In numpy 2.0, -1 as uint8 is out of bounds, whereas
previously it would be converted to 255.

This affected the test helper function `reduced_bitwise_and`.
The helper function was changed to use 255 instead of -1 if
the dtype was uint8, since this is what is needed to match the
behavior of the "bitwise and" op.

`reduced_bitwise_and` was only used by `TestCAReduce`
in `tests/tensor/test_elemwise.py`, so it was moved
there from `tests/tensor/test_math.py`

`np.MAXDIMS` was removed from the public API and
no replacement is given in the migration docs.

In numpy <= 1.26, the value of `np.MAXDIMS` was 32.
This was often used as a flag to mean `axis=None`.

In numpy >= 2.0, the maximum number of dims of an
array has been increased to 64; simultaneously, a
constant `NPY_RAVEL_AXIS` was added to the C-API to
indicate that `axis=None`.

In most cases, the use of `np.MAXDIMS` to
check for `axis=None` can be replaced by the
new constant `NPY_RAVEL_AXIS`.

To make this constant accessible when using numpy <= 1.26,
I added a function to insert `npy_2_compat.h` into the support
code for the affected ops.

numpy.random.Generator.__getstate__()
now returns none; to see the state of
the bit generator, you need to use
Generator.bit_generator.state.

This change affects `RandomGeneratorType`, and
several of the random tests (including some for Jax.)

This was done for the python linker and numba linker.

deepcopy seems to be the recommended method for
copying a numpy Generator.

After this numpy PR:
https://github.com/numpy/numpy/pull/26293/commits/44ba7ca07984557f2006f9a6916adb8e3ecfca61
`copy` didn't seem to actually make an independent copy of
the `np.random.Generator` objects spawned by `RandomStream`.

This was causing the "test values" computed by e.g.
`RandomStream.uniform` to increment the RNG state, which
was causing tests that rely on `RandomStream` to fail.

Here is some related discussion:
https://github.com/numpy/numpy/issues/24086

I didn't see any official documentation about
a change in numpy that would make copy stop
working.

MapIter was removed from the public numpy C-API in
version 2.0, so we raise a not implemented error to
default to the python code for the AdvancedInSubtensor1.

The python version, defined in `AdvancedInSubtensor1.perform`
calls `np.add.at`, which uses `MapIter` behind the scenes.
There is active development on Numpy to improve the efficiency
of `np.add.at`.

To skip the C implementation and use the Python implementation,
we raise a NotImplementedError for this op's c code if numpy>=2.0.

This is done using C++ generic functions
to get/set the real/imag parts of complex numbers.

This gives us an easy way to support Numpy v < 2.0,
and allows the type underlying the bit width types,
like pytensor_complex128, to be correctly inferred
from the numpy complex types they inherit from.

Updated pytensor_complex struct to use get/set real/imag
aliases defined above. Also updated operators such as
`Abs` to use get_real, get_imag.

Macros have been added to ensure compatibility with numpy < 2.0

Note: redefining the complex arithmetic here means that we
aren't treating NaNs and infinities as carefully as the C99
standard suggets (see Appendix G of the standard).

The code has been like this since it was added to Theano,
so we're keeping the existing behavior.

Anything `Hashable` should work, but I've made the
return type `tuple[Hashable]` to keep with the current style.

This means, e.g., we can use strings in the cache version.

- replace `->elsize` by `PyArray_ITEMSIZE`
- don't use deprecated PyArray_MoveInto

Some macros were removed from npy_3k_compat.h.
Following numpy, I updated the affected functions
to the Python 3 names, and removed support for Python 2.

Also updated lazylinker_c version to indicate substantial changes to the
C code.

- Replace np.cast with np.asarray: in numpy 2.0,
  `np.cast[new_dtype](arr)` is deprecated.
  The literal replacement is `np.asarray(arr, dtype=new_dtype)`.

- Replace np.sctype2char and np.obj2sctype.
  Added try/except to handle change in behavior
  of `np.dtype`

- Replace np.find_common_type with np.result_type

Further changes to `TensorType`:

TensorType.dtype must be a string, so the code
has been changed from `self.dtype = np.dtype(dtype).type`,
where the right-hand side is of type `np.generic`, to
`self.dtype = str(np.dtype(dtype))`, where the right-hand
side is a string that satisfies:

`self.dtype == str(np.dtype(self.dtype))`

This doesn't change the behavior of `np.array(..., dtype=self.dtype)`
etc.

- replaced np.AxisError with np.exceptions.AxisError
- the `numpy.core` submodule has been renamed to `numpy._core`
- some parts of `numpy.core` have been moved to `numpy.lib.array_utils`

Except for `AxisError`, the updated imports are conditional on
the version of numpy, so the imports should work for numpy >= 1.26.

The conditional imports have been added to `npy_2_compat.py`, so the
imports elsewhere are unconditonal.

Also fixes bug in Scan L_op and Max R_op
Co-authored-by: Adrian Seyboldt <aseyboldt@users.noreply.github.com>

Also remove bad default values

Bumps [pypa/gh-action-pypi-publish](https://github.com/pypa/gh-action-pypi-publish) from 1.12.2 to 1.12.4.
- [Release notes](https://github.com/pypa/gh-action-pypi-publish/releases)
- [Commits](https://github.com/pypa/gh-action-pypi-publish/compare/v1.12.2...v1.12.4)

---
updated-dependencies:
- dependency-name: pypa/gh-action-pypi-publish
  dependency-type: direct:production
  update-type: version-update:semver-patch
...
Signed-off-by: dependabot[bot] <support@github.com>

Also cleans up implementation and documentation

* Split and inverse

* PyTorch inline constants in dispatch to avoid graph breaks

Deprecate obscure ndim kwarg

A shortcut in the numpy implementation of einsum_path when there's nothing to optimize, creates a default path that can combine more than 2 operands. Our implementation only works with 2 or 1 operand operations at each step.

https://github.com/numpy/numpy/blob/cc5851e654bfd82a23f2758be4bd224be84fc1c3/numpy/_core/einsumfunc.py#L945-L951

Nothing clever was going on, unknown dims were simply faked as having length 8 for JAX polymorphism export