Trac #18578: Add special function __truediv__() to some pyx-modules

This also increases the number of methods of "MatrixSpace(QQ,2)" in
coercion_and_categories.rst by one.

src/doc/en/thematic_tutorials/coercion_and_categories.rst

@@ -471,7 +471,7 @@ And indeed, ``MS2`` has *more* methods than ``MS1``::
     sage: len([s for s in dir(MS1) if inspect.ismethod(getattr(MS1,s,None))])
     57
     sage: len([s for s in dir(MS2) if inspect.ismethod(getattr(MS2,s,None))])
-    85
+    86
 
 This is because the class of ``MS2`` also inherits from the parent
 class for algebras::

src/sage/libs/ntl/ntl_GF2.pyx

@@ -127,7 +127,7 @@ cdef class ntl_GF2:
         GF2_mul(r.x, (<ntl_GF2>self).x, (<ntl_GF2>other).x)
         return r
 
-    def __div__(self, other):
+    def __truediv__(self, other):
         """
             sage: o = ntl.GF2(1)
             sage: z = ntl.GF2(0)
@@ -149,6 +149,9 @@ cdef class ntl_GF2:
         GF2_div(r.x, (<ntl_GF2>self).x, (<ntl_GF2>other).x)
         return r
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def __sub__(self, other):
         """
             sage: o = ntl.GF2(1)

src/sage/libs/ntl/ntl_GF2E.pyx

@@ -257,7 +257,7 @@ cdef class ntl_GF2E:
         GF2E_add(r.x, self.x, (<ntl_GF2E>other).x)
         return r
 
-    def __div__(ntl_GF2E self, other):
+    def __truediv__(ntl_GF2E self, other):
         """
         EXAMPLES:
             sage: ctx = ntl.GF2EContext(ntl.GF2X([1,1,0,1,1,0,0,0,1]))
@@ -274,6 +274,9 @@ cdef class ntl_GF2E:
         GF2E_div(r.x, self.x, (<ntl_GF2E>other).x)
         return r
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def __neg__(ntl_GF2E self):
         """
         EXAMPLES:

src/sage/libs/ntl/ntl_GF2X.pyx

@@ -195,7 +195,7 @@ cdef class ntl_GF2X:
         GF2X_mul(r.x, self.x, (<ntl_GF2X>other).x)
         return r
 
-    def __div__(ntl_GF2X self, b):
+    def __truediv__(ntl_GF2X self, b):
         """
         EXAMPLES:
             sage: a = ntl.GF2X(4)
@@ -217,6 +217,9 @@ cdef class ntl_GF2X:
             raise ArithmeticError, "self (=%s) is not divisible by b (=%s)"%(self, b)
         return q
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def DivRem(ntl_GF2X self, b):
         """
         EXAMPLES:

src/sage/libs/ntl/ntl_ZZX.pyx

@@ -321,7 +321,7 @@ cdef class ntl_ZZX:
         sig_off()
         return r
 
-    def __div__(ntl_ZZX self, ntl_ZZX other):
+    def __truediv__(ntl_ZZX self, ntl_ZZX other):
         """
         Compute quotient self / other, if the quotient is a polynomial.
         Otherwise an Exception is raised.
@@ -351,6 +351,9 @@ cdef class ntl_ZZX:
         result = make_ZZX_sig_off(q)
         return result
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def __mod__(ntl_ZZX self, ntl_ZZX other):
         """
         Given polynomials a, b in ZZ[X], there exist polynomials q, r

src/sage/libs/ntl/ntl_ZZ_pEX.pyx

@@ -341,7 +341,7 @@ cdef class ntl_ZZ_pEX:
         sig_off()
         return r
 
-    def __div__(ntl_ZZ_pEX self, ntl_ZZ_pEX other):
+    def __truediv__(ntl_ZZ_pEX self, ntl_ZZ_pEX other):
         """
         Compute quotient self / other, if the quotient is a polynomial.
         Otherwise an Exception is raised.
@@ -371,6 +371,9 @@ cdef class ntl_ZZ_pEX:
             raise ArithmeticError, "self (=%s) is not divisible by other (=%s)"%(self, other)
         return r
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def __mod__(ntl_ZZ_pEX self, ntl_ZZ_pEX other):
         """
         Given polynomials a, b in ZZ_pE[X], if p is prime and the defining modulus irreducible,

src/sage/libs/ntl/ntl_ZZ_pX.pyx

@@ -377,7 +377,7 @@ cdef class ntl_ZZ_pX:
         sig_off()
         return r
 
-    def __div__(ntl_ZZ_pX self, ntl_ZZ_pX other):
+    def __truediv__(ntl_ZZ_pX self, ntl_ZZ_pX other):
         """
         Compute quotient self / other, if the quotient is a polynomial.
         Otherwise an Exception is raised.
@@ -410,6 +410,9 @@ cdef class ntl_ZZ_pX:
             raise ArithmeticError, "self (=%s) is not divisible by other (=%s)"%(self, other)
         return r
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def __mod__(ntl_ZZ_pX self, ntl_ZZ_pX other):
         """
         Given polynomials a, b in ZZ_p[X], if p is prime, then there exist polynomials q, r

src/sage/libs/ntl/ntl_lzz_p.pyx

@@ -237,7 +237,7 @@ cdef class ntl_zz_p:
         zz_p_mul(y.x, self.x, (<ntl_zz_p>other).x)
         return y
 
-    def __div__(ntl_zz_p self, other):
+    def __truediv__(ntl_zz_p self, other):
         """
         EXAMPLES:
             sage: ntl.zz_p(5,23) / ntl.zz_p(2,23)
@@ -255,6 +255,9 @@ cdef class ntl_zz_p:
         sig_off()
         return q
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def __pow__(ntl_zz_p self, long n, ignored):
         """
         Return the n-th nonnegative power of self.

src/sage/libs/ntl/ntl_lzz_pX.pyx

@@ -321,7 +321,7 @@ cdef class ntl_zz_pX:
         sig_off()
         return y
 
-    def __div__(ntl_zz_pX self, other):
+    def __truediv__(ntl_zz_pX self, other):
         """
         Compute quotient self / other, if the quotient is a polynomial.
         Otherwise an Exception is raised.
@@ -359,6 +359,9 @@ cdef class ntl_zz_pX:
             raise ArithmeticError, "self (=%s) is not divisible by other (=%s)"%(self, other)
         return q
 
+    def __div__(self, other):
+        return PyNumber_TrueDivide(self, other)
+
     def __mod__(ntl_zz_pX self, other):
         """
         Given polynomials a, b in ZZ[X], there exist polynomials q, r

src/sage/rings/polynomial/polynomial_element.pyx

@@ -1722,7 +1722,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
             return self.roots(ring=ring, multiplicities=False)[0]
 
 
-    def __div__(self, right):
+    def __truediv__(self, right):
         """
         EXAMPLES::
 
@@ -1797,6 +1797,8 @@ cdef class Polynomial(CommutativeAlgebraElement):
             pass
         return RingElement.__div__(self, right)
 
+    def __div__(self, other):
+        return Polynomial.__truediv__(self, other)
 
     def __pow__(self, right, modulus):
         """

src/sage/schemes/elliptic_curves/period_lattice_region.pyx

@@ -370,7 +370,7 @@ cdef class PeriodicRegion:
         m, n = self.data.shape
         return self.data[int(m * i), int(n * j)]
 
-    def __div__(self, unsigned int n):
+    def __truediv__(self, unsigned int n):
         """
         Returns a new region of the same resolution that is the image
         of this region under the map z -> z/n.
@@ -446,6 +446,9 @@ cdef class PeriodicRegion:
                             new_data[(a*rows+i)//n, (b*cols+j)//n] = data[i,j]
         return PeriodicRegion(self.w1, self.w2, new_data)
 
+    def __div__(self, other):
+        return PeriodicRegion.__truediv__(self, other)
+
     def __invert__(self):
         """
         Returns the complement of this region.