What happened?

I have a DataArray with a single dimension and multiple (Pandas)Indexes assigned to various coordinates for efficient indexing using sel.

Edit: the problem is even worse than originally described below: such a DataArray breaks all alignment and it's basically unusable...

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When I try to add an additional coordinate without any index (I simply use the tuple[dimension, values] way) I get a ValueError about aligning with conflicting indexes.

If the original DataArray only has a single (Pandas)Index everything works as expected.

What did you expect to happen?

I expected that I can simply assign new coordinates without an index.

Minimal Complete Verifiable Example

```Python import xarray as xr

da = xr.DataArray( [1, 2, 3], dims="t", coords={ "a": ("t", [3, 4, 5]), "b": ("t", [5, 6, 7]) } )

set one index

da2 = da.set_xindex("a")

set second index (same dimension, maybe thats a problem?)

da3 = da2.set_xindex("b")

this works

da2.coords["c"] = ("t", [2, 3, 4])

this does not

da3.coords["c"] = ("t", [2, 3, 4]) ```

MVCE confirmation

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

Relevant log output

ValueError: cannot re-index or align objects with conflicting indexes found for the following dimensions: 't' (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: None python: 3.9.10 (main, Mar 21 2022, 13:08:11) [GCC 4.8.5 20150623 (Red Hat 4.8.5-44)] python-bits: 64 OS: Linux OS-release: 3.10.0-1160.66.1.el7.x86_64 machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_US.UTF-8 LOCALE: ('en_US', 'UTF-8') libhdf5: 1.12.2 libnetcdf: 4.9.0 xarray: 2022.12.0 pandas: 2.0.2 numpy: 1.24.3 scipy: 1.10.0 netCDF4: 1.6.2 pydap: None h5netcdf: None h5py: None Nio: None zarr: None cftime: 1.6.2 nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: None iris: None bottleneck: None dask: None distributed: None matplotlib: 3.6.3 cartopy: None seaborn: None numbagg: None fsspec: None cupy: None pint: None sparse: None flox: None numpy_groupies: None setuptools: 58.1.0 pip: 21.2.4 conda: None pytest: 7.3.2 mypy: 1.0.0 IPython: 8.8.0 sphinx: None

I have not yet tried this with a newer version of xarray....