(n) for n in range(3))
         True
 
     You can get the set of maximal cells or a dictionary of all cells::
@@ -853,14 +852,14 @@ class :class:`Cube`, or lists or tuples suitable for conversion to
 
         sage: T = S1.product(S1); T
         Cubical complex with 16 vertices and 64 cubes
-        sage: T.chain_complex()                                                         # needs sage.modules
+        sage: T.chain_complex()
         Chain complex with at most 3 nonzero terms over Integer Ring
-        sage: T.homology(base_ring=QQ)                                                  # needs sage.modules
+        sage: T.homology(base_ring=QQ)
         {0: Vector space of dimension 0 over Rational Field,
          1: Vector space of dimension 2 over Rational Field,
          2: Vector space of dimension 1 over Rational Field}
         sage: RP2 = cubical_complexes.RealProjectivePlane()
-        sage: RP2.cohomology(dim=[1, 2], base_ring=GF(2))                               # needs sage.modules
+        sage: RP2.cohomology(dim=[1, 2], base_ring=GF(2))
         {1: Vector space of dimension 1 over Finite Field of size 2,
          2: Vector space of dimension 1 over Finite Field of size 2}
 
@@ -1191,7 +1190,6 @@ def chain_complex(self, subcomplex=None, augmented=False,
 
         EXAMPLES::
 
-            sage: # needs sage.modules
             sage: S2 = cubical_complexes.Sphere(2)
             sage: S2.chain_complex()
             Chain complex with at most 3 nonzero terms over Integer Ring
@@ -1210,7 +1208,6 @@ def chain_complex(self, subcomplex=None, augmented=False,
 
         Check that :issue:`32203` has been fixed::
 
-            sage: # needs sage.modules
             sage: Square = CubicalComplex([([0,1],[0,1])])
             sage: EdgesLTR = CubicalComplex([([0,0],[0,1]),([0,1],[1,1]),([1,1],[0,1])])
             sage: EdgesLBR = CubicalComplex([([0,0],[0,1]),([0,1],[0,0]),([1,1],[0,1])])
@@ -1507,7 +1504,7 @@ def disjoint_union(self, other):
 
             sage: S1 = cubical_complexes.Sphere(1)
             sage: S2 = cubical_complexes.Sphere(2)
-            sage: S1.disjoint_union(S2).homology()                                      # needs sage.modules
+            sage: S1.disjoint_union(S2).homology()
             {0: Z, 1: Z, 2: Z}
         """
         embedded_left = len(tuple(self.maximal_cells()[0]))
@@ -1545,7 +1542,7 @@ def wedge(self, other):
 
             sage: S1 = cubical_complexes.Sphere(1)
             sage: S2 = cubical_complexes.Sphere(2)
-            sage: S1.wedge(S2).homology()                                               # needs sage.modules
+            sage: S1.wedge(S2).homology()
             {0: 0, 1: Z, 2: Z}
         """
         embedded_left = len(tuple(self.maximal_cells()[0]))
@@ -1582,12 +1579,12 @@ def connected_sum(self, other):
 
             sage: T = cubical_complexes.Torus()
             sage: S2 = cubical_complexes.Sphere(2)
-            sage: T.connected_sum(S2).cohomology() == T.cohomology()                    # needs sage.modules
+            sage: T.connected_sum(S2).cohomology() == T.cohomology()
             True
             sage: RP2 = cubical_complexes.RealProjectivePlane()
-            sage: T.connected_sum(RP2).homology(1)                                      # needs sage.modules
+            sage: T.connected_sum(RP2).homology(1)
             Z x Z x C2
-            sage: RP2.connected_sum(RP2).connected_sum(RP2).homology(1)                 # needs sage.modules
+            sage: RP2.connected_sum(RP2).connected_sum(RP2).homology(1)
             Z x Z x C2
         """
         # connected_sum: first check whether the complexes are pure
@@ -1703,7 +1700,6 @@ def algebraic_topological_model(self, base_ring=None):
 
         EXAMPLES::
 
-            sage: # needs sage.modules
             sage: RP2 = cubical_complexes.RealProjectivePlane()
             sage: phi, M = RP2.algebraic_topological_model(GF(2))
             sage: M.homology()
@@ -1764,7 +1760,7 @@ def _simplicial_(self):
 
             sage: Ts = T._simplicial_(); Ts
             Simplicial complex with 16 vertices and 32 facets
-            sage: T.homology() == Ts.homology()                                         # needs sage.modules
+            sage: T.homology() == Ts.homology()
             True
 
         Each `n`-dimensional cube produces `n!` `n`-simplices::