Hi!

I am currently working on a project that uses SymPy to calculate 
large-scale expansions of symbolic objects with non-integer indices (in 
general). We then convert the final expression into a numeric one, with the 
eventual goal of calculating a metric for optimization tasks. 

I would like to understand what happens under the hood when we add two 
indexed symbolic terms together. An example would be something like 
expanding the expression (a[0.0292*I (this is a complex number), 0, 0, 0] 
+  a[0.0292*I, 0, 0, 0])^2. I have read that expressions, such that those 
that are indexed, are stored in a tree-based representation. What does 
SymPy check for when adding, multiplying, etc different symbols?  Would 
there be a resource which would already discuss this? 

An ulterior motivation (and potentially a separate question) would be to 
combine our symbolic expansions with auto-differentiable frameworks like 
JAX. I am aware that there are packages like Sympy2Jax, but they don't seem 
to interface with Indexed expressions in my experience. What challenges 
might there be with adapting Indexed expressions to support this, 
particularly with very large expansions of indexed symbolic terms? 

Thanks! 
Tareq 

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