Add new tests for Jacobi elliptic function simplification.

[NadiaYvette]

This adds addition theorems, Pythagorean analogues, and derivatives where absent for cos, sin, cosh, sinh, and sn, cn, and dn in a new file in test/ -- Jacobi.hs derived from Sym.hs (mostly a copy with some new primops and rewrite rules).

[alt-romes]

This is great work! Thanks for doing it.
A couple of comments

• If you could squash the commits it'd be great
• A few more identities would be amazing, you've already set all the infrastructure inplace, so it seems worth using it a bit further

[alt-romes]

Looking good (modulo the squashing, no hurries though). How's the situation?
Let me know if you need any help.

[NadiaYvette]

@alt-romes The squash will definitely be done, and maybe I should do one even before passing the tests. There's just a little trouble at the moment getting things to pass the tests. Achieving sum-of-products while collecting powers of variables in monomials is taking some thought to figure out how to deal with by using a cost function.

[alt-romes]

I see, that doesn't sound easy indeed!
OK, good luck, ping me when you're ready, or stuck 😄

[NadiaYvette]

I see, that doesn't sound easy indeed! OK, good luck, ping me when you're ready, or stuck smile

@alt-romes It's probably safe to say that I'm a little stuck. The good news is that the rules seem to be involved enough to get testcases to spin for something like 45s.

[alt-romes]

Great @NadiaYvette! That's good for benchmarking and optimizing the library further.

I would argue that getting a cost function to arrive at a SOP simplification is not all that too important, not for the testsuite at least (it would be different if this were a symbolic maths library -- i'd like to do that some time in the image of Metatheory.jl, but in a separate project).

Is your problem only that the simplification doesn't end up exactly as the one you wrote for the test?

If so, I suggest you look at whatever it actually does rewrite the expressions too, and manually see if they are equivalent to the ones you were expecting, and if they were in fact simplified. If all is good, just write the thing it produces as the expected output -- even if that isn't exactly what you'd expect from a computer algebra system.

[alt-romes]

I've rebased your PR and fixed the build and a TODO @NadiaYvette.
I looked into the second test taking a long time but it never terminates for me. The test seemingly runs forever.
I profiled it but the issue seems to be caused by some exponential rule application.
To debug I guess one would try to see which rules are firing throughout eq-sat. Unfortunately I'm not too familiar with the Jacobi domain here, so it's hard for me to debug.