symbolic function args prevent forced conversion of result to numeric

[rws]

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.

[rws]

New commits:

​f0fe6f4

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

[vdelecroix]

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

[vdelecroix]

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
**********************************************************************

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​8cca1a2	Merge branch 'develop' into t/17953/inconsistency_in_returned_type_of_builtinfunction_result
​adc230d	17953: fix doctest

[vdelecroix]

Simpler way of doing

symbolic_input = any(parent_c(arg) is SR for arg in args)

[rws]

Replying to vdelecroix:

Simpler way of doing

symbolic_input = any(parent_c(arg) is SR for arg in args)

True. Not worth a commit however.

[mmezzarobba]

Replying to vdelecroix:

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.

I tend to agree, but the present ticket is a step in the right direction in any case: it fixes some of the issues without making it harder to improve things later on.