Docstring edits

Remove excessive blank lines around INPUT, OUTPUT, EXAMPLES, and before
docstring ending """. (sagemath#2)

src/sage/categories/fields.py

@@ -119,7 +119,6 @@ def __contains__(self, x):
             sage: _ = gc.collect()
             sage: len([X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) - n
             0
-
         """
         from sage.rings.ring import _is_Field
         try:
@@ -154,7 +153,6 @@ def _contains_helper(cls):
             True
             sage: F._contains_helper(Q)
             True
-
         """
         return Category_contains_method_by_parent_class(cls())
 
@@ -407,7 +405,6 @@ def is_perfect(self):
                 True
                 sage: FunctionField(GF(2), 'x').is_perfect()
                 False
-
             """
             if self.characteristic() == 0:
                 return True

src/sage/categories/finite_coxeter_groups.py

@@ -511,7 +511,6 @@ def inversion_sequence(self, word):
 
                 sage: [t.reduced_word() for t in CoxeterGroup(["A",3]).inversion_sequence([2,1,3,2,1,3])]
                 [[2], [1, 2, 1], [2, 3, 2], [1, 2, 3, 2, 1], [3], [1]]
-
             """
             return [self.from_reduced_word(word[:i+1]+list(reversed(word[:i])))
                     for i in range(len(word))]
@@ -741,7 +740,6 @@ def permutahedron(self, point=None, base_ring=None):
                 W = CoxeterGroup(['I',7])
                 p = W.permutahedron()
                 sphinx_plot(p)
-
             """
             n = self.one().canonical_matrix().rank()
             weights = self.fundamental_weights()

src/sage/categories/finite_dimensional_modules_with_basis.py

@@ -1059,6 +1059,5 @@ def extra_super_categories(self):
                 sage: C.FiniteDimensional()
                 Category of tensor products of
                  finite dimensional modules with basis over Integer Ring
-
             """
             return [self.base_category()]

src/sage/categories/finite_lattice_posets.py

@@ -36,7 +36,6 @@ class FiniteLatticePosets(CategoryWithAxiom):
         sage: C is FiniteLatticePosets().Finite()
         True
         sage: TestSuite(C).run()
-
     """
 
     class ParentMethods:

src/sage/categories/finite_permutation_groups.py

@@ -322,7 +322,6 @@ def profile(self, n, using_polya=True):
                 sage: D8 = DihedralGroup(8)
                 sage: D8.profile(4, using_polya=False)
                 8
-
             """
 
             if using_polya:

src/sage/categories/finite_posets.py

@@ -44,7 +44,6 @@ class FinitePosets(CategoryWithAxiom):
         sage: C is Posets().Finite()
         True
         sage: TestSuite(C).run()
-
     """
 
     class ParentMethods:
@@ -265,7 +264,6 @@ def is_poset_morphism(self, f, codomain):
                 Finite poset containing 0 elements
                 sage: P.is_poset_morphism(f, P)
                 True
-
             """
             for x in self:
                 for y in self.upper_covers(x):
@@ -1475,7 +1473,6 @@ def rowmotion_orbits_plots(self):
                 sage: P = Poset({})
                 sage: P.rowmotion_orbits_plots()
                 Graphics Array of size 1 x 1
-
             """
             from sage.plot.plot import graphics_array
             plot_of_orb_plots = []
@@ -1562,7 +1559,6 @@ def toggling_orbits_plots(self, vs):
                 sage: P = Poset({})
                 sage: P.toggling_orbits_plots([])
                 Graphics Array of size 1 x 1
-
             """
             from sage.plot.plot import graphics_array
             plot_of_orb_plots = []

src/sage/categories/finitely_generated_semigroups.py

@@ -58,7 +58,6 @@ def extra_super_categories(self):
 
             sage: Semigroups().FinitelyGenerated().extra_super_categories()
             [Category of enumerated sets]
-
         """
         return [EnumeratedSets()]
 
@@ -121,7 +120,6 @@ def succ_generators(self, side='twosided'):
                 ('ca', 'cab', 'ca', 'cad')
                 sage: S.succ_generators("twosided" )(S('ca'))
                 ('ac', 'bca', 'ca', 'dca', 'ca', 'cab', 'ca', 'cad')
-
             """
             left = (side == "left" or side == "twosided")
             right = (side == "right" or side == "twosided")

src/sage/categories/functor.pyx

@@ -52,7 +52,6 @@ def _Functor_unpickle(Cl, D, domain, codomain):
         True
         sage: F.domain(), loads(dumps(F)).domain()
         (Category of rings, Category of rings)
-
     """
     F = Functor.__new__(Cl)
     Functor.__init__(F, domain, codomain)
@@ -163,7 +162,6 @@ cdef class Functor(SageObject):
         sage: F(f)(p)
         (-a^2 - 2*a*b - b^2 + a + b)*t^2 + (a^2 + 2*a*b + b^2 - a - b)*t
         - 4*a^2 - 8*a*b - 4*b^2 - a - b + 1
-
     """
     def __init__(self, domain, codomain):
         """
@@ -177,7 +175,6 @@ cdef class Functor(SageObject):
             Rational Field
             sage: F(GF(2))
             Finite Field of size 2
-
         """
         if not isinstance(domain, category.Category):
             raise TypeError("domain (=%s) must be a category" % domain)
@@ -234,7 +231,6 @@ cdef class Functor(SageObject):
             sage: F = Functor(FiniteFields(), Fields())
             sage: F._apply_functor(ZZ)
             Rational Field
-
         """
         return self.__codomain(x)
 
@@ -383,7 +379,6 @@ cdef class Functor(SageObject):
             TypeError: Functor from Category of rings to Category of rings
             is ill-defined, since it sends x (=Rational Field) to something
             that is not in Category of rings.
-
         """
         from sage.categories.morphism import Morphism
         if isinstance(x, Morphism):
@@ -402,7 +397,6 @@ cdef class Functor(SageObject):
             sage: F = ForgetfulFunctor(FiniteFields(), Fields())
             sage: F.domain()
             Category of finite enumerated fields
-
         """
         return self.__domain
 
@@ -415,7 +409,6 @@ cdef class Functor(SageObject):
             sage: F = ForgetfulFunctor(FiniteFields(), Fields())
             sage: F.codomain()
             Category of fields
-
         """
         return self.__codomain
 
@@ -444,7 +437,6 @@ def is_Functor(x):
         The forgetful functor from Category of fields to Category of rings
         sage: is_Functor(F2)
         True
-
     """
     return isinstance(x, Functor)
 
@@ -472,7 +464,6 @@ class ForgetfulFunctor_generic(Functor):
            to Category of fields
         sage: F(GF(3))
         Finite Field of size 3
-
     """
     def __reduce__(self):
         """
@@ -492,7 +483,6 @@ class ForgetfulFunctor_generic(Functor):
             sage: F  # indirect doctest
             The forgetful functor from Category of finite enumerated fields
              to Category of fields
-
         """
         return "The forgetful functor from %s to %s" % (self.domain(),
                                                         self.codomain())
@@ -586,7 +576,6 @@ class IdentityFunctor_generic(ForgetfulFunctor_generic):
             True
             sage: F
             The identity functor on Category of groups
-
         """
         ForgetfulFunctor_generic.__init__(self, C, C)
 
@@ -627,7 +616,6 @@ class IdentityFunctor_generic(ForgetfulFunctor_generic):
 
             sage: F._apply_functor(ZZ)
             Integer Ring
-
         """
         return x
 

src/sage/categories/graded_hopf_algebras_with_basis.py

@@ -72,7 +72,6 @@ def super_categories(self):
             TESTS::
 
                 sage: TestSuite(GradedHopfAlgebrasWithBasis(QQ).WithRealizations()).run()
-
             """
             from sage.categories.graded_hopf_algebras import GradedHopfAlgebras
             R = self.base_category().base_ring()

src/sage/categories/groupoid.py

@@ -67,7 +67,6 @@ def _make_named_class_key(self, name):
 
             sage: Groupoid(DihedralGroup(3)).parent_class is Groupoid(ZZ).parent_class
             True
-
         """
         return None
 

src/sage/categories/groups.py

@@ -430,7 +430,6 @@ class provides even greater flexibility, including changing
             AUTHOR:
 
             - Rob Beezer (2010-03-15)
-
             """
             from sage.matrix.operation_table import OperationTable
             import operator

src/sage/categories/homsets.py

@@ -148,7 +148,6 @@ def base(self):
 
             sage: ModulesWithBasis(ZZ).Homsets().base()
             Integer Ring
-
         """
         from sage.categories.category_types import Category_over_base
         for C in self._all_super_categories_proper:

src/sage/categories/hopf_algebras_with_basis.py

@@ -256,7 +256,6 @@ def _test_antipode(self, **options):
 
                 sage: s = SymmetricFunctions(QQ).schur()                                # needs sage.combinat sage.modules
                 sage: s._test_antipode()                                                # needs lrcalc_python sage.combinat sage.modules
-
             """
             tester = self._tester(**options)
 

src/sage/categories/integral_domains.py

@@ -130,7 +130,6 @@ def _test_fraction_field(self, **options):
             EXAMPLES::
 
                 sage: ZZ._test_fraction_field()
-
             """
             tester = self._tester(**options)
             try:

src/sage/categories/lambda_bracket_algebras.py

@@ -34,7 +34,6 @@ class LambdaBracketAlgebras(Category_over_base_ring):
 
     This is an abstract base category for Lie conformal algebras and
     super Lie conformal algebras.
-
     """
     @staticmethod
     def __classcall_private__(cls, R, check=True):

src/sage/categories/lattice_posets.py

@@ -38,7 +38,6 @@ class LatticePosets(Category):
 
         sage: C = LatticePosets()
         sage: TestSuite(C).run()
-
     """
     @cached_method
     def super_categories(self):

src/sage/categories/magmas.py

@@ -1029,7 +1029,6 @@ def is_idempotent(self):
                 'x'
                 sage: x.is_idempotent()
                 True
-
             """
             return self * self == self
 
@@ -1178,7 +1177,6 @@ def product_by_coercion(self, left, right):
                     sage: y = Out.an_element()
                     sage: Out.product(x, y)
                     Out[{}] + 4*Out[{1}] + 9*Out[{2}] + Out[{1, 2}]
-
                 """
                 R = self.realization_of().a_realization()
                 return self(R(left) * R(right))

src/sage/categories/magmatic_algebras.py

@@ -65,7 +65,6 @@ def super_categories(self):
             sage: from sage.categories.additive_semigroups import AdditiveSemigroups
             sage: MA.is_subcategory((AdditiveSemigroups() & Magmas()).Distributive())
             True
-
         """
         R = self.base_ring()
         # Note: The specifications impose `self` to be a subcategory
@@ -219,7 +218,6 @@ def _product_from_product_on_basis_multiply( self, left, right ):
                     sage: a, b, c = A.algebra_generators()                                          # needs sage.combinat sage.modules
                     sage: A._product_from_product_on_basis_multiply(a*b + 2*c, a - b)               # needs sage.combinat sage.modules
                     B[word: aba] - B[word: abb] + 2*B[word: ca] - 2*B[word: cb]
-
                 """
                 return self.linear_combination((self.product_on_basis(mon_left, mon_right), coeff_left * coeff_right )
                                                 for (mon_left, coeff_left) in left.monomial_coefficients(copy=False).items()

src/sage/categories/map.pyx

@@ -1711,7 +1711,6 @@ cdef class FormalCompositeMap(Map):
             Traceback (most recent call last):
             ...
             IndexError: list index out of range
-
         """
         return self.__list[i]
 
@@ -1932,7 +1931,6 @@ cdef class FormalCompositeMap(Map):
             sage: f = QQ.hom(QQbar) * ZZ.hom(QQ)                                        # needs sage.rings.number_field
             sage: f.is_injective()                                                      # needs sage.rings.number_field
             True
-
         """
         try:
             # we try the category first

src/sage/categories/modules.py

@@ -558,7 +558,6 @@ def extra_super_categories(self):
                     sage: Modules(QQ).FiniteDimensional().TensorProducts().FiniteDimensional()
                     Category of tensor products of finite dimensional vector spaces
                      over Rational Field
-
                 """
                 return [self.base_category()]
 
@@ -681,7 +680,6 @@ def module_morphism(self, *, function, category=None, codomain, **keywords):
                  2-dimensional vector space over the Rational Field
                 sage: neg(e[0])
                 Element -e_0 of the 2-dimensional vector space over the Rational Field
-
             """
             # Make sure that we only create a module morphism, even if
             # domain and codomain have more structure
@@ -717,7 +715,6 @@ def quotient(self, submodule, check=True, **kwds):
                 <bound method Rings.ParentMethods.quotient of
                  Tensor Algebra of Free module generated by {'a', 'b', 'c'}
                  over Rational Field>
-
             """
             return self.quotient_module(submodule, check=check, **kwds)
 

src/sage/categories/modules_with_basis.py

@@ -139,7 +139,6 @@ class ModulesWithBasis(CategoryWithAxiom_over_base_ring):
         0
 
         sage: TestSuite(ModulesWithBasis(ZZ)).run()
-
     """
 
     def _call_(self, x):
@@ -558,7 +557,6 @@ def module_morphism(self, on_basis=None, matrix=None, function=None,
                 Traceback (most recent call last):
                 ...
                 ValueError: diagonal (=3) should be a function
-
             """
             if len([x for x in [matrix, on_basis, function, diagonal] if x is not None]) != 1:
                 raise ValueError("module_morphism() takes exactly one option out of `matrix`, `on_basis`, `function`, `diagonal`")
@@ -1407,7 +1405,6 @@ def random_element(self, n=2):
                 sage: F = Foo(QQ, tuple(), category=C)                                  # needs sage.modules
                 sage: F.random_element() == F.zero()                                    # needs sage.modules
                 True
-
             """
             indices = self.basis().keys()
             a = self.zero()
@@ -2165,7 +2162,6 @@ def map_coefficients(self, f, new_base_ring=None):
                 0
                 sage: B['a'].map_coefficients(lambda c: GF(2)(c), QQ)
                 B['a']
-
             """
             R = self.parent()
             if isinstance(f, Map):