* Add jax dispatch for CholeskySolve

* Better typehints on user-facing `cho_solve`

* Rename test

* Created some tests that fail due to #1476

* Fixes 1476 and other ways to create a log1mexp

* Reimplemented logmexpm1_to_log1mexp by tracking expm1 and then looking through the clients

* Absorbed the rewrite log1pexp_to_softplus into the new rewrite for log1mexp

* Fixed bug where I forgot to check whether result of is_neg was None or not before proceeding

---------
Co-authored-by: Luca Citi <lciti@ieee.org>

* Avoid pytest warning for variable name

* Respect core type shape in gradient of Blockwise

* Refactor Blockwise L_op

Reuse `cholesky` decomposition with `cho_solve` in graphs with multiple `pt.solve` when `assume_a = "pos"` (#1467)

* Extend decomp+solve rewrite machinery to `assume_a="pos"`

* Update rewrite name in test

* Refactor tests to be nicer

* Respect core op `lower` flag when rewriting to ChoSolve

* Expose `pt.optimize`

* Clean up imports in optimize.py

* Add example notebook for `optimize.root`

* Small updates

* Add doc file

* Link to optimize docs in tensor index

* Add docs to user-facing functions.

* Move `scipy.optimize` imports into `perform` methods

* Use global import strategy

* Remove props and overload __str__

* rerun example notebook

* Implement `optimize.minimize`

* Add more tests

* Code cleanup

* Add RootOp, fix gradient tests (they are failing)

* Correct gradients for `minimize`

* Mypy

* remove debug flag

* minimize works

* Implement minimize_scalar

* Use LRU cache wrapper for hessian option

* Remove useless Blockwise

* Feedback

* use truncated_graph_inputs and refactor

* Implement Root Op

* Factor out shared functions

* Implement `root_scalar`

* mypy 😍

* Add specialized `build_fn` to each Op to handle scipy quirks

* Changes to support float32 inputs

* Check inputs to RootOp

* More mypy

* Fix bug when minimize gets scalar input

Changes:
1. Remove references to c-code which apply to `COp` but not `Op`
2. Fix failing doctests
3. Improve explanation of `make_node`
4. Emphasize distinction between itypes/otypes and make-node
5. Show `L_op` instead of `grad`
6. Show how to test `L_op` and `infer_shape` implementation
7. Simplify explanation of `__props__` and illustrate in example.
8. Introduce more complex multi-output Op to drive these details home
9. Remove old references to numba/ random variable Ops

* More robust shape check for `grad` fallback in `jacobian`

* Update scalar test

https://github.com/numpy/numpy/issues/17864