Trac #15947: Weaken types for _rmul_ and _lmul_

As a step towards removing the old parent with gens and using
categories, we need to have `_rmul_` and `_lmul_` take any `Element`,
not just `RingElement`.

URL: https://trac.sagemath.org/15947
Reported by: tscrim
Ticket author(s): Jeroen Demeyer
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/algebras/letterplace/free_algebra_element_letterplace.pxd

@@ -7,12 +7,9 @@
 #
 ###############################################################################
 
-cdef class FreeAlgebraElement_letterplace
-
-from sage.structure.element cimport AlgebraElement, ModuleElement, RingElement, Element
+from sage.structure.element cimport AlgebraElement, ModuleElement, Element
 from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomialRing_libsingular, MPolynomial_libsingular
 from sage.algebras.letterplace.free_algebra_letterplace cimport FreeAlgebra_letterplace
 
 cdef class FreeAlgebraElement_letterplace(AlgebraElement):
     cdef MPolynomial_libsingular _poly
-

src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx

@@ -555,7 +555,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         right._poly = A._current_ring(right._poly)
         return FreeAlgebraElement_letterplace(self._parent,self._poly-right._poly,check=False)
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         Multiplication from the right with an element of the base ring.
 
@@ -569,7 +569,7 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
         """
         return FreeAlgebraElement_letterplace(self._parent,self._poly._lmul_(right),check=False)
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         Multiplication from the left with an element of the base ring.
 

src/sage/algebras/quatalg/quaternion_algebra_element.pyx

@@ -524,7 +524,7 @@ cdef class QuaternionAlgebraElement_abstract(AlgebraElement):
         """
         return ~self.reduced_norm() * self.conjugate()
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         Return left*self, where left is in the base ring.
 
@@ -538,7 +538,7 @@ 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 _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         Return self*right, where right is in the base ring.
 

src/sage/interfaces/gap.py

@@ -185,6 +185,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.docs.instancedoc import instancedoc
 from sage.interfaces.tab_completion import ExtraTabCompletion
+from sage.structure.element import ModuleElement
 import re
 import os
 import pexpect
@@ -963,8 +964,10 @@ def get_record_element(self, record, name):
         return self('%s.%s' % (record.name(), name))
 
 
+# We need to inherit from ModuleElement to support
+# sage.structure.coerce_actions.ModuleAction
 @instancedoc
-class GapElement_generic(ExtraTabCompletion, ExpectElement):
+class GapElement_generic(ModuleElement, ExtraTabCompletion, ExpectElement):
     r"""
     Generic interface to the GAP3/GAP4 interpreters.
 

src/sage/matrix/matrix0.pyx

@@ -4830,8 +4830,7 @@ cdef class Matrix(sage.structure.element.Matrix):
         """
         return self.change_ring(self._base_ring.quotient_ring(p))
 
-
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         EXAMPLES::
 
@@ -4868,7 +4867,7 @@ cdef class Matrix(sage.structure.element.Matrix):
                 ans.set_unsafe(r, c, x * self.get_unsafe(r, c))
         return ans
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES:
 

src/sage/matrix/matrix_cyclo_dense.pyx

@@ -561,7 +561,7 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
         A._matrix = self._matrix - (<Matrix_cyclo_dense>right)._matrix
         return A
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         Multiply a dense cyclotomic matrix by a scalar.
 

src/sage/matrix/matrix_gf2e_dense.pyx

@@ -633,7 +633,7 @@ cdef class Matrix_gf2e_dense(matrix_dense.Matrix_dense):
         sig_off()
         return ans
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         Return ``a*B`` for ``a`` an element of the base field.
 

src/sage/matrix/matrix_gfpn_dense.pyx

@@ -1113,7 +1113,7 @@ cdef class Matrix_gfpn_dense(Matrix_dense):
             raise ValueError("The matrix must not be empty")
         return self._lmul_(self._base_ring(-1))
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES::
 

src/sage/matrix/matrix_integer_dense.pyx

@@ -871,8 +871,7 @@ cdef class Matrix_integer_dense(Matrix_dense):
         sig_off()
         return M
 
-
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES::
 

src/sage/matrix/matrix_integer_sparse.pyx

@@ -186,7 +186,7 @@ cdef class Matrix_integer_sparse(Matrix_sparse):
     # def _multiply_classical(left, matrix.Matrix _right):
     # def _list(self):
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES::
 

src/sage/matrix/matrix_modn_dense_template.pxi

@@ -850,7 +850,7 @@ cdef class Matrix_modn_dense_template(Matrix_dense):
         sig_off()
         return M
 
-    cpdef _lmul_(self, RingElement left):
+    cpdef _lmul_(self, Element left):
         """
         EXAMPLES::
 

src/sage/matrix/matrix_rational_dense.pyx

@@ -422,7 +422,7 @@ cdef class Matrix_rational_dense(Matrix_dense):
     #   * _dict -- sparse dictionary of underlying elements (need not be a copy)
     ########################################################################
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES::
 

src/sage/matrix/matrix_rational_sparse.pyx

@@ -331,7 +331,7 @@ cdef class Matrix_rational_sparse(Matrix_sparse):
     # def _list(self):
 
 # TODO
-##     cpdef _lmul_(self, RingElement right):
+##     cpdef _lmul_(self, Element right):
 ##         """
 ##         EXAMPLES:
 ##             sage: a = matrix(QQ,2,range(6))

src/sage/matrix/matrix_sparse.pyx

@@ -295,7 +295,7 @@ cdef class Matrix_sparse(matrix.Matrix):
 
         return left.new_matrix(left._nrows, right._ncols, entries=e, coerce=False, copy=False)
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         Left scalar multiplication. Internal usage only.
 

src/sage/modular/pollack_stevens/dist.pyx

@@ -996,7 +996,7 @@ cdef class Dist_vector(Dist):
         """
         return self._addsub(<Dist_vector>_right, True)
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         r"""
         Scalar product of a distribution with a ring element that coerces into the base ring.
 

src/sage/modules/free_module_element.pyx

@@ -4158,7 +4158,7 @@ cdef class FreeModuleElement_generic_dense(FreeModuleElement):
         v = [(<RingElement> a[i])._sub_(<RingElement> b[i]) for i in range(left._degree)]
         return left._new_c(v)
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         EXAMPLES::
 
@@ -4172,7 +4172,7 @@ cdef class FreeModuleElement_generic_dense(FreeModuleElement):
             v = [left * x for x in self._entries]
         return self._new_c(v)
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES::
 
@@ -4608,7 +4608,7 @@ cdef class FreeModuleElement_generic_sparse(FreeModuleElement):
                 v[i] = -a
         return left._new_c(v)
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES::
 
@@ -4624,7 +4624,7 @@ cdef class FreeModuleElement_generic_sparse(FreeModuleElement):
                     v[i] = prod
         return self._new_c(v)
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         EXAMPLES::
 

src/sage/modules/vector_double_dense.pyx

@@ -359,7 +359,7 @@ cdef class Vector_double_dense(FreeModuleElement):
 
         return self._new(_left._vector_numpy * _right._vector_numpy)
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         Multiply a scalar and vector
 
@@ -375,8 +375,7 @@ cdef class Vector_double_dense(FreeModuleElement):
 
         return self._new(self._python_dtype(left)*self._vector_numpy)
 
-
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         Multiply a scalar and vector
 

src/sage/modules/vector_integer_dense.pyx

@@ -282,7 +282,7 @@ cdef class Vector_integer_dense(free_module_element.FreeModuleElement):
             mpz_mul(z._entries[i], self._entries[i], r._entries[i])
         return z
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         cdef Vector_integer_dense z
         cdef Integer a
         a = left
@@ -292,7 +292,7 @@ cdef class Vector_integer_dense(free_module_element.FreeModuleElement):
             mpz_mul(z._entries[i], self._entries[i], a.value)
         return z
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         cdef Vector_integer_dense z
         cdef Integer a
         a = right

src/sage/modules/vector_mod2_dense.pyx

@@ -404,7 +404,7 @@ cdef class Vector_mod2_dense(free_module_element.FreeModuleElement):
             z._entries.rows[0][i] = (self._entries.rows[0][i] & r._entries.rows[0][i])
         return z
 
-    cpdef _lmul_(self, RingElement left):
+    cpdef _lmul_(self, Element left):
         """
         EXAMPLES::
 

src/sage/modules/vector_modn_dense.pyx

@@ -308,7 +308,7 @@ cdef class Vector_modn_dense(free_module_element.FreeModuleElement):
             z._entries[i] = (self._entries[i] * r._entries[i]) % self._p
         return z
 
-    cpdef _lmul_(self, RingElement left):
+    cpdef _lmul_(self, Element left):
         cdef Vector_modn_dense z
 
         cdef mod_int a = ivalue(left)

src/sage/modules/vector_rational_dense.pyx

@@ -317,7 +317,7 @@ cdef class Vector_rational_dense(free_module_element.FreeModuleElement):
             mpq_mul(z._entries[i], self._entries[i], r._entries[i])
         return z
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         cdef Vector_rational_dense z
         cdef Rational a
         if isinstance(left, Rational):
@@ -334,8 +334,7 @@ cdef class Vector_rational_dense(free_module_element.FreeModuleElement):
             mpq_mul(z._entries[i], self._entries[i], a.value)
         return z
 
-
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         cdef Vector_rational_dense z
         cdef Rational a
         if isinstance(right, Rational):

src/sage/modules/with_basis/indexed_element.pxd

@@ -7,6 +7,6 @@ cdef class IndexedFreeModuleElement(Element):
 
     cpdef dict monomial_coefficients(self, bint copy=*)
     cpdef _coefficient_fast(self, m)
-    cpdef _lmul_(self, RingElement right)
-    cpdef _rmul_(self, RingElement left)
+    cpdef _lmul_(self, Element right)
+    cpdef _rmul_(self, Element left)
 

src/sage/modules/with_basis/indexed_element.pyx

@@ -816,7 +816,7 @@ cdef class IndexedFreeModuleElement(Element):
                           scal(scalar, self._monomial_coefficients,
                                factor_on_left=not self_on_left))
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         For backward compatibility.
 
@@ -828,7 +828,7 @@ cdef class IndexedFreeModuleElement(Element):
         """
         return self._acted_upon_(right, True)
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         For backward compatibility.
 

src/sage/numerical/linear_functions.pyx

@@ -957,7 +957,7 @@ cdef class LinearFunction(LinearFunctionOrConstraint):
         P = self.parent()
         return P(e)
 
-    cpdef _lmul_(self, RingElement b):
+    cpdef _lmul_(self, Element b):
         r"""
         Multiplication by scalars
 

src/sage/numerical/linear_tensor_element.pyx

@@ -22,7 +22,7 @@ Here is an example of a linear function tensored with a vector space::
 from cpython.object cimport *
 
 from sage.misc.fast_methods cimport hash_by_id
-from sage.structure.element cimport ModuleElement, RingElement
+from sage.structure.element cimport ModuleElement, Element
 from sage.numerical.linear_functions cimport LinearFunction, is_LinearFunction
 
 
@@ -331,7 +331,7 @@ cdef class LinearTensor(ModuleElement):
             result[key] = self._f.get(key, 0) - coeff
         return self.parent()(result)
 
-    cpdef _lmul_(self, RingElement b):
+    cpdef _lmul_(self, Element b):
         r"""
         Return multiplication by scalar.
 

src/sage/quivers/algebra_elements.pyx

@@ -1203,7 +1203,7 @@ cdef class PathAlgebraElement(RingElement):
 
 ## (scalar) multiplication
 
-    cpdef _lmul_(self, RingElement right):
+    cpdef _lmul_(self, Element right):
         """
         EXAMPLES::
 
@@ -1234,7 +1234,7 @@ cdef class PathAlgebraElement(RingElement):
             return self._new_(outnxt)
         return self._new_(out)
 
-    cpdef _rmul_(self, RingElement left):
+    cpdef _rmul_(self, Element left):
         """
         EXAMPLES::
 

src/sage/rings/laurent_series_ring_element.pyx

@@ -737,10 +737,10 @@ cdef class LaurentSeries(AlgebraElement):
                           self.__u * right.__u,
                           self.__n + right.__n)
 
-    cpdef _rmul_(self, RingElement c):
+    cpdef _rmul_(self, Element c):
         return type(self)(self._parent, self.__u._rmul_(c), self.__n)
 
-    cpdef _lmul_(self, RingElement c):
+    cpdef _lmul_(self, Element c):
         return type(self)(self._parent, self.__u._lmul_(c), self.__n)
 
     def __pow__(_self, r, dummy):