Trac #18578: Add special function __truediv__() for Py3

In Python 3 the division operator "/" calls the special function
__truediv__() instead of __div__() (as in Py2).
This change defines __truediv__() and assigns __div __ = __truediv__
to prepare for both "from __future__ import division" and Python 3.

src/sage/algebras/weyl_algebra.py

@@ -436,7 +436,7 @@ def list(self):
 
     # This is essentially copied from
     #   sage.combinat.free_module.CombinatorialFreeModuleElement
-    def __div__(self, x, self_on_left=False):
+    def __truediv__(self, x, self_on_left=False):
         """
         Division by coefficients.
 
@@ -463,6 +463,8 @@ def __div__(self, x, self_on_left=False):
             return self.__class__(F, D)
 
         return self.__class__(F, {t: _divide_if_possible(D[t], x) for t in D})
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
 class DifferentialWeylAlgebra(Algebra, UniqueRepresentation):
     r"""

src/sage/categories/rings.py

@@ -687,7 +687,7 @@ 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
@@ -703,6 +703,8 @@ def __div__(self, I):
                 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.")
+        # for Python 2 without from __future__ import division
+        __div__ = __truediv__
 
         def __getitem__(self, arg):
             """

src/sage/combinat/binary_tree.py

@@ -2473,6 +2473,8 @@ def over(self, bt):
             return B([self[0], self[1].over(bt)])
 
     __div__ = over
+    # for Python 3 and for Python 2 with from __future__ import division 
+    __truediv__ = over
 
     @combinatorial_map(name="Under operation on Binary Trees")
     def under(self, bt):

src/sage/combinat/free_module.py

@@ -918,7 +918,7 @@ def _acted_upon_(self, scalar, self_on_left = False):
     _lmul_ = _acted_upon_
     _rmul_ = _acted_upon_
 
-    def __div__(self, x, self_on_left=False ):
+    def __truediv__(self, x, self_on_left=False ):
         """
         Division by coefficients
 
@@ -950,6 +950,8 @@ def __div__(self, x, self_on_left=False ):
             return F._from_dict( D, remove_zeros=False )
         else:
             return self.map_coefficients(lambda c: _divide_if_possible(c, x))
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
 def _divide_if_possible(x, y):
     """

src/sage/combinat/partition.py

@@ -1075,7 +1075,7 @@ def pp(self):
         """
         print self.ferrers_diagram()
 
-    def __div__(self, p):
+    def __truediv__(self, p):
         """
         Returns the skew partition ``self / p``.
 
@@ -1097,6 +1097,8 @@ def __div__(self, p):
             raise ValueError("To form a skew partition p/q, q must be contained in p.")
 
         return SkewPartition([self[:], p])
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def power(self, k):
         r"""

src/sage/combinat/tableau.py

@@ -699,7 +699,7 @@ def _latex_diagram(self):
         from output import tex_from_array
         return tex_from_array(self)
 
-    def __div__(self, t):
+    def __truediv__(self, t):
         """
         Return the skew tableau ``self``/``t``, where ``t`` is a partition
         contained in the shape of ``self``.
@@ -734,6 +734,8 @@ def __div__(self, t):
 
         from sage.combinat.skew_tableau import SkewTableau
         return SkewTableau(st)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def __call__(self, *cell):
         r"""

src/sage/geometry/polyhedron/base.py

@@ -2546,7 +2546,7 @@ def __neg__(self):
         """
         return self.dilation(-1)
 
-    def __div__(self, scalar):
+    def __truediv__(self, scalar):
         """
         Divide by a scalar factor.
 
@@ -2559,6 +2559,8 @@ def __div__(self, scalar):
             (A vertex at (2/5, 4/5, 8/5), A vertex at (3/5, 9/5, 27/5))
         """
         return self.dilation(1/scalar)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     @coerce_binop
     def convex_hull(self, other):

src/sage/groups/free_group.py

@@ -905,3 +905,5 @@ def quotient(self, relations):
         return FinitelyPresentedGroup(self, tuple(map(self, relations) ) )
 
     __div__ = quotient
+    # for Python 3 and for Python 2 with from __future__ import division
+    __truediv__ = quotient

src/sage/misc/sage_input.py

@@ -1520,7 +1520,7 @@ def __mul__(self, other):
         """
         return self._sie_binop('*', other)
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         r"""
         Compute an expression tree for ``self / other``.
 
@@ -1533,6 +1533,8 @@ def __div__(self, other):
             {binop:/ {atomic:3} {atomic:4}}
         """
         return self._sie_binop('/', other)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def __add__(self, other):
         r"""

src/sage/modular/abvar/abvar.py

@@ -977,7 +977,7 @@ def quotient(self, other):
         """
         return self.__div__(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.
@@ -1036,6 +1036,8 @@ def __div__(self, other):
             return self._quotient_by_abelian_subvariety(other)
         else:
             raise TypeError("other must be a subgroup or abelian subvariety")
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def degeneracy_map(self, M_ls, t_ls):
         """

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.
@@ -463,6 +463,8 @@ def __div__(self, other):
         if not other.is_submodule(self):
             raise ValueError("other must be a submodule of self")
         return self._module_constructor(self._V, other._V+self._W)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def __eq__(self, other):
         """

src/sage/modules/free_module.py

@@ -2984,7 +2984,7 @@ 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, check=True):
         """
         Return the quotient of self by the given submodule sub.
 
@@ -3000,6 +3000,8 @@ def __div__(self, sub, check=True):
             Finitely generated module V/W over Integer Ring with invariants (4, 12)
         """
         return self.quotient(sub, check)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
 class FreeModule_generic_field(FreeModule_generic_pid):
     """
@@ -3821,7 +3823,7 @@ 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, check=True):
         """
         Return the quotient of self by the given subspace sub.
 
@@ -3847,6 +3849,8 @@ def __div__(self, sub, check=True):
             (0.0)
         """
         return self.quotient(sub, check)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def quotient(self, sub, check=True):
         """

src/sage/plot/colors.py

@@ -775,7 +775,7 @@ def __rmul__(self, left):
         """
         return self * left
 
-    def __div__(self, right):
+    def __truediv__(self, right):
         """
         Return a color whose RGB coordinates are this color's
         coordinates divided by a scalar.  This method is called for
@@ -812,33 +812,8 @@ def __div__(self, right):
             TypeError: float() argument must be a string or a number
         """
         return self * (float(1.0) / float(right))
-
-    def __truediv__(self, right):
-        """
-        Return a color whose RGB coordinates are this color's
-        coordinates divided by a scalar.  This method is called for
-        "true division."
-
-        INPUT:
-
-        - ``right`` - a float-convertible, non-zero number
-
-        OUTPUT:
-
-        - a **new** instance of :class:`Color`
-
-        EXAMPLES::
-
-            sage: from __future__ import division
-            sage: from sage.plot.colors import yellow, gold
-            sage: yellow / 4
-            RGB color (0.25, 0.25, 0.0)
-            sage: yellow.__truediv__(4)
-            RGB color (0.25, 0.25, 0.0)
-            sage: gold / pi + yellow * e
-            RGB color (0.51829585732141..., 0.49333037605210..., 0.0)
-        """
-        return self.__div__(right)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def __int__(self):
         """

src/sage/quivers/representation.py

@@ -1501,21 +1501,6 @@ 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.
@@ -1529,6 +1514,8 @@ def __truediv__(self, sub):
             True
         """
         return self.quotient(sub)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def _submodule(self, spaces={}):
         """

src/sage/rings/number_field/number_field_ideal.py

@@ -1802,7 +1802,7 @@ def prime_factors(self):
         """
         return [x[0] for x in self.factor()]
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         """
         Return the quotient self / other.
 
@@ -1818,6 +1818,8 @@ def __div__(self, other):
             True
         """
         return self * other.__invert__()
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def __invert__(self):
         """

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.
 
@@ -394,6 +394,8 @@ def __div__(self, Y):
             Affine Space of dimension 3 over Finite Field of size 7
         """
         return self.base_extend(Y)
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def base_ring(self):
         """

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.
 
@@ -804,6 +804,8 @@ def __div__(self, other):
             NotImplementedError: Quotients of the Chow group are not implemented.
         """
         raise NotImplementedError('Quotients of the Chow group are not implemented.')
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
 
     def _repr_(self):

src/sage/structure/factorization.py

@@ -1143,7 +1143,7 @@ def __invert__(self):
         return Factorization([(p,-e) for p,e in reversed(self)],
             cr=self._cr(), unit=self.unit()**(-1))
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         r"""
         Return the quotient of two factorizations, which is obtained by
         multiplying the first by the inverse of the second.
@@ -1166,6 +1166,8 @@ def __div__(self, other):
         if not isinstance(other, Factorization):
             return self / Factorization([(other, 1)])
         return self * other**-1
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def value(self):
         """

src/sage/tensor/modules/comp.py

@@ -1492,7 +1492,7 @@ def __rmul__(self, other):
         return result
 
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         r"""
         Division (by a scalar).
 
@@ -1518,6 +1518,8 @@ def __div__(self, other):
         for ind, val in self._comp.iteritems():
             result._comp[ind] = val / other
         return result
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
     def trace(self, pos1, pos2):
         r"""

src/sage/tensor/modules/free_module_tensor.py

@@ -1817,7 +1817,7 @@ def __mul__(self, other):
         return result
 
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         r"""
         Division (by a scalar).
 
@@ -1843,6 +1843,8 @@ def __div__(self, other):
         for basis in self._components:
             result._components[basis] = self._components[basis] / other
         return result
+    # for Python 2 without from __future__ import division
+    __div__ = __truediv__
 
 
     def __call__(self, *args):