Trac #20312: parent of argument lost with Functions

Some Python objects as function arguments lose their parent, i.e. the
code in the specific function can no longer access it because the object
was coerced into SR. This can result in violation of the rule that
function input and output should be of the same type.
{{{
sage: S.<y> = PolynomialRing(RR)
sage: ex = sin(asin(y)); ex
y
sage: type(ex)
<type 'sage.symbolic.expression.Expression'>
sage: ex.is_symbol()
True
}}}
The specific function (here sin) code cannot remedy this because there
the damage is already done. The problem is in
`symbolic/function.pyx:BuiltinFunction.__call__` where the parent of
function arguments is lost.

See also #18832 and maybe #17790.

URL: http://trac.sagemath.org/20312
Reported by: rws
Ticket author(s): Ralf Stephan
Reviewer(s): Volker Braun

src/sage/symbolic/function.pyx

@@ -986,7 +986,7 @@ cdef class BuiltinFunction(Function):
                 if (isinstance(arg_parent, PolynomialRing_commutative)
                     or isinstance(arg_parent, MPolynomialRing_polydict_domain)):
                     try:
-                        return res.polynomial(ring=arg_parent)
+                        return SR(res).polynomial(ring=arg_parent)
                     except TypeError:
                         return res
                 else: