Detect whether the base ring is GF(2) in a consistent and robust way.

src/sage/homology/homology_vector_space_with_basis.py

@@ -410,7 +410,7 @@ def dual(self):
             sage: coh.dual() is hom
             True
         """
-        if self.base_ring() == GF(2):
+        if is_GF2(self.base_ring()):
             if self._cohomology:
                 return HomologyVectorSpaceWithBasis_mod2(self.base_ring(),
                                                          self.complex())
@@ -590,7 +590,7 @@ def __init__(self, base_ring, cell_complex, category=None):
             sage: H = simplicial_complexes.Sphere(3).homology_with_basis(GF(2))
             sage: TestSuite(H).run()
         """
-        if base_ring != GF(2):
+        if not is_GF2(base_ring):
             raise ValueError
         category = Modules(base_ring).WithBasis().Graded().FiniteDimensional().or_subcategory(category)
         category = Category.join((category,
@@ -641,7 +641,7 @@ def _acted_upon_(self, a, self_on_left):
 
             .. MATH::
 
-                (f \cdot a) (x) = f (a \cdot x)
+                (f \cdot a) (x) = f (a \cdot x).
 
             So given `f` (a.k.a. ``self``) and `a`, we compute `f (a
             \cdot x)` for all basis elements `x` in `H^{m-n}`,
@@ -1015,7 +1015,7 @@ def __init__(self, base_ring, cell_complex):
             sage: H = RP2.cohomology_ring(GF(2))
             sage: TestSuite(H).run()
         """
-        if base_ring != GF(2):
+        if not is_GF2(base_ring):
             raise ValueError("the base ring must be GF(2)")
         category = Algebras(base_ring).WithBasis().Graded().FiniteDimensional()
         category = Category.join((category,
@@ -1105,11 +1105,12 @@ def Sq(self, i):
                 P = scomplex.cohomology_ring(self.base_ring())
                 self = P.sum_of_terms(self.monomial_coefficients().items())
             if not isinstance(scomplex, (SimplicialComplex, SimplicialSet_arbitrary)):
+                print(scomplex, isinstance(scomplex, SimplicialComplex))
                 raise NotImplementedError('Steenrod squares are not implemented for '
                                           'this type of cell complex')
             scomplex = P.complex()
             base_ring = P.base_ring()
-            if base_ring.characteristic() != 2:
+            if not is_GF2(base_ring):
                 # This should never happen: the class should only be
                 # instantiated in characteristic 2.
                 raise ValueError('Steenrod squares are only defined in characteristic 2')
@@ -1428,3 +1429,19 @@ def sum_indices(k, i_k_plus_one, S_k_plus_one):
         return [[S_k]]
     return [[i_k] + l for i_k in range(S_k, i_k_plus_one)
             for l in sum_indices(k-1, i_k, S_k)]
+
+def is_GF2(R):
+    """
+    Return ``True`` iff ``R`` is isomorphic to the field GF(2).
+
+    EXAMPLES::
+
+        sage: from sage.homology.homology_vector_space_with_basis import is_GF2
+        sage: is_GF2(GF(2))
+        True
+        sage: is_GF2(GF(2, impl='ntl'))
+        True
+        sage: is_GF2(GF(3))
+        False
+    """
+    return 2 == R.cardinality() == R.characteristic()

src/sage/topology/cell_complex.py

@@ -47,7 +47,6 @@
 from sage.structure.sage_object import SageObject
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.misc.abstract_method import abstract_method
 
 
@@ -866,10 +865,12 @@ def homology_with_basis(self, base_ring=QQ, cohomology=False):
             [h^{3,0}]
         """
         from sage.homology.homology_vector_space_with_basis import \
-            HomologyVectorSpaceWithBasis, HomologyVectorSpaceWithBasis_mod2
+            HomologyVectorSpaceWithBasis, HomologyVectorSpaceWithBasis_mod2, \
+            is_GF2
+
         if cohomology:
             return self.cohomology_ring(base_ring)
-        if base_ring == GF(2):
+        if is_GF2(base_ring):
             return HomologyVectorSpaceWithBasis_mod2(base_ring, self)
         return HomologyVectorSpaceWithBasis(base_ring, self, cohomology)
 
@@ -977,8 +978,10 @@ def cohomology_ring(self, base_ring=QQ):
             Cohomology ring of Simplicial complex with 9 vertices and
              18 facets over Rational Field
         """
-        from sage.homology.homology_vector_space_with_basis import CohomologyRing, CohomologyRing_mod2
-        if base_ring == GF(2):
+        from sage.homology.homology_vector_space_with_basis import CohomologyRing, \
+            CohomologyRing_mod2, is_GF2
+
+        if is_GF2(base_ring):
             return CohomologyRing_mod2(base_ring, self)
         return CohomologyRing(base_ring, self)