Implement division as true division for CategoryObject

src/doc/en/thematic_tutorials/coercion_and_categories.rst

@@ -104,14 +104,14 @@ it makes sense to build on top of the base class
 This base class provides a lot more methods than a general parent::
 
     sage: [p for p in dir(Field) if p not in dir(Parent)]
-    ['__div__',
-     '__fraction_field',
+    ['__fraction_field',
      '__ideal_monoid',
      '__iter__',
      '__pow__',
-     '__rdiv__',
      '__rpow__',
+     '__rtruediv__',
      '__rxor__',
+     '__truediv__',
      '__xor__',
      '_an_element',
      '_an_element_c',

src/sage/categories/rings.py

@@ -688,7 +688,7 @@ def quotient_ring(self, I, names=None):
             """
             return self.quotient(I,names=names)
 
-        def __div__(self, I):
+        def __truediv__(self, I):
             """
             Since assigning generator names would not work properly,
             the construction of a quotient ring using division syntax

src/sage/modular/abvar/abvar.py

@@ -975,9 +975,9 @@ def quotient(self, other):
             sage: J0(11).direct_product(J1(13))
             Abelian variety J0(11) x J1(13) of dimension 3
         """
-        return self.__div__(other)
+        return self / other
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         """
         Compute the quotient of self and other, where other is either an
         abelian subvariety of self or a finite subgroup of self.

src/sage/modules/fg_pid/fgp_module.py

@@ -440,7 +440,7 @@ def _repr_(self):
         I = str(self.invariants()).replace(',)',')')
         return "Finitely generated module V/W over %s with invariants %s"%(self.base_ring(), I)
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         """
         Return the quotient self/other, where other must be a
         submodule of self.

src/sage/modules/free_module.py

@@ -2989,12 +2989,10 @@ def quotient(self, sub, check=True):
         else:
             raise NotImplementedError("quotients of modules over rings other than fields or ZZ is not fully implemented")
 
-    def __div__(self, sub, check=True):
+    def __truediv__(self, sub):
         """
         Return the quotient of self by the given submodule sub.
 
-        This just calls self.quotient(sub, check).
-
         EXAMPLES::
 
             sage: V1 = ZZ^2; W1 = V1.span([[1,2],[3,4]])
@@ -3004,7 +3002,7 @@ def __div__(self, sub, check=True):
             sage: V2/W2
             Finitely generated module V/W over Integer Ring with invariants (4, 12)
         """
-        return self.quotient(sub, check)
+        return self.quotient(sub, check=True)
 
 class FreeModule_generic_field(FreeModule_generic_pid):
     """
@@ -3826,12 +3824,10 @@ def linear_dependence(self, vectors, zeros='left', check=True):
         A = sage.matrix.constructor.matrix(vectors)  # as rows, so get left kernel
         return A.left_kernel(basis=basis).basis()
 
-    def __div__(self, sub, check=True):
+    def __truediv__(self, sub):
         """
         Return the quotient of self by the given subspace sub.
 
-        This just calls self.quotient(sub, check)
-
         EXAMPLES::
 
             sage: V = RDF^3; W = V.span([[1,0,-1], [1,-1,0]])
@@ -3851,7 +3847,7 @@ def __div__(self, sub, check=True):
             sage: Q(W.0)
             (0.0)
         """
-        return self.quotient(sub, check)
+        return self.quotient(sub, check=True)
 
     def quotient(self, sub, check=True):
         """

src/sage/quivers/representation.py

@@ -1501,24 +1501,9 @@ def _repr_(self):
         """
         return "Representation with dimension vector {}".format(self.dimension_vector())
 
-    def __div__(self, sub):
-        """
-        This and :meth:`__truediv__` below together overload the ``/``
-        operator.
-
-        TESTS::
-
-            sage: Q = DiGraph({1:{2:['a']}}).path_semigroup()
-            sage: P = Q.P(GF(3), 1)
-            sage: R = P.radical()
-            sage: (P/R).is_simple()
-            True
-        """
-        return self.quotient(sub)
-
     def __truediv__(self, sub):
         """
-        This and :meth:`__div__` above together overload the ``/`` operator.
+        Overload the ``/`` operator.
 
         TESTS::
 

src/sage/rings/ring.pyx

@@ -635,7 +635,7 @@ cdef class Ring(ParentWithGens):
         """
         return self.quotient(I, names=names)
 
-    def __div__(self, I):
+    def __truediv__(self, I):
         """
         Dividing one ring by another is not supported because there is no good
         way to specify generator names.
@@ -647,8 +647,7 @@ cdef class Ring(ParentWithGens):
             ...
             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."
-        #return self.quotient(I, names=None)
+        raise TypeError("Use self.quo(I) or self.quotient(I) to construct the quotient ring.")
 
     def quotient_ring(self, I, names=None):
         """

src/sage/schemes/generic/scheme.py

@@ -377,7 +377,7 @@ def _point_homset(self, *args, **kwds):
         """
         raise NotImplementedError
 
-    def __div__(self, Y):
+    def __truediv__(self, Y):
         """
         Return the base extension of self to Y.
 

src/sage/schemes/toric/chow_group.py

@@ -786,7 +786,7 @@ def _rational_equivalence_relations(self, V):
         return V.span(relations)
 
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         r"""
         Return the quotient of the Chow group by a subgroup.
 

src/sage/structure/category_object.pyx

@@ -46,6 +46,8 @@ This example illustrates generators for a free module over `\ZZ`.
     ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1))
 """
 
+from __future__ import division
+
 #*****************************************************************************
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
@@ -800,6 +802,31 @@ cdef class CategoryObject(sage_object.SageObject):
             self._hash_value = hash(repr(self))
         return self._hash_value
 
+    ##############################################################################
+    # For compatibility with Python 2
+    ##############################################################################
+    def __div__(self, other):
+        """
+        Implement Python 2 division as true division.
+
+        EXAMPLES::
+
+            sage: V = QQ^2
+            sage: V.__div__(V.span([(1,3)]))
+            Vector space quotient V/W of dimension 1 over Rational Field where
+            V: Vector space of dimension 2 over Rational Field
+            W: Vector space of degree 2 and dimension 1 over Rational Field
+            Basis matrix:
+            [1 3]
+            sage: V.__truediv__(V.span([(1,3)]))
+            Vector space quotient V/W of dimension 1 over Rational Field where
+            V: Vector space of dimension 2 over Rational Field
+            W: Vector space of degree 2 and dimension 1 over Rational Field
+            Basis matrix:
+            [1 3]
+        """
+        return self / other
+
 
 class localvars:
     r"""