Simplify and generalize `differentiate`

[greimel]

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I have rewritten differentiate. First, I've split up the functions. Second, I've removed the @generated. Third, I've added a three state version. I think it would be quite easy to make it one function for arbitrary dimensional state spaces.

I changed the bound for the julia version, because I am using the (; a) == (a = a, ) syntax.

Correctness

• Tests pass locally
• Since you don't have any tests that check numbers (do you?), I kept the old functions and left the code I used to test the equivalence of the functions
• I left some comments in the cross_difference function, where I believe the wrong Delta is used at the boundaries. I've left it consistent with the current implementation

To do

• I've not yet tried to 3-d code
• I will add an example to the examples folder

[matthieugomez]

Hey! I need to look at this more closely. That being said, i would really like to avoid adding two new dependences.

[greimel]

Sure! I'll leave them for more convenient developing until you are happy with the rest.

[matthieugomez]

Okay, I am back from holidays. Before I look into it,

• I think it would be useful to remove the two new dependences, so that I can look at the final version directly.
• Did you check benchmarks? I do not care that much about the first run, i.e. compile time, but I do care about the second run.

Let me know when you want me to look into it (by de-drafting your PR).

[matthieugomez]

For your cross_difference function, you may be right. Could you explain a bit more what you want to change (and why)?

[azev77]

@greimel has there been any progress on this?