Ondrej,

Thanks for the detailed explanation. I get the significance of an AST now.
I will continue with what I am doing now as you mentioned. I will see if I 
can make the switch once you send that PR.
If not possible now, then I will definitely work on switching to it later.
I also plan on writing extensive test cases.

Regarding my status:
I will soon be done with the mathematical entities. I will start with the 
symbolic dynamics parts right after that.
 
There were some issues I faced :

1. Some output results differ between Autolev and SymPy.
For example: 

e = 4*x**2 + 7*x*y + 21*x + 4*y**2 + 21*y
factor(e, x) in Autolev
e.factor(x) in SymPy

outputs:

21*y + 4*y^2 + 4*x*(5.25 + x +1.75*y) 
in Autolev
and

(7*y + 21)*x + 4*x**2 + 4*y**2 + 21*y
in SymPy

Do differences like these matter? Is there a way to get the same result in 
this case?
Should we try to get the exact same outputs in cases like these?
I am in the mindset that end numerical results are more important than 
equivalence of intermediate expressions.

2. One major issue I was facing was with dynamicsymbols.
The thing is I need to define all the Autolev variables as dynamicsymbols 
and constants as symbols.
I need to do this because Autolev simply uses Variables and Constants for 
everything and I need the variables to be defined as
dynamicsymbols for them to work with the physical entities.
Although the dynamicsymbols would work like they should with the physics 
entities, that doesn't seem to be the case with the 
mathematical entities of SymPy as they do not seem to be written with 
dynamicsymbols in mind.

In particular, I have found that dynamicsymbols do not work with dsolve, 
solveset.nonlinsolve and series expansions.

See this issue:
https://github.com/sympy/sympy/issues/12044

I will have to use these when I tackle the solvers after I am done with 
parsing the basic physics entities.
It would be great if someone could look into this.

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