src/sage/rings/ring.pyx: Remove methods duplicated from category

src/sage/categories/rings.py

@@ -866,6 +866,16 @@ def quo(self, I, names=None, **kwds):
                   [0 1]
                 )
 
+            A test with a subclass of :class:`~sage.rings.ring.Ring`::
+
+                sage: R.<x,y> = PolynomialRing(QQ,2)
+                sage: S.<a,b> = R.quo((x^2, y))
+                sage: S
+                Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y)
+                sage: S.gens()
+                (a, 0)
+                sage: a == b
+                False
             """
             return self.quotient(I,names=names,**kwds)
 
@@ -875,7 +885,22 @@ def quotient_ring(self, I, names=None, **kwds):
 
             NOTE:
 
-            This is a synonyme for :meth:`quotient`.
+            This is a synonym for :meth:`quotient`.
+
+            INPUT:
+
+            - ``I`` -- an ideal of `R`
+
+            - ``names`` -- (optional) names of the generators of the quotient. (If
+              there are multiple generators, you can specify a single character
+              string and the generators are named in sequence starting with 0.)
+
+            - further named arguments that may be passed to the quotient ring
+              constructor.
+
+            OUTPUT:
+
+            - ``R/I`` -- the quotient ring of `R` by the ideal `I`
 
             EXAMPLES::
 
@@ -906,8 +931,24 @@ def quotient_ring(self, I, names=None, **kwds):
                   [0 1]
                 )
 
+            A test with a subclass of :class:`~sage.rings.ring.Ring`::
+
+                sage: R.<x> = PolynomialRing(ZZ)
+                sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
+                sage: S = R.quotient_ring(I, 'a')
+                sage: S.gens()
+                (a,)
+
+                sage: R.<x,y> = PolynomialRing(QQ,2)
+                sage: S.<a,b> = R.quotient_ring((x^2, y))
+                sage: S
+                Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y)
+                sage: S.gens()
+                (a, 0)
+                sage: a == b
+                False
             """
-            return self.quotient(I,names=names, **kwds)
+            return self.quotient(I, names=names, **kwds)
 
         def __truediv__(self, I):
             """
@@ -923,6 +964,11 @@ def __truediv__(self, I):
                 Traceback (most recent call last):
                 ...
                 TypeError: Use self.quo(I) or self.quotient(I) to construct the quotient ring.
+
+                sage: QQ['x'] / ZZ
+                Traceback (most recent call last):
+                ...
+                TypeError: Use self.quo(I) or self.quotient(I) to construct the quotient ring.
             """
             raise TypeError("Use self.quo(I) or self.quotient(I) to construct the quotient ring.")
 

src/sage/rings/ring.pyx

@@ -650,76 +650,6 @@ cdef class Ring(ParentWithGens):
         import sage.rings.quotient_ring
         return sage.rings.quotient_ring.QuotientRing(self, I, names=names, **kwds)
 
-    def quo(self, I, names=None, **kwds):
-        """
-        Create the quotient of `R` by the ideal `I`.  This is a synonym for :meth:`.quotient`
-
-        EXAMPLES::
-
-            sage: R.<x,y> = PolynomialRing(QQ,2)
-            sage: S.<a,b> = R.quo((x^2, y))
-            sage: S
-            Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y)
-            sage: S.gens()
-            (a, 0)
-            sage: a == b
-            False
-        """
-        return self.quotient(I, names=names, **kwds)
-
-    def __truediv__(self, I):
-        """
-        Dividing one ring by another is not supported because there is no good
-        way to specify generator names.
-
-        EXAMPLES::
-
-            sage: QQ['x'] / ZZ
-            Traceback (most recent call last):
-            ...
-            TypeError: Use self.quo(I) or self.quotient(I) to construct the quotient ring.
-        """
-        raise TypeError("Use self.quo(I) or self.quotient(I) to construct the quotient ring.")
-
-    def quotient_ring(self, I, names=None, **kwds):
-        """
-        Return the quotient of self by the ideal `I` of ``self``.
-        (Synonym for ``self.quotient(I)``.)
-
-        INPUT:
-
-        - ``I`` -- an ideal of `R`
-
-        - ``names`` -- (optional) names of the generators of the quotient. (If
-          there are multiple generators, you can specify a single character
-          string and the generators are named in sequence starting with 0.)
-
-        - further named arguments that may be passed to the quotient ring
-          constructor.
-
-        OUTPUT:
-
-        - ``R/I`` -- the quotient ring of `R` by the ideal `I`
-
-        EXAMPLES::
-
-            sage: R.<x> = PolynomialRing(ZZ)
-            sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
-            sage: S = R.quotient_ring(I, 'a')
-            sage: S.gens()
-            (a,)
-
-            sage: R.<x,y> = PolynomialRing(QQ,2)
-            sage: S.<a,b> = R.quotient_ring((x^2, y))
-            sage: S
-            Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2, y)
-            sage: S.gens()
-            (a, 0)
-            sage: a == b
-            False
-        """
-        return self.quotient(I, names, **kwds)
-
     def zero(self):
         """
         Return the zero element of this ring (cached).