Docstring edits

Docstring beginnings: "Returns" to "Return" and addition of dots.

src/sage/algebras/commutative_dga.py

@@ -2084,7 +2084,7 @@ def __classcall__(cls, A, differential):
 
     def __init__(self, A, differential):
         """
-        Initialize ``self``
+        Initialize ``self``.
 
         INPUT:
 

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_element.pyx

@@ -339,7 +339,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
 
     def __getitem__(self, m):
         """
-        Return the `m`-th coefficient of ``self``
+        Return the `m`-th coefficient of ``self``.
 
         EXAMPLES::
 

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_ideal.py

@@ -72,7 +72,7 @@ def __init__(self, A, gens=None, given_by_matrix=False):
 
     def _richcmp_(self, other, op):
         r"""
-        Comparisons
+        Comparisons.
 
         TESTS::
 

src/sage/algebras/fusion_rings/fusion_double.py

@@ -473,7 +473,7 @@ def Nk_ij(self, i, j, k, use_characters=False):
     @cached_method
     def field(self):
         """
-        Returns a cyclotomic field large enough to contain the values
+        Return a cyclotomic field large enough to contain the values
         of R-matrices and twists that can arise for this fusion ring.
 
         EXAMPLES::

src/sage/algebras/fusion_rings/poly_tup_engine.pyx

@@ -259,7 +259,7 @@ cpdef list get_variables_degrees(list eqns, int nvars):
 
 cpdef list variables(tuple eq_tup):
     """
-    Return indices of all variables appearing in eq_tup
+    Return indices of all variables appearing in eq_tup.
 
     EXAMPLES::
 

src/sage/algebras/hecke_algebras/cubic_hecke_algebra.py

@@ -1125,7 +1125,7 @@ def check_base_ring_embedding(base_ring_embedding):
     ############################################################################
     def _repr_(self):
         r"""
-        Return a string representation
+        Return a string representation.
 
         OUTPUT: string describing ``self``
 
@@ -1575,7 +1575,7 @@ def product_on_basis(self, g1, g2):
     ############################################################################
     def _basis_tietze(self):
         r"""
-        Return the complete finite sub basis as list of Tietze tuples
+        Return the complete finite sub basis as list of Tietze tuples.
 
         EXAMPLES::
 

src/sage/algebras/lie_algebras/nilpotent_lie_algebra.py

@@ -340,7 +340,7 @@ def __classcall_private__(cls, R, r, s, names=None, naming=None, category=None,
 
     def __init__(self, R, r, s, names, naming, category, **kwds):
         r"""
-        Initialize ``self``
+        Initialize ``self``.
 
         EXAMPLES::
 

src/sage/algebras/lie_algebras/subalgebra.py

@@ -770,7 +770,7 @@ def leading_monomials(self):
 
     def from_vector(self, v, order=None, coerce=False):
         r"""
-        Return the element of ``self`` corresponding to the vector ``v``
+        Return the element of ``self`` corresponding to the vector ``v``.
 
         INPUT:
 

src/sage/algebras/steenrod/steenrod_algebra.py

@@ -1125,7 +1125,7 @@ def one_basis(self):
 
     def product_on_basis(self, t1, t2):
         """
-        The product of two basis elements of this algebra
+        The product of two basis elements of this algebra.
 
         INPUT:
 
@@ -1228,7 +1228,7 @@ def product_on_basis(self, t1, t2):
 
     def coproduct_on_basis(self, t, algorithm=None):
         r"""
-        The coproduct of a basis element of this algebra
+        The coproduct of a basis element of this algebra.
 
         INPUT:
 
@@ -1435,7 +1435,7 @@ def coprod(x):
 
     def antipode_on_basis(self, t):
         r"""
-        The antipode of a basis element of this algebra
+        The antipode of a basis element of this algebra.
 
         INPUT:
 
@@ -1716,7 +1716,7 @@ def _milnor_on_basis(self, t):
     @lazy_attribute
     def milnor(self):
         """
-        Convert an element of this algebra to the Milnor basis
+        Convert an element of this algebra to the Milnor basis.
 
         INPUT:
 
@@ -1820,7 +1820,7 @@ def _change_basis_on_basis(self, t, basis='milnor'):
 
     def _change_basis(self, x, basis='milnor'):
         """
-        Convert an element of this algebra to the specified basis
+        Convert an element of this algebra to the specified basis.
 
         INPUT:
 
@@ -3802,7 +3802,7 @@ def Sq(self, *nums):
 
 def SteenrodAlgebra(p=2, basis='milnor', generic='auto', **kwds):
     r"""
-    The mod `p` Steenrod algebra
+    The mod `p` Steenrod algebra.
 
     INPUT:
 

src/sage/arith/misc.py

@@ -575,7 +575,7 @@ def is_prime(n) -> bool:
 
 def is_pseudoprime(n):
     r"""
-    Test whether ``n`` is a pseudo-prime
+    Test whether ``n`` is a pseudo-prime.
 
     The result is *NOT* proven correct - *this is a pseudo-primality test!*.
 
@@ -610,7 +610,7 @@ def is_pseudoprime(n):
 
 def is_prime_power(n, get_data=False):
     r"""
-    Test whether ``n`` is a positive power of a prime number
+    Test whether ``n`` is a positive power of a prime number.
 
     This function simply calls the method :meth:`Integer.is_prime_power()
     <sage.rings.integer.Integer.is_prime_power>` of Integers.
@@ -1861,7 +1861,7 @@ def gcd(a, b=None, **kwargs):
 
 def __GCD_sequence(v, **kwargs):
     """
-    Internal function returning the gcd of the elements of a sequence
+    Internal function returning the gcd of the elements of a sequence.
 
     INPUT:
 
@@ -3637,7 +3637,7 @@ def CRT_vectors(X, moduli):
 
 def binomial(x, m, **kwds):
     r"""
-    Return the binomial coefficient
+    Return the binomial coefficient.
 
     .. MATH::
 
@@ -5318,7 +5318,7 @@ def integer_floor(x):
 
 def integer_trunc(i):
     """
-    Truncate to the integer closer to zero
+    Truncate to the integer closer to zero.
 
     EXAMPLES::
 

src/sage/calculus/calculus.py

@@ -2112,7 +2112,7 @@ def dummy_inverse_laplace(*args):
 
 def dummy_pochhammer(*args):
     """
-    This function is called to create formal wrappers of Pochhammer symbols
+    This function is called to create formal wrappers of Pochhammer symbols.
 
     EXAMPLES::
 

src/sage/categories/additive_magmas.py

@@ -951,7 +951,7 @@ def extra_super_categories(self):
             class ParentMethods:
                 def zero(self):
                     r"""
-                    Returns the zero of this group
+                    Return the zero of this group.
 
                     EXAMPLES::
 

src/sage/categories/affine_weyl_groups.py

@@ -17,7 +17,7 @@
 
 class AffineWeylGroups(Category_singleton):
     """
-    The category of affine Weyl groups
+    The category of affine Weyl groups.
 
     .. TODO:: add a description of this category
 

src/sage/categories/algebra_modules.py

@@ -67,7 +67,7 @@ def __init__(self, A):
     @classmethod
     def an_instance(cls):
         """
-        Returns an instance of this class
+        Return an instance of this class.
 
         EXAMPLES::
 

src/sage/categories/algebras.py

@@ -62,7 +62,7 @@ class Algebras(CategoryWithAxiom_over_base_ring):
     # For backward compatibility?
     def __contains__(self, x):
         """
-        Membership testing
+        Membership testing.
 
         EXAMPLES::
 
@@ -224,7 +224,7 @@ class ElementMethods:
         # TODO: move the content of AlgebraElement here or higher in the category hierarchy
         def _div_(self, y):
             """
-            Division by invertible elements
+            Division by invertible elements.
 
             # TODO: move in Monoids
 
@@ -273,7 +273,7 @@ def algebra_generators(self):
 
     class CartesianProducts(CartesianProductsCategory):
         """
-        The category of algebras constructed as Cartesian products of algebras
+        The category of algebras constructed as Cartesian products of algebras.
 
         This construction gives the direct product of algebras. See
         discussion on:
@@ -327,7 +327,7 @@ class DualObjects(DualObjectsCategory):
 
         def extra_super_categories(self):
             r"""
-            Return the dual category
+            Return the dual category.
 
             EXAMPLES:
 

src/sage/categories/algebras_with_basis.py

@@ -309,7 +309,7 @@ class ParentMethods:
             @cached_method
             def one_basis(self):
                 """
-                Returns the index of the one of this tensor product of
+                Return the index of the one of this tensor product of
                 algebras, as per ``AlgebrasWithBasis.ParentMethods.one_basis``
 
                 It is the tuple whose operands are the indices of the

src/sage/categories/bialgebras.py

@@ -20,7 +20,7 @@
 
 class Bialgebras(Category_over_base_ring):
     """
-    The category of bialgebras
+    The category of bialgebras.
 
     EXAMPLES::
 

src/sage/categories/category.py

@@ -608,7 +608,7 @@ def _repr_(self):
 
     def _latex_(self):
         r"""
-        Returns the latex representation of this category.
+        Return the latex representation of this category.
 
         EXAMPLES::
 
@@ -682,7 +682,7 @@ def _subcategory_hook_(self, category):
 
     def __contains__(self, x):
         """
-        Membership testing
+        Membership testing.
 
         Returns whether ``x`` is an object in this category, that is
         if the category of ``x`` is a subcategory of ``self``.
@@ -785,7 +785,7 @@ def is_abelian(self):
 
     def category_graph(self):
         r"""
-        Returns the graph of all super categories of this category
+        Return the graph of all super categories of this category.
 
         EXAMPLES::
 
@@ -926,7 +926,7 @@ def _set_of_super_categories(self):
 
     def all_super_categories(self, proper=False):
         """
-        Returns the list of all super categories of this category.
+        Return the list of all super categories of this category.
 
         INPUT:
 
@@ -1399,7 +1399,7 @@ def _test_category_graph(self, **options):
 
     def _test_category(self, **options):
         r"""
-        Run generic tests on this category
+        Run generic tests on this category.
 
         .. SEEALSO:: :class:`TestSuite`.
 
@@ -1746,7 +1746,7 @@ def morphism_class(self):
 
     def required_methods(self):
         """
-        Returns the methods that are required and optional for parents
+        Return the methods that are required and optional for parents
         in this category and their elements.
 
         EXAMPLES::
@@ -1761,7 +1761,7 @@ def required_methods(self):
     # Operations on the lattice of categories
     def is_subcategory(self, c):
         """
-        Returns ``True`` if self is naturally embedded as a subcategory of `c`.
+        Return ``True`` if self is naturally embedded as a subcategory of `c`.
 
         EXAMPLES::
 
@@ -1880,7 +1880,7 @@ def _is_subclass(self, c):
     @cached_method
     def _meet_(self, other):
         """
-        Returns the largest common subcategory of self and other:
+        Return the largest common subcategory of self and other.
 
         EXAMPLES::
 
@@ -1937,7 +1937,7 @@ def _meet_(self, other):
     @staticmethod
     def meet(categories):
         """
-        Returns the meet of a list of categories
+        Return the meet of a list of categories.
 
         INPUT:
 
@@ -2504,7 +2504,7 @@ def category(self):
 
     def example(self, *args, **keywords):
         """
-        Returns an object in this category. Most of the time, this is a parent.
+        Return an object in this category. Most of the time, this is a parent.
 
         This serves three purposes:
 
@@ -2561,7 +2561,7 @@ def example(self, *args, **keywords):
 
 def is_Category(x):
     """
-    Returns ``True`` if `x` is a category.
+    Return ``True`` if `x` is a category.
 
     EXAMPLES::
 
@@ -2940,7 +2940,7 @@ class JoinCategory(CategoryWithParameters):
 
     def __init__(self, super_categories, **kwds):
         """
-        Initializes this JoinCategory
+        Initializes this JoinCategory.
 
         INPUT:
 
@@ -3000,7 +3000,7 @@ def _make_named_class_key(self, name):
 
     def super_categories(self):
         """
-        Returns the immediate super categories, as per :meth:`Category.super_categories`.
+        Return the immediate super categories, as per :meth:`Category.super_categories`.
 
         EXAMPLES::
 
@@ -3026,7 +3026,7 @@ def additional_structure(self):
 
     def _subcategory_hook_(self, category):
         """
-        Returns whether ``category`` is a subcategory of this join category
+        Return whether ``category`` is a subcategory of this join category.
 
         INPUT: