I was getting a NameError from the list
comprehensions saying that e.g. `pytensor_scalar`
was not defined. I'm not sure why, but this is another
(more verbose) way to do the same thing.

1. Changed autocaster due to new promotion rules

With "weak promotion" of python types in Numpy 2.0,
the statement `1.1 == np.asarray(1.1).astype('float32')` is True,
whereas in Numpy 1.26, it was false.

However, in numpy 1.26, `1.1 == np.asarray([1.1]).astype('float32')`
was true, so the scalar behavior and array behavior are the same
in Numpy 2.0, while they were different in numpy 1.26.

Essentially, in Numpy 2.0, if python floats are used in operations
with numpy floats or arrays, then the type of the numpy object will
be used (i.e. the python value will be treated as the type of the numpy
objects).

To preserve the behavior of `NumpyAutocaster` from numpy <= 1.26, I've
added an explicit conversion of the value to be converted to a numpy
type using `np.asarray` during the check that decides what dtype to
cast to.

2. Updates due to new numpy conversion rules for out-of-bounds python
ints

In numpy 2.0, out of bounds python ints will not be automatically
converted, and will raise an `OverflowError` instead.
For instance, converting 255 to int8 will raise an error, instead of
returning -1.

To explicitly force conversion, we must use
`np.asarray(value).astype(dtype)`, rather than
`np.asarray(value, dtype=dtype)`.

The code in `TensorType.filter` has been changed to the new recommended
way to downcast, and the error type caught by some tests has been
changed to OverflowError from TypeError

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