Fix Expression substitution interface inconsistency

[rwst]

From tomchor on #78

...
>>> a1=var('a_1')
>>> E=x^a1
>>> E(a1=1)

 a₁
x  
>>> E(a_1=1)
x
...
>>> E.subs({a1:1})
x

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/23320

[tscrim]

comment:1

I disagree. I would say this is a misuse and tomchor is backwards on what is a representation and what is a variable. a1 is the representation (i.e., a pointer) in !Python/Sage of the variable a_1 that is used by the symbolic expression. One reason why we should keep things the way they are is

a1 = var('x')
a2 = var('x')
f = (a1 + e^a2)

is a function in x and cannot be evaluated separately by a1 and a2.

[rwst]

comment:2

I agree with your explanation. But note that this ticket is about the inconsistency between

sage: E.subs({a1:1})
x
sage: E(a1=1)
x^a_1

It happens because the dict key is immediately replaced but the kwds dict key in a1=1 is not:

sage: {a1:1}
{a_1: 1}

[tscrim]

comment:3

There is no way around that either because it points to the "correct" variable and because they key of the dict is the variable, not a string. So by the time you are doing the substitution, it is evaluated to 'a_1'. It is the same problem if I called the Python variable x. It comes down to understanding the difference between a python variable and the actual symbolic variable. IMO, this is the correct behavior.

[rwst]

comment:4

You are sure that the entry a1 in the kwds dict that is created with E(a1=1) cannot be replaced with a_1, in order to make the behaviour consistent? I disagree. The dict entry there is a string, and the problem is 'just' to get the object that is pointed to. This knowledge is somewhere in the ipython shell, isn't it?

[tscrim]

comment:5

Replying to @rwst:

You are sure that the entry a1 in the kwds dict that is created with E(a1=1) cannot be replaced with a_1, in order to make the behaviour consistent? I disagree. The dict entry there is a string, and the problem is 'just' to get the object that is pointed to. This knowledge is somewhere in the ipython shell, isn't it?

Yes, I am sure. In the kwds dict, the input is the string 'a1', not the variable a1. We could search the Python namespace for a variable named a1. However, this has a number of shortcomings: the Python a1 could be anything, or worse, someone did a1 = var('x') and then the behavior is extremely unexpected (albeit a slightly contrived of an example). Also, how would you differentiate if someone wanted to use variables a1 and a_1? What about if it is defined as a local variable in a function?

I believe that anytime we have to go find a variable in all Python variables (which is very [relatively] expensive) gives off a very strong code smell. In my mind, the variable is a_1, not the Python pointer a1, and we should not move away from that as it is a huge can of worms.

[rwst]

comment:7

IMHO for this inherent inconsistency the usage of ex.subs(a=b) should be discouraged in favor of ex.subs(a==b).

[embray]

comment:8

Closing tickets in the sage-duplicate/invalid/wontfix module with positive_review (i.e. someone has confirmed they should be closed).