Drop return type from single-underscore arithmetic methods

src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx

@@ -470,7 +470,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
 
     ################################
     ## Arithmetic
-    cpdef ModuleElement _neg_(self):
+    cpdef _neg_(self):
         """
         TEST::
 
@@ -484,7 +484,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
 
         """
         return FreeAlgebraElement_letterplace(self._parent,-self._poly,check=False)
-    cpdef ModuleElement _add_(self, ModuleElement other):
+    cpdef _add_(self, ModuleElement other):
         """
         Addition, under the side condition that either one summand
         is zero, or both summands have the same degree.
@@ -517,7 +517,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         right._poly = A._current_ring(right._poly)
         return FreeAlgebraElement_letterplace(self._parent,self._poly+right._poly,check=False)
 
-    cpdef ModuleElement _sub_(self, ModuleElement other):
+    cpdef _sub_(self, ModuleElement other):
         """
         Difference, under the side condition that either one summand
         is zero or both have the same weighted degree.
@@ -556,7 +556,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         right._poly = A._current_ring(right._poly)
         return FreeAlgebraElement_letterplace(self._parent,self._poly-right._poly,check=False)
 
-    cpdef ModuleElement _lmul_(self, RingElement right):
+    cpdef _lmul_(self, RingElement right):
         """
         Multiplication from the right with an element of the base ring.
 
@@ -570,7 +570,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         """
         return FreeAlgebraElement_letterplace(self._parent,self._poly._lmul_(right),check=False)
 
-    cpdef ModuleElement _rmul_(self, RingElement left):
+    cpdef _rmul_(self, RingElement left):
         """
         Multiplication from the left with an element of the base ring.
 
@@ -584,7 +584,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         """
         return FreeAlgebraElement_letterplace(self._parent,self._poly._rmul_(left),check=False)
 
-    cpdef RingElement _mul_(self, RingElement other):
+    cpdef _mul_(self, RingElement other):
         """
         Product of two free algebra elements in letterplace implementation.
 

src/sage/algebras/quatalg/quaternion_algebra_element.pyx

@@ -487,7 +487,7 @@ cdef class QuaternionAlgebraElement_abstract(AlgebraElement):
         """
         return ~self.reduced_norm() * self.conjugate()
 
-    cpdef ModuleElement _rmul_(self, RingElement left):
+    cpdef _rmul_(self, RingElement left):
         """
         Return left*self, where left is in the base ring.
 
@@ -501,7 +501,7 @@ cdef class QuaternionAlgebraElement_abstract(AlgebraElement):
         """
         return self.__class__(self._parent, (left*self[0], left*self[1], left*self[2], left*self[3]), check=False)
 
-    cpdef ModuleElement _lmul_(self, RingElement right):
+    cpdef _lmul_(self, RingElement right):
         """
         Return self*right, where right is in the base ring.
 
@@ -515,7 +515,7 @@ cdef class QuaternionAlgebraElement_abstract(AlgebraElement):
         """
         return self.__class__(self._parent, (self[0]*right, self[1]*right, self[2]*right, self[3]*right), check=False)
 
-    cpdef RingElement _div_(self, RingElement right):
+    cpdef _div_(self, RingElement right):
         """
         Return quotient of self by right.
 
@@ -724,7 +724,7 @@ cdef class QuaternionAlgebraElement_generic(QuaternionAlgebraElement_abstract):
         return (unpickle_QuaternionAlgebraElement_generic_v0,
                 (self._parent, (self.x, self.y, self.z, self.w)))
 
-    cpdef ModuleElement _add_(self, ModuleElement _right):
+    cpdef _add_(self, ModuleElement _right):
         """
         Return the sum of self and _right.
 
@@ -740,7 +740,7 @@ cdef class QuaternionAlgebraElement_generic(QuaternionAlgebraElement_abstract):
         # TODO -- make this, etc. use __new__
         return QuaternionAlgebraElement_generic(self._parent, (self.x + right.x, self.y + right.y, self.z + right.z, self.w + right.w), check=False)
 
-    cpdef ModuleElement _sub_(self, ModuleElement _right):
+    cpdef _sub_(self, ModuleElement _right):
         """
         Return the difference of self and _right.
 
@@ -755,7 +755,7 @@ cdef class QuaternionAlgebraElement_generic(QuaternionAlgebraElement_abstract):
         cdef QuaternionAlgebraElement_generic right = _right
         return QuaternionAlgebraElement_generic(self._parent, (self.x - right.x, self.y - right.y, self.z - right.z, self.w - right.w), check=False)
 
-    cpdef RingElement _mul_(self, RingElement _right):
+    cpdef _mul_(self, RingElement _right):
         """
         Return the product of self and _right.
 
@@ -1076,7 +1076,7 @@ cdef class QuaternionAlgebraElement_rational_field(QuaternionAlgebraElement_abst
         return (unpickle_QuaternionAlgebraElement_rational_field_v0,
                 (self._parent, (self[0], self[1], self[2], self[3])))
 
-    cpdef ModuleElement _add_(self, ModuleElement _right):
+    cpdef _add_(self, ModuleElement _right):
         """
         EXAMPLES::
 
@@ -1132,7 +1132,7 @@ cdef class QuaternionAlgebraElement_rational_field(QuaternionAlgebraElement_abst
         mpz_set(result.b, self.b)
         return result
 
-    cpdef ModuleElement _sub_(self, ModuleElement _right):
+    cpdef _sub_(self, ModuleElement _right):
         """
         EXAMPLES::
 
@@ -1173,7 +1173,7 @@ cdef class QuaternionAlgebraElement_rational_field(QuaternionAlgebraElement_abst
         mpz_set(result.b, self.b)
         return result
 
-    cpdef RingElement _mul_(self, RingElement _right):
+    cpdef _mul_(self, RingElement _right):
         """
         EXAMPLES::
 
@@ -1739,7 +1739,7 @@ cdef class QuaternionAlgebraElement_number_field(QuaternionAlgebraElement_abstra
         return (unpickle_QuaternionAlgebraElement_number_field_v0,
                 (self._parent, (self[0], self[1], self[2], self[3])))
 
-    cpdef ModuleElement _add_(self, ModuleElement _right):
+    cpdef _add_(self, ModuleElement _right):
         """
         Add self and _right:
 
@@ -1810,7 +1810,7 @@ cdef class QuaternionAlgebraElement_number_field(QuaternionAlgebraElement_abstra
 
         return result
 
-    cpdef ModuleElement _sub_(self, ModuleElement _right):
+    cpdef _sub_(self, ModuleElement _right):
         """
         Subtract _right from self.
 
@@ -1860,7 +1860,7 @@ cdef class QuaternionAlgebraElement_number_field(QuaternionAlgebraElement_abstra
 
         return result
 
-    cpdef RingElement _mul_(self, RingElement _right):
+    cpdef _mul_(self, RingElement _right):
         """
         Multiply self and _right.
 

src/sage/geometry/toric_lattice_element.pyx

@@ -316,7 +316,7 @@ cdef class ToricLatticeElement(Vector_integer_dense):
     # We need to override this function to prohibit default behaviour.
     # It seems to be called when right is in the same lattice as self, which
     # is wrong from our point of view.
-    cpdef Element _dot_product_(self, Vector right):
+    cpdef _dot_product_(self, Vector right):
         """
         Raise a ``TypeError`` exception.
 

src/sage/groups/libgap_wrapper.pxd

@@ -5,8 +5,3 @@ from sage.libs.gap.element cimport GapElement
 cdef class ElementLibGAP(MultiplicativeGroupElement):
     cdef GapElement _libgap
     cpdef GapElement gap(self)
-    cpdef MonoidElement _mul_(left, MonoidElement right)
-    cpdef MultiplicativeGroupElement _div_(self, MultiplicativeGroupElement right)
-
-
-

src/sage/groups/libgap_wrapper.pyx

@@ -540,7 +540,7 @@ cdef class ElementLibGAP(MultiplicativeGroupElement):
             from sage.misc.latex import latex
             return latex(self._repr_())
 
-    cpdef MonoidElement _mul_(left, MonoidElement right):
+    cpdef _mul_(left, MonoidElement right):
         """
         Multiplication of group elements
 
@@ -585,7 +585,7 @@ cdef class ElementLibGAP(MultiplicativeGroupElement):
         return cmp((<ElementLibGAP>left)._libgap,
                    (<ElementLibGAP>right)._libgap)
 
-    cpdef MultiplicativeGroupElement _div_(left, MultiplicativeGroupElement right):
+    cpdef _div_(left, MultiplicativeGroupElement right):
         """
         Division of group elements.
 

src/sage/groups/matrix_gps/group_element.pyx

@@ -302,7 +302,7 @@ cdef class MatrixGroupElement_generic(MultiplicativeGroupElement):
         """
         return self._matrix
 
-    cpdef MonoidElement _mul_(self, MonoidElement other):
+    cpdef _mul_(self, MonoidElement other):
         """
         Return the product of ``self`` and`` other``, which must
         have identical parents.

src/sage/groups/perm_gps/permgroup_element.pyx

@@ -842,7 +842,7 @@ cdef class PermutationGroupElement(MultiplicativeGroupElement):
             elif is_Matrix(left):
                 return left.with_permuted_rows(self)
 
-    cpdef MonoidElement _mul_(left, MonoidElement _right):
+    cpdef _mul_(left, MonoidElement _right):
         """
         EXAMPLES::
 

src/sage/groups/semimonomial_transformations/semimonomial_transformation.pyx

@@ -171,7 +171,7 @@ cdef class SemimonomialTransformation(MultiplicativeGroupElement):
         """
         return hash(self.v) + hash(self.perm) + hash(self.get_autom())
 
-    cpdef MonoidElement _mul_(left, MonoidElement _right):
+    cpdef _mul_(left, MonoidElement _right):
         r"""
         Multiplication of elements.
         

src/sage/libs/gap/element.pxd

@@ -42,10 +42,6 @@ cdef class GapElement(RingElement):
 
     cdef _initialize(self, parent, libGAP_Obj obj)
     cpdef _type_number(self)
-    cpdef ModuleElement _add_(self, ModuleElement right)
-    cpdef ModuleElement _sub_(self, ModuleElement right)
-    cpdef RingElement _mul_(self, RingElement right)
-    cpdef RingElement _div_(self, RingElement right)
     cpdef is_bool(self)
 
 

src/sage/libs/gap/element.pyx

@@ -690,7 +690,7 @@ cdef class GapElement(RingElement):
             libgap_exit()
         return result
 
-    cpdef ModuleElement _add_(self, ModuleElement right):
+    cpdef _add_(self, ModuleElement right):
         r"""
         Add two GapElement objects.
 
@@ -723,7 +723,7 @@ cdef class GapElement(RingElement):
         return make_any_gap_element(self.parent(), result)
 
 
-    cpdef ModuleElement _sub_(self, ModuleElement right):
+    cpdef _sub_(self, ModuleElement right):
         r"""
         Subtract two GapElement objects.
 
@@ -756,7 +756,7 @@ cdef class GapElement(RingElement):
         return make_any_gap_element(self.parent(), result)
 
 
-    cpdef RingElement _mul_(self, RingElement right):
+    cpdef _mul_(self, RingElement right):
         r"""
         Multiply two GapElement objects.
 
@@ -789,7 +789,7 @@ cdef class GapElement(RingElement):
         return make_any_gap_element(self.parent(), result)
 
 
-    cpdef RingElement _div_(self, RingElement right):
+    cpdef _div_(self, RingElement right):
         r"""
         Divide two GapElement objects.
 

src/sage/libs/pari/gen.pyx

@@ -240,19 +240,19 @@ cdef class gen(gen_auto):
         s = repr(self)
         return (objtogen, (s,))
 
-    cpdef ModuleElement _add_(self, ModuleElement right):
+    cpdef _add_(self, ModuleElement right):
         sig_on()
         return P.new_gen(gadd(self.g, (<gen>right).g))
 
-    cpdef ModuleElement _sub_(self, ModuleElement right):
+    cpdef _sub_(self, ModuleElement right):
         sig_on()
         return P.new_gen(gsub(self.g, (<gen> right).g))
 
-    cpdef RingElement _mul_(self, RingElement right):
+    cpdef _mul_(self, RingElement right):
         sig_on()
         return P.new_gen(gmul(self.g, (<gen>right).g))
 
-    cpdef RingElement _div_(self, RingElement right):
+    cpdef _div_(self, RingElement right):
         sig_on()
         return P.new_gen(gdiv(self.g, (<gen>right).g))
 

src/sage/matrix/matrix0.pyx

@@ -4592,7 +4592,7 @@ cdef class Matrix(sage.structure.element.Matrix):
     ###################################################
     # Arithmetic
     ###################################################
-    cdef Vector _vector_times_matrix_(self, Vector v):
+    cdef _vector_times_matrix_(self, Vector v):
         """
         Returns the vector times matrix product.
 
@@ -4650,7 +4650,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         return sum([v[i] * self.row(i, from_list=True)
                     for i in xrange(self._nrows)], M(0))
 
-    cdef Vector _matrix_times_vector_(self, Vector v):
+    cdef _matrix_times_vector_(self, Vector v):
         """
         EXAMPLES::
 
@@ -4760,7 +4760,7 @@ cdef class Matrix(sage.structure.element.Matrix):
             MS = self.matrix_space(n, m)
             return MS(X).transpose()
 
-    cpdef ModuleElement _add_(self, ModuleElement _right):
+    cpdef _add_(self, ModuleElement _right):
         """
         Add two matrices with the same parent.
 
@@ -4783,7 +4783,7 @@ cdef class Matrix(sage.structure.element.Matrix):
                 A.set_unsafe(i,j,self.get_unsafe(i,j)._add_(right.get_unsafe(i,j)))
         return A
 
-    cpdef ModuleElement _sub_(self, ModuleElement _right):
+    cpdef _sub_(self, ModuleElement _right):
         """
         Subtract two matrices with the same parent.
 
@@ -4849,7 +4849,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         return self.change_ring(self._base_ring.quotient_ring(p))
 
 
-    cpdef ModuleElement _rmul_(self, RingElement left):
+    cpdef _rmul_(self, RingElement left):
         """
         EXAMPLES::
 
@@ -4886,7 +4886,7 @@ cdef class Matrix(sage.structure.element.Matrix):
                 ans.set_unsafe(r, c, x * self.get_unsafe(r, c))
         return ans
 
-    cpdef ModuleElement _lmul_(self, RingElement right):
+    cpdef _lmul_(self, RingElement right):
         """
         EXAMPLES:
 

src/sage/matrix/matrix_cyclo_dense.pyx

@@ -469,7 +469,7 @@ cdef class Matrix_cyclo_dense(matrix_dense.Matrix_dense):
     #   * _dict -- sparse dictionary of underlying elements (need not be a copy)
     ########################################################################
 
-    cpdef ModuleElement _add_(self, ModuleElement right):
+    cpdef _add_(self, ModuleElement right):
         """
         Return the sum of two dense cyclotomic matrices.
 
@@ -497,7 +497,7 @@ cdef class Matrix_cyclo_dense(matrix_dense.Matrix_dense):
         A._matrix = self._matrix + (<Matrix_cyclo_dense>right)._matrix
         return A
 
-    cpdef ModuleElement _sub_(self, ModuleElement right):
+    cpdef _sub_(self, ModuleElement right):
         """
         Return the difference of two dense cyclotomic matrices.
 
@@ -524,7 +524,7 @@ cdef class Matrix_cyclo_dense(matrix_dense.Matrix_dense):
         A._matrix = self._matrix - (<Matrix_cyclo_dense>right)._matrix
         return A
 
-    cpdef ModuleElement _lmul_(self, RingElement right):
+    cpdef _lmul_(self, RingElement right):
         """
         Multiply a dense cyclotomic matrix by a scalar.
 
@@ -566,7 +566,7 @@ cdef class Matrix_cyclo_dense(matrix_dense.Matrix_dense):
             A._matrix = T * self._matrix
         return A
 
-    cdef baseMatrix _matrix_times_matrix_(self, baseMatrix right):
+    cdef _matrix_times_matrix_(self, baseMatrix right):
         """
         Return the product of two cyclotomic dense matrices.