`get_variables` drops metadata for callables

[SebastianM-C]

It looks like there are some cases in which get_variables drops variable metadata, leading to the variables that are return to not be isequal to the original ones. This seems to be the case for callables, which are currently generated by the @mtkmodel macro as pointed out in #1364 (comment).

MWE

using Symbolics

@variables t x(..)
x = x(t)

Symbolics.get_variables(x + 1)
# 2-element Vector{SymbolicUtils.BasicSymbolic}:
# x
# t

isequal(Symbolics.get_variables(x + 1)[1], Symbolics.value(x)) # false

Symbolics.metadata(Symbolics.value(x))
# Base.ImmutableDict{DataType, Any} with 2 entries:
#   CallWithParent => x⋆
#   VariableSource => (:variables, :x)

Symbolics.metadata(Symbolics.get_variables(x + 1)[1]) # nothing

While SciML/ModelingToolkit.jl#3217 could help avoid the issue for @mtkmodel based systems, I would expect the metadata to still be there.

[ChrisRackauckas]

@AayushSabharwal might this be related to one of your changes?

[AayushSabharwal]

Yeah so #1361 made get_variables search inside x(t) IF x is declared as @variables x(..). Previously, get_variables would return x(t) and now it returns x(..) and t. The problem is that when x(..) is called, the metadata is attached to the called object x(t) and not to the function x(..). The consensus from #1364 was that get_variables should be reverted and the MTK functions should get a kwarg for the search function to use. I'll make this change

[AayushSabharwal]

This can be closed via SciML/ModelingToolkit.jl#3217 instead of #1364.