rst fixes in rings and interacts

src/sage/interacts/library.py

@@ -91,8 +91,8 @@ def library_interact(
     INPUT:
 
     - ``**widgets`` -- keyword arguments that are passed to the
-      ``interact`` function to create the widgets. Each value must be a callable that
-        returns a widget.
+      ``interact`` function to create the widgets. Each value must
+      be a callable that returns a widget.
 
     EXAMPLES::
 

src/sage/rings/localization.py

@@ -1,11 +1,11 @@
-# -*- coding: utf-8 -*-
 r"""
 Localization
 
-Localization is an important ring construction tool. Whenever you have to extend a given
-integral domain such that it contains the inverses of a finite set of elements but should
-allow non injective homomorphic images this construction will be needed. See the example
-on Ariki-Koike algebras below for such an application.
+Localization is an important ring construction tool. Whenever you have
+to extend a given integral domain such that it contains the inverses
+of a finite set of elements but should allow non injective homomorphic
+images this construction will be needed. See the example on
+Ariki-Koike algebras below for such an application.
 
 EXAMPLES::
 
@@ -32,8 +32,8 @@
     sage: u = [u0, u1, u2]
     sage: S = Set(u)
     sage: I = S.cartesian_product(S)
-    sage: add_units = u + [q, q+1] + [ui -uj for ui, uj in I if ui != uj]\
-                        + [q*ui -uj for ui, uj in I if ui != uj]
+    sage: add_units = u + [q, q+1] + [ui -uj for ui, uj in I if ui != uj]
+    ....:                + [q*ui -uj for ui, uj in I if ui != uj]
     sage: L = R.localization(tuple(add_units)); L
     Multivariate Polynomial Ring in u0, u1, u2, q over Integer Ring localized at
     (q, q + 1, u2, u1, u1 - u2, u0, u0 - u2, u0 - u1, u2*q - u1, u2*q - u0,
@@ -42,12 +42,12 @@
 Define the representation matrices (of one of the three dimensional irreducible representations)::
 
     sage: m1 = matrix(L, [[u1, 0, 0],[0, u0, 0],[0, 0, u0]])
-    sage: m2 = matrix(L, [[(u0*q - u0)/(u0 - u1), (u0*q - u1)/(u0 - u1), 0],\
-                          [(-u1*q + u0)/(u0 - u1), (-u1*q + u1)/(u0 - u1), 0],\
-                          [0, 0, -1]])
-    sage: m3 = matrix(L, [[-1, 0, 0],\
-                          [0, u0*(1 - q)/(u1*q - u0), q*(u1 - u0)/(u1*q - u0)],\
-                          [0, (u1*q^2 - u0)/(u1*q - u0), (u1*q^ 2 - u1*q)/(u1*q - u0)]])
+    sage: m2 = matrix(L, [[(u0*q - u0)/(u0 - u1), (u0*q - u1)/(u0 - u1), 0],
+    ....:                 [(-u1*q + u0)/(u0 - u1), (-u1*q + u1)/(u0 - u1), 0],
+    ....:                 [0, 0, -1]])
+    sage: m3 = matrix(L, [[-1, 0, 0],
+    ....:                 [0, u0*(1 - q)/(u1*q - u0), q*(u1 - u0)/(u1*q - u0)],
+    ....:                 [0, (u1*q^2 - u0)/(u1*q - u0), (u1*q^ 2 - u1*q)/(u1*q - u0)]])
     sage: m1.base_ring() == L
     True
 
@@ -100,7 +100,6 @@
     [ 0  4  5]
     [ 0  7  6]
 
-
 Obtain specializations in characteristic 0::
 
     sage: fQ = L.hom((3,5,7,11), codomain=QQ); fQ

src/sage/rings/number_field/number_field_ideal.py

@@ -3009,13 +3009,15 @@ def _p_quotient(self, p):
         computing the quotient of the ring of integers by a prime ideal.
 
         INPUT:
-            p -- a prime number contained in self.
+
+        - ``p`` -- a prime number contained in ``self``
 
         OUTPUT:
-            V -- a vector space of characteristic p
-            quo -- a partially defined quotient homomorphism from the
-                   ambient number field to V
-            lift -- a section of quo.
+
+        - ``V`` -- a vector space of characteristic ``p``
+        - ``quo`` -- a partially defined quotient homomorphism from the
+          ambient number field to ``V``
+        - ``lift`` -- a section of ``quo``.
 
         EXAMPLES::
 
@@ -3250,7 +3252,7 @@ def __call__(self, x):
         return self.__Q( list(w) )
 
     def __repr__(self):
-        """
+        r"""
         Return a string representation of this QuotientMap.
 
         EXAMPLES::
@@ -3315,7 +3317,7 @@ def __call__(self, x):
         return self.__OK(sum(z[i] * self.__Kgen ** i for i in range(len(z))))
 
     def __repr__(self):
-        """
+        r"""
         Return a string representation of this QuotientMap.
 
         EXAMPLES::

src/sage/rings/padics/padic_lattice_element.py

@@ -617,10 +617,10 @@ def _div_(self, other):
         r"""
         Return the quotient of this element and ``other``.
 
-        NOTE::
+        .. NOTE::
 
-        The result of division always lives in the fraction field,
-        even if the element to be inverted is a unit.
+            The result of division always lives in the fraction field,
+            even if the element to be inverted is a unit.
 
         EXAMPLES::
 
@@ -660,10 +660,10 @@ def __invert__(self):
         r"""
         Return the multiplicative inverse of this element.
 
-        NOTE::
+        .. NOTE::
 
-        The result of division always lives in the fraction field,
-        even if the element to be inverted is a unit.
+            The result of division always lives in the fraction field,
+            even if the element to be inverted is a unit.
 
         EXAMPLES::
 
@@ -1278,10 +1278,10 @@ def _is_exact_zero(self):
         r"""
         Return ``True`` if this element is exactly zero.
 
-        NOTE::
+        .. NOTE::
 
-        Since exact zeros are not supported in the precision lattice
-        model, this function always returns ``False``.
+            Since exact zeros are not supported in the precision lattice
+            model, this function always returns ``False``.
 
         EXAMPLES::
 

src/sage/rings/quotient_ring.py

@@ -15,7 +15,7 @@
     sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
     sage: S = R.quotient_ring(I)
 
-.. todo::
+.. TODO::
 
     The following skipped tests should be removed once :trac:`13999` is fixed::