Objects with multiple identical `xindex`s on a dim aren't alignable

[max-sixty]

What happened?

I'm less up to speed on the xindex functionality, but a colleagues shared a similar issue to this, so some people are finding their way to them (good news!)

But one issue — it seems like here if we have an index u and v on the u dimension, we can't do something like foo + foo

What did you expect to happen?

Either it works, or — like the old days — it doesn't work but then we shouldn't allow getting the object into that state

Minimal Complete Verifiable Example

ds = xr.Dataset(
    data_vars=dict(
        x=(("u",), [1, 2, 3, 4]),
        y=(("u",), [100, 200, 300, 400]),
    ),
    coords=dict(
        u=[1, 2, 3, 4],
        v=(("u",), [1, 2, 1, 2]),
    ),
).set_xindex("v")

# <xarray.Dataset> Size: 128B
# Dimensions:  (u: 4)
# Coordinates:
#   * u        (u) int64 32B 1 2 3 4
#   * v        (u) int64 32B 1 2 1 2
# Data variables:
#     x        (u) int64 32B 1 2 3 4
#     y        (u) int64 32B 100 200 300 400

ds.x * ds.y

# Error below

MVCE confirmation

• Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• Complete example — the example is self-contained, including all data and the text of any traceback.
• Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• New issue — a search of GitHub Issues suggests this is not a duplicate.
• Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

File ~/workspace/xarray/xarray/core/_typed_ops.py:253, in DataArrayOpsMixin.__mul__(self, other)
    252 def __mul__(self, other: DaCompatible) -> Self:
--> 253     return self._binary_op(other, operator.mul)

File ~/workspace/xarray/xarray/core/dataarray.py:4747, in DataArray._binary_op(self, other, f, reflexive)
   4745 if isinstance(other, DataArray):
   4746     align_type = OPTIONS["arithmetic_join"]
-> 4747     self, other = align(self, other, join=align_type, copy=False)
   4748 other_variable_or_arraylike: DaCompatible = getattr(other, "variable", other)
   4749 other_coords = getattr(other, "coords", None)

File ~/workspace/xarray/xarray/core/alignment.py:887, in align(join, copy, indexes, exclude, fill_value, *objects)
    691 """
    692 Given any number of Dataset and/or DataArray objects, returns new
    693 objects with aligned indexes and dimension sizes.
   (...)
    877 
    878 """
    879 aligner = Aligner(
    880     objects,
    881     join=join,
   (...)
    885     fill_value=fill_value,
    886 )
--> 887 aligner.align()
    888 return aligner.results

File ~/workspace/xarray/xarray/core/alignment.py:578, in Aligner.align(self)
    576 self.find_matching_indexes()
    577 self.find_matching_unindexed_dims()
--> 578 self.assert_no_index_conflict()
    579 self.align_indexes()
    580 self.assert_unindexed_dim_sizes_equal()

File ~/workspace/xarray/xarray/core/alignment.py:322, in Aligner.assert_no_index_conflict(self)
    318 pprint(self.indexes)
    319 items_msg = ", ".join(
    320     f"{k!r} ({v} conflicting indexes)" for k, v in dup.items()
    321 )
--> 322 raise ValueError(
    323     "cannot re-index or align objects with conflicting indexes found for "
    324     f"the following {msg}: {items_msg}\n"
    325     "Conflicting indexes may occur when\n"
    326     "- they relate to different sets of coordinate and/or dimension names\n"
    327     "- they don't have the same type\n"
    328     "- they may be used to reindex data along common dimensions"
    329 )

ValueError: cannot re-index or align objects with conflicting indexes found for the following dimensions: 'u' (2 conflicting indexes)
Conflicting indexes may occur when
- they relate to different sets of coordinate and/or dimension names
- they don't have the same type
- they may be used to reindex data along common dimensions

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS

commit: 9735216
python: 3.11.10 (main, Sep 7 2024, 01:03:31) [Clang 15.0.0 (clang-1500.3.9.4)]
python-bits: 64
OS: Darwin
OS-release: 23.6.0
machine: arm64
processor: arm
byteorder: little
LC_ALL: None
LANG: None
LOCALE: ('en_US', 'UTF-8')
libhdf5: 1.14.3
libnetcdf: 4.9.2

xarray: 2024.7.1.dev68+gcc74d3ae
pandas: 2.2.2
numpy: 2.0.2
scipy: 1.14.1
netCDF4: 1.7.1.post2
pydap: None
h5netcdf: 1.3.0
h5py: 3.11.0
zarr: 2.18.3
cftime: 1.6.4
nc_time_axis: 1.4.1
iris: None
bottleneck: 1.4.0
dask: 2024.8.2
distributed: 2024.8.2
matplotlib: 3.9.2
cartopy: None
seaborn: 0.13.2
numbagg: 0.8.1
fsspec: 2024.9.0
cupy: None
pint: None
sparse: None
flox: 0.9.11
numpy_groupies: 0.11.2
setuptools: 69.2.0
pip: 24.0
conda: None
pytest: 8.3.3
mypy: 1.11.2
IPython: 8.24

[dcherian]

Looks like a dupe of #7695

[max-sixty]

Sorry, thanks @dcherian