diff(f,t) should work even with Function objects

[rwst]

sage: t = var('t')
sage: sage: f = function('f')(t)
sage: diff(f,x,x)
0
sage: desolve(diff(f,t) - (f+1)/(t+1), f)
(_C - 1/(t + 1))*(t + 1)

sage: sage: f = function('f')
sage: diff(f,t) 
...
TypeError: unable to convert f to a symbolic expression
sage: diff(sin,t)
...
TypeError: unable to convert f to a symbolic expression

The same error can be had with the simple SR(sin), i.e., any function object in contrast to the resp. function call, which returns an Expression.

Since function objects can be used in other context it seems they should be part of symbolic expressions too. This ticket however will limit itself to giving a better error message in SR.coerce and handling Function objects in calculus/functional.py:derivative().

See also #15025

Component: calculus

Author: Ralf Stephan

Branch/Commit: u/rws/diff_f_t__should_work_even_with_function_objects @ 0cecec3

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/17701

[kcrisman]

comment:1

Possibly related to the shenanigans induced by the distinction at #17447? So maybe user error (though obviously completely understandable given the terrible documentation for this)? Agreed on the uselessness of the error message, though presumably the traceback would help an experienced Sage developer... who is not the likely recipient of an error message on this, unfortunately! More like someone in calculus or ODE. Yuck.

[rwst]

comment:2

Replying to @kcrisman:

Possibly related to the shenanigans induced by the distinction at #17447?

That too but I think either SR(f) or diff(f,t) should work even with NewSymbolicFunction. If not improve the error message.

[rwst]

Description changed:

--- 
+++ 
@@ -6,4 +6,6 @@
 ...
 TypeError: 
 ```
-Don't know yet if it's a bug. At least it's an extremely uninformative error.
+The same error can be had with the simple `SR(sin)`, i.e., any function object in contrast to the resp. function call, which returns an `Expression`.
+
+Since function objects can be used in other context it seems they should be part of symbolic expressions too. This ticket however will limit itself to giving a better error message in `SR.coerce` and handling `Function` objects in `calculus/functional.py:derivative()`.

[rwst]

comment:5

However, having diff(f,t) a shortcut for diff(f(t),t) is less useful because the other instances of f in the argument to desolve would still have to be coerced. And it is impossible to know what is the variable there.

[rwst]

Branch: u/rws/diff_f_t__should_work_even_with_function_objects

[rwst]

Author: Ralf Stephan

[rwst]

New commits:

0cecec3

17701: diff(f,t) should work even with Function objects