Remove function call syntax for symbolic expressions

[ppurka]

The function call syntax for symbolic expressions has been deprecated for about 12 years. It is about time it raised some errors. This will prevent people from getting confused because of behavior like this.

See also the threads

• http://groups.google.com/group/sage-devel/t/de97f91d548cc0ec
• http://groups.google.com/group/sage-devel/t/5f2705b2b8d21593/b11079d8299a03b5

Update in 9.4.beta4: The deprecation warning introduced in #5930 was not issued in direct interactive use since Sage 8.4 (despite being doctested):

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.4.beta4, Release Date: 2021-07-01               │
│ Using Python 3.9.5. Type "help()" for help.                        │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable.     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: var('y')
y
sage: a = x+y
sage: a(2, 3)
5
sage: warnings.resetwarnings()
sage: a(2, 3)
/Users/mkoeppe/s/sage/sage-rebasing/worktree-gcc11/local/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3343: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
See http://trac.sagemath.org/5930 for details.
  exec(code_obj, self.user_global_ns, self.user_ns)
5

(fixed in #32139)

Follow-up: #32227 Deprecate methods arguments (alias: args), number_of_arguments, _fast_callable_ for non-callable symbolic expressions

CC: @nthiery @kini @DaveWitteMorris @nbruin @egourgoulhon

Component: symbolics

Author: Punarbasu Purkayastha, Matthias Koeppe

Branch/Commit: 9891a51

Reviewer: Matthias Koeppe, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/14270

[ppurka]

Author: Punarbasu Purkayastha

[ppurka]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 The function call syntax for symbolic expressions has been deprecated for over four years. It is about time it raised some errors. This will prevent people from getting confused because of behavior [like this](http://ask.sagemath.org/question/2357/the-difference-between-fx3-and-f3-of-callable).
+
+Apply [attachment: trac_14270-raise_error_on_function-call.patch](https://github.com/sagemath/sage-prod/files/10657375/trac_14270-raise_error_on_function-call.patch.gz) to devel/sage.

[ppurka]

Work Issues: fix doctests

[ppurka]

Changed work issues from fix doctests to fix combinat/tutorial.py

[ppurka]

comment:3

I am able to fix all the doctests except for the following one in combinat/tutorial.py.

The example which fails seems to make no sense to me. A substitute_function method is being used to substitute a function with a symbolic expression.

sage: C, z = var('C,z');
sage: sys = [ C == z + C*C ]
sage: sol = solve(sys, C, solution_dict=True); sol
[{C: -1/2*sqrt(-4*z + 1) + 1/2}, {C: 1/2*sqrt(-4*z + 1) + 1/2}]
sage: s0 = sol[0][C]; s1 = sol[1][C]

...

sage: C = s0; C
-1/2*sqrt(-4*z + 1) + 1/2

...

sage: equadiff
(4*z - 1)*D[0](C)(z) - 2*C(z) + 1 == 0
sage: Cf = sage.symbolic.function_factory.function('C')
sage: equadiff.substitute_function(Cf, s0)  # Original answer is the deprecation + answer
...
TypeError: %d format: a number is required, not NoneType

Let us try to "fix" this (z is a symbolic variable). Somehow the following works (beats me why it does):

sage: equadiff.substitute_function(Cf(z), s0)
(4*z - 1)*D[0](C)(z) - 2*C(z) + 1 == 0     # OK, so this seems to work

But now the next command in the tutorial gives False instead of True

sage: bool(equadiff.substitute_function(Cf(z), s0))  
False

Why is all this happening? Looking at the documentation of substitute_function shows that it should be used for substituting functions, not anything else

    def substitute_function(self, original, new):
        """
        Returns this symbolic expressions all occurrences of the
        function *original* replaced with the function *new*.

And what exactly are we substituting above?

sage: type(Cf)
sage.symbolic.function_factory.NewSymbolicFunction
sage: type(s0)
sage.symbolic.expression.Expression

We are substituting a symbolic function with a symbolic expression! How was this even working earlier?

What should I do with this portion of the tutorial? Delete this?

[ppurka]

Apply to devel/sage

[kcrisman]

comment:4

Attachment: trac_14270-raise_error_on_function-call.patch.gz

Replying to @ppurka:

I am able to fix all the doctests except for the following one in combinat/tutorial.py.

> What should I do with this portion of the tutorial? Delete this?

I'm cc:ing Nicolas, who should know what is going on here.