BuiltinFunction overriding GiNaC function

[rwst]

The attempt to create a symbolic function that prints with a name that is also used by a reserved GiNaC function results in unexpected behaviour when evaluating. The following should output x^2 but completely bypasses AFunction.eval:

sage: from sage.symbolic.function import BuiltinFunction
sage: class AFunction(BuiltinFunction):
....:       def __init__(self, name, exp=1):
....:           self.exponent=exp
....:           BuiltinFunction.__init__(self, name, nargs=1)
....:       def _eval_(self, arg):
....:               return arg**self.exponent
sage: p2 = AFunction('exp', 2)
sage: p2(x)
e^x

If the name is however e.g. p2 then AFunction.eval gets called as expected. Compare the above with

...
sage: p2 = AFunction('p2', 2)
sage: p2(x)
x^2

This prevents creation of BuiltinFunctions as wrapper for functions reserved by Pynac with the same name like factorial (#17489), and forces every change into Pynac.

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/17547

[rwst]

Description changed:

--- 
+++ 
@@ -10,8 +10,6 @@
 sage: p2 = AFunction('exp', 2)
 sage: p2(x)
 e^x
-sage: _.function()
-() |--> e^x
 ```
 The attempt at creation should give an error (plus respective documentation warnings).
 

[rwst]

comment:2

I came to this from #17489 when I tried to create a symbolic factorial function without usage of GinacFunction, which wreaks havoc when expression conversion to/from e.g. Maxima is involved.

[jdemeyer]

Replying to @rwst:

The attempt at creation should give an error

I don't understand the problem, what's wrong?

[rwst]

Description changed:

--- 
+++ 
@@ -11,6 +11,14 @@
 sage: p2(x)
 e^x
 ```
+If the name is e.g. `p2` `AFunction.eval` gets called, but not with name equal to a function provided with GiNaC. Compare the above with
+
+```
+...
+sage: p2 = AFunction('p2', 2)
+sage: p2(x)
+x^2
+```
 The attempt at creation should give an error (plus respective documentation warnings).
 
 Alternatively, search first for user-defined function names, then GiNaC core, to allow overriding.

[rwst]

comment:4

If the name is e.g. p2 AFunction.eval gets called, but not with name equal to a function provided with GiNaC. Compare the above with

...
sage: p2 = AFunction('p2', 2)
sage: p2(x)
x^2

[rwst]

Description changed:

--- 
+++ 
@@ -1,3 +1,4 @@
+The attempt to create a symbolic function that prints with a name that is also used by a reserved GiNaC function results in unexpected behaviour when evaluating. The following should output `x^2` but completely bypasses `AFunction.eval`:
 
 ```
 sage: from sage.symbolic.function import BuiltinFunction
@@ -11,7 +12,7 @@
 sage: p2(x)
 e^x
 ```
-If the name is e.g. `p2` `AFunction.eval` gets called, but not with name equal to a function provided with GiNaC. Compare the above with
+If the name is however e.g. `p2` then `AFunction.eval` gets called as expected. Compare the above with
 
 ```
 ...
@@ -19,6 +20,4 @@
 sage: p2(x)
 x^2
 ```
-The attempt at creation should give an error (plus respective documentation warnings).
-
-Alternatively, search first for user-defined function names, then GiNaC core, to allow overriding.
+This prevents creation of `BuiltinFunction`s as wrapper for functions reserved by Pynac with the same name like `factorial` (#17489), and forces every change into Pynac.