symbolic function args prevent forced conversion of result to numeric

[rwst]

It is generally preferred that the returned result type matches the argument type when calling a builtin function. For example this is as expected:

sage: factorial(8).parent()
Integer Ring
sage: factorial(SR(8)).parent()
Symbolic Ring
sage: exp(0).parent()
Integer Ring
sage: exp(SR(0)).parent()
Symbolic Ring

but this is not:

from sage.symbolic.function import BuiltinFunction

class TestFunction(BuiltinFunction):
    def __init__(self):
        BuiltinFunction.__init__(self, "testfun", nargs=2)
    def _eval_(self, n, x, *args, **kwds):
        print (parent(n), parent(x))
        return SR(5)

sage: TestFunction()(SR(1),GF(2)(1))
(Integer Ring, Finite Field of size 2)
5
sage: type(_)
<type 'int'>

An explanation could be that factorial and exp derive from GinacFunction.

CC: @jdemeyer

Component: symbolics

Author: Ralf Stephan

Branch/Commit: adc230d

Reviewer: Marc Mezzarobba

Issue created by migration from https://trac.sagemath.org/ticket/17953

[rwst]

Description changed:

--- 
+++ 
@@ -13,8 +13,19 @@
 but this is not:
 
 ```
-sage: lambert_w(SR(0)).parent()
-Integer Ring
+from sage.symbolic.function import BuiltinFunction
+
+class TestFunction(BuiltinFunction):
+    def __init__(self):
+        BuiltinFunction.__init__(self, "testfun", nargs=2)
+    def _eval_(self, n, x, *args, **kwds):
+        print (parent(n), parent(x))
+        return SR(5)
+
+sage: TestFunction()(SR(1),GF(2)(1))
+(Integer Ring, Finite Field of size 2)
+5
+sage: type(_)
+<type 'int'>
 ```
-
-This ticket serves as a catch-all for such unexpected types.
+An explanation could be that `factorial` and `exp` derive from `GinacFunction`.

[rwst]

Branch: u/rws/inconsistency_in_returned_type_of_builtinfunction_result

[rwst]

New commits:

f0fe6f4

17953: any symbolic function arg prevents forced result conversion to numeric

[rwst]

Commit: f0fe6f4

[rwst]

Author: Ralf Stephan

[videlec]

comment:5

Hello,

First of all, I think that the content of the branch is ok (I am running the test right now).

But I found the following behavior weird

sage: exp(0).parent()
Integer ring

In my opinion, a function should have a well defined domain and range. In some cases, the function preserves some subset. Like the function x -> x^2 defined in the complex numbers preserves integers, rationals and algebraic. But considering that {0} is a subset of the real numbers on which exp preserve the integers is going too far.

Vincent

[videlec]

comment:6

sage -t --long src/sage/functions/log.py
**********************************************************************
File "src/sage/functions/log.py", line 628, in sage.functions.log.Function_lambert_w._eval_
Failed example:
    parent(lambert_w(e))
Expected:
    Integer Ring
Got:
    Symbolic Ring
**********************************************************************