How do I acces the name of a symbolic function in sage?

Question

Well, the question is pretty simple. I have a symbolic function like

var('U I')
Z = U / I

and now I want to create a dictionary, where the name of the function (as a string), here Z, maps to the corresponding function. It's simple to do by hand

{ 'Z' : Z }

but I want it to be created automatically. Using str(Z) returns U/I, so this isn't helpful. I went through some documentation, but did not find any method that returns the name of a function as string. So how do I do it? Thanks in advance for answers.

Answer 1

The problem here is that you have not created a function at all. You have created a Python variable, which refers to U/I, which is a "symbolic expression", and as such (for better or worse) is just itself. See e.g. this SO question which I think is relevant. This is also true for things like Z(U/I)=U/I and friends.

You could do

sage: def z(U,I):
....:     return U/I
....: 
sage: z
<function __main__.z>
sage: z.func_name
'z'

but that is a Python function and doesn't have the methods of a Sage function.

The following seems to work, but has a mysterious error I don't have time to track down right now, presumably because something in the hash method wants the code from a Python function, which isn't what we have here for Z.

sage: Z(U,I) = U/I
sage: z = function("z", nargs=2, eval_func=Z)
Exception AttributeError: AttributeError('sage.symbolic.expression.Expression' object has no attribute '__code__',) in 'sage.symbolic.function.SymbolicFunction._hash_' ignored
sage: z(2,3)
2/3
sage: z.name
<function name>
sage: z.name()
'z'