Implement __floordiv__ in the coercion model

src/sage/combinat/q_analogues.py

@@ -313,13 +313,13 @@ def q_binomial(n, k, q=None, algorithm='auto'):
         else:
             num = prod(one - q**i for i in range(n-k+1, n+1))
             try:
-                return num//denom
-            except TypeError:
                 try:
-                    return num/denom
-                except (TypeError,ZeroDivisionError):
-                    #try a substitution
-                    return q_binomial(n,k)(q)
+                    return num // denom
+                except TypeError:
+                    return num / denom
+            except (TypeError, ZeroDivisionError):
+                # use substitution instead
+                return q_binomial(n,k)(q)
     elif algorithm == 'cyclo_generic':
         from sage.rings.polynomial.cyclotomic import cyclotomic_value
         return prod(cyclotomic_value(d,q)

src/sage/rings/finite_rings/integer_mod.pyx

@@ -1653,21 +1653,16 @@ cdef class IntegerMod_abstract(FiniteRingElement):
                 return infinity
         return r
 
-    def __floordiv__(self, other):
+    cpdef RingElement _floordiv_(self, RingElement right):
         """
         Exact division for prime moduli, for compatibility with other fields.
 
-        EXAMPLES:
-        sage: GF(7)(3) // GF(7)(5)
-        2
+        EXAMPLES::
+
+            sage: GF(7)(3) // 5
+            2
         """
-        # needs to be rewritten for coercion
-        if other.parent() is not self.parent():
-            other = self.parent().coerce(other)
-        if self.parent().is_field():
-            return self / other
-        else:
-            raise TypeError, "Floor division not defined for non-prime modulus"
+        return self._mul_(~right)
 
     def _repr_(self):
         return str(self.lift())

src/sage/rings/integer.pyx

@@ -1732,7 +1732,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
         # we can't cimport rationals.
         return the_integer_ring._div(self, right)
 
-    def __floordiv__(x, y):
+    cpdef RingElement _floordiv_(self, RingElement right):
         r"""
         Computes the whole part of `\frac{x}{y}`.
 
@@ -1769,34 +1769,17 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
             sage: [int(a) // b for a,b in signs] == control
             True
         """
-        cdef Integer z = <Integer>PY_NEW(Integer)
-        cdef long yy, res
-        if type(x) is type(y):
-            if not mpz_sgn((<Integer>y).value):
-                raise ZeroDivisionError, "Integer division by zero"
-            if mpz_size((<Integer>x).value) > 100000:
-                sig_on()
-                mpz_fdiv_q(z.value, (<Integer>x).value, (<Integer>y).value)
-                sig_off()
-            else:
-                mpz_fdiv_q(z.value, (<Integer>x).value, (<Integer>y).value)
-            return z
-
-        elif PyInt_CheckExact(y):
-            yy = PyInt_AS_LONG(y)
-            if yy > 0:
-                mpz_fdiv_q_ui(z.value, (<Integer>x).value, yy)
-            elif yy == 0:
-                raise ZeroDivisionError, "Integer division by zero"
-            else:
-                res = mpz_fdiv_q_ui(z.value, (<Integer>x).value, -yy)
-                mpz_neg(z.value, z.value)
-                if res:
-                    mpz_sub_ui(z.value, z.value, 1)
-            return z
+        if not mpz_sgn((<Integer>right).value):
+            raise ZeroDivisionError("Integer division by zero")
 
+        cdef Integer z = <Integer>PY_NEW(Integer)
+        if mpz_size(self.value) > 1000:
+            sig_on()
+            mpz_fdiv_q(z.value, self.value, (<Integer>right).value)
+            sig_off()
         else:
-            return bin_op(x, y, operator.floordiv)
+            mpz_fdiv_q(z.value, self.value, (<Integer>right).value)
+        return z
 
     def __pow__(self, n, modulus):
         r"""

src/sage/rings/padics/padic_generic_element.pyx

@@ -269,7 +269,7 @@ cdef class pAdicGenericElement(LocalGenericElement):
             sage: (a // b) * b + a % b
             3 + 2*5^4 + 5^5 + 3*5^6 + 5^7 + O(5^16)
 
-            The alternative definition:
+        The alternative definition::
 
             sage: a
             3 + 2*5^4 + 5^5 + 3*5^6 + 5^7 + O(5^20)

src/sage/rings/polynomial/laurent_polynomial.pyx

@@ -641,19 +641,23 @@ cdef class LaurentPolynomial_univariate(LaurentPolynomial_generic):
             raise ValueError("exponent must be an integer")
         return LaurentPolynomial_univariate(self._parent, self.__u**right, self.__n*right)
 
-    def __floordiv__(LaurentPolynomial_univariate self, RingElement rhs):
+    cpdef RingElement _floordiv_(self, RingElement rhs):
         """
         Perform division with remainder and return the quotient.
 
         EXAMPLES::
 
             sage: L.<x> = LaurentPolynomialRing(QQ)
-            sage: f = x**3 + x^-3
+            sage: f = x^3 + x^-3
             sage: g = x^-1 + x
             sage: f // g
             x^-2 - 1 + x^2
             sage: g * (f // g) == f
             True
+            sage: f // 1
+            x^-3 + x^3
+            sage: 1 // f
+            0
         """
         cdef LaurentPolynomial_univariate right = <LaurentPolynomial_univariate> rhs
         return LaurentPolynomial_univariate(self._parent,
@@ -2029,23 +2033,27 @@ cdef class LaurentPolynomial_mpair(LaurentPolynomial_generic):
         ans._poly = self._poly * (<LaurentPolynomial_mpair>right)._poly
         return ans
 
-    def __floordiv__(LaurentPolynomial_mpair self, RingElement right):
+    cpdef RingElement _floordiv_(self, RingElement right):
         """
         Perform division with remainder and return the quotient.
 
         EXAMPLES::
 
             sage: L.<x,y> = LaurentPolynomialRing(QQ)
-            sage: f = x**3 + y^-3
+            sage: f = x^3 + y^-3
             sage: g = y + x
             sage: f // g
             x^5*y^-3 - x^4*y^-2 + x^3*y^-1
 
-            sage: h = x + y**(-1)
+            sage: h = x + y^(-1)
             sage: f // h
             x^2 - x*y^-1 + y^-2
             sage: h * (f // h) == f
             True
+            sage: f // 1
+            x^3 + y^-3
+            sage: 1 // f
+            0
 
         TESTS:
 

src/sage/rings/polynomial/multi_polynomial_element.py

@@ -1443,7 +1443,7 @@ def __nonzero__(self):
         """
         return self._MPolynomial_element__element.dict()!={}
 
-    def __floordiv__(self,right):
+    def _floordiv_(self, right):
         r"""
         Quotient of division of self by other. This is denoted //.
 
@@ -1464,9 +1464,6 @@ def __floordiv__(self,right):
             sage: type(0//y)
             <class 'sage.rings.polynomial.multi_polynomial_element.MPolynomial_polydict'>
         """
-        if type(self) is not type(right) or self.parent() is not right.parent():
-            self, right = canonical_coercion(self, right)
-            return self // right  # this looks like recursion, but, in fact, it may be that self, right are a totally new composite type
         # handle division by monomials without using Singular
         if len(right.dict()) == 1:
             P = self.parent()

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -3889,7 +3889,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
         else:
             return False
 
-    def __floordiv__(MPolynomial_libsingular self, right):
+    cpdef RingElement _floordiv_(self, RingElement right):
         """
         Perform division with remainder and return the quotient.
 
@@ -3935,20 +3935,15 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
         cdef poly *temp
         cdef poly *p
 
-        _self = self
-
-        if not isinstance(right, MPolynomial_libsingular) \
-                or (parent is not (<MPolynomial_libsingular>right)._parent):
-            _right = parent._coerce_c(right)
-        else:
-            _right = right
-
         if right.is_zero():
             raise ZeroDivisionError
 
         if self._parent._base.is_finite() and self._parent._base.characteristic() > 1<<29:
             raise NotImplementedError, "Division of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented."
 
+        _self = <MPolynomial_libsingular>self
+        _right = <MPolynomial_libsingular>right
+
         if r.ringtype != 0:
             if r.ringtype == 4:
                 P = parent.change_ring(RationalField())

src/sage/rings/polynomial/polynomial_element.pyx

@@ -75,7 +75,7 @@ from sage.rings.complex_double import is_ComplexDoubleField, CDF
 from sage.rings.real_mpfi import is_RealIntervalField
 
 from sage.structure.element import generic_power
-from sage.structure.element cimport parent_c as parent
+from sage.structure.element cimport parent_c as parent, have_same_parent_c
 from sage.structure.element cimport (Element, RingElement,
         ModuleElement, MonoidElement, coercion_model)
 
@@ -2270,8 +2270,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
         """
         raise IndexError("polynomials are immutable")
 
-
-    def __floordiv__(self,right):
+    cpdef RingElement _floordiv_(self, RingElement right):
         """
         Quotient of division of self by other. This is denoted //.
 
@@ -8036,18 +8035,25 @@ cdef class Polynomial_generic_dense(Polynomial):
 
         TESTS:
 
-        Check that #13048 has been fixed::
+        Check that :trac:`13048` and :trac:`2034` are fixed::
 
             sage: R.<x> = QQbar[]
-            sage: x//x
+            sage: x // x
             1
-            sage: x//1
+            sage: x // 1
             x
-
+            sage: x // int(1)
+            x
+            sage: x //= int(1); x
+            x
+            sage: int(1) // x  # check that this doesn't segfault
+            Traceback (most recent call last):
+            ...
+            AttributeError: type object 'int' has no attribute 'base_ring'
         """
-        P = (<Element>self)._parent
-        if right.parent() == P:
-            return Polynomial.__floordiv__(self, right)
+        if have_same_parent_c(self, right):
+            return (<Polynomial_generic_dense>self)._floordiv_(<Polynomial_generic_dense>right)
+        P = parent(self)
         d = P.base_ring()(right)
         cdef Polynomial_generic_dense res = (<Polynomial_generic_dense>self)._new_c([c // d for c in (<Polynomial_generic_dense>self).__coeffs], P)
         res.__normalize()

src/sage/rings/polynomial/polynomial_modn_dense_ntl.pyx

@@ -914,7 +914,7 @@ cdef class Polynomial_dense_modn_ntl_zz(Polynomial_dense_mod_n):
         sig_off()
         return q, r
 
-    def __floordiv__(self, right):
+    cpdef RingElement _floordiv_(self, RingElement right):
         """
         Returns the whole part of self/right, without remainder.
 
@@ -929,9 +929,6 @@ cdef class Polynomial_dense_modn_ntl_zz(Polynomial_dense_mod_n):
             sage: f - q*g
             x + 1
         """
-        if not have_same_parent_c(self, right):
-            self, right = canonical_coercion(self, right)
-            return self // right
         cdef Polynomial_dense_modn_ntl_zz numer = <Polynomial_dense_modn_ntl_zz>self
         cdef Polynomial_dense_modn_ntl_zz denom = <Polynomial_dense_modn_ntl_zz>right
         cdef Polynomial_dense_modn_ntl_zz q = numer._new()
@@ -1472,7 +1469,7 @@ cdef class Polynomial_dense_modn_ntl_ZZ(Polynomial_dense_mod_n):
         sig_off()
         return q, r
 
-    def __floordiv__(self, right):
+    cpdef RingElement _floordiv_(self, RingElement right):
         """
         Returns the whole part of self/right, without remainder.
 
@@ -1487,9 +1484,6 @@ cdef class Polynomial_dense_modn_ntl_ZZ(Polynomial_dense_mod_n):
             sage: f - q*g
             x + 1
         """
-        if not have_same_parent_c(self, right):
-            self, right = canonical_coercion(self, right)
-            return self // right
         cdef Polynomial_dense_modn_ntl_ZZ numer = <Polynomial_dense_modn_ntl_ZZ>self
         cdef Polynomial_dense_modn_ntl_ZZ denom = <Polynomial_dense_modn_ntl_ZZ>right
         cdef Polynomial_dense_modn_ntl_ZZ q = numer._new()

src/sage/rings/polynomial/polynomial_template.pxi

@@ -408,7 +408,7 @@ cdef class Polynomial_template(Polynomial):
         #assert(t._parent(tp) == t)
         return r,s,t
 
-    def __floordiv__(self, right):
+    cpdef RingElement _floordiv_(self, RingElement right):
         """
         EXAMPLE::
 
@@ -418,11 +418,6 @@ cdef class Polynomial_template(Polynomial):
             sage: (x + 1)//x
             1
         """
-        # We can't use @coerce_binop for operators in cython classes,
-        # so we use sage.structure.element.bin_op to handle coercion.
-        if type(self) is not type(right) or \
-                (<Polynomial_template>self)._parent is not (<Polynomial_template>right)._parent:
-            return bin_op(self, right, operator.mod)
         cdef Polynomial_template _right = <Polynomial_template>right
 
         if celement_is_zero(&_right.x, (<Polynomial_template>self)._cparent):

src/sage/structure/element.pxd

@@ -78,6 +78,7 @@ cdef class AdditiveGroupElement(ModuleElement):
 cdef class RingElement(ModuleElement):
     cpdef RingElement _mul_(self, RingElement right)
     cpdef RingElement _div_(self, RingElement right)
+    cpdef RingElement _floordiv_(self, RingElement right)
 
     cdef RingElement _add_long(self, long n)