Extract common functionality from `SINDy` to `_BaseSINDy`

[Jacob-Stevens-Haas]

Begin #351

This pull request begins the abstraction of the SINDy class, which handles a lot of methods with special cases, to a variety of classes that reflect fundamental differences between problem formulations. Here, I pull out _BaseSINDy, which contains basic information about the feature library, system dimension, and printing the equations.

Future PRs will make Weak and discrete their own classes, modify feature libraries to be amenable to jax, numpy, and cvxpy arrays, and introduce the Single-Step SINDy class and associated optimizer/problem setup.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 92.66055% with 8 lines in your changes missing coverage. Please review.

Project coverage is 95.26%. Comparing base (ddf8d6d) to head (22329dd). Report is 12 commits behind head on master.

Files with missing lines	Patch %	Lines
pysindy/pysindy.py	91.37%	5 Missing :warning:
pysindy/feature_library/base.py	66.66%	3 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #562 +/- ## ========================================== - Coverage 95.28% 95.26% -0.02% ========================================== Files 38 39 +1 Lines 4069 4099 +30 ========================================== + Hits 3877 3905 +28 - Misses 192 194 +2 ```

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[Jacob-Stevens-Haas]

Hey Alan, I put you as a reviewer in case you want an eye into this process. This is the beginning of what we talked about in the last meeting.

@ahsu98, @malachitewind, I'm going to add you as collaborators so you can review these changes too.

[Jacob-Stevens-Haas]

I'm going to merge it, and turn the last commit into an issue