Add _repr_inline_ documentation to CustomIndex docs

doc/internals/how-to-create-custom-index.rst

@@ -128,6 +128,44 @@ e.g., a kd-tree object may not be easily indexed. If ``Index.isel()`` is not
 implemented, the index in just dropped in the DataArray or Dataset resulting
 from the selection.
 
+Custom representation
+---------------------
+
+When a :py:class:`Dataset` or :py:class:`DataArray` is displayed, Xarray shows
+a summary of its indexes. By default, the base :py:class:`Index` class returns
+just the class name. You can customize this by implementing the
+:py:meth:`Index._repr_inline_` method, which should return a short, single-line
+string representation of the index.
+
+The ``_repr_inline_`` method receives a ``max_width`` argument (number of
+characters) that indicates the available space for the representation. The
+output of the method must not exceed this width.
+
+Here are some examples from Xarray's built-in indexes:
+
+- :py:class:`~xarray.indexes.RangeIndex` returns: ``RangeIndex (start=0, stop=1, step=0.1)``
+- :py:class:`~xarray.indexes.NDPointIndex` returns: ``NDPointIndex (KDTree)``
+
+This representation appears in the indexes section when displaying a Dataset or
+DataArray:
+
+.. jupyter-execute::
+
+    import numpy as np
+    import xarray as xr
+    from xarray import Index
+
+    class MyIndex(Index):
+        def __init__(self, data):
+            self._data = data
+
+        def _repr_inline_(self, max_width: int) -> str:
+            # Return a concise representation
+            return f"{type(self).__name__} (size={len(self._data)})"
+
+    # Demonstrate how it looks in a DataArray
+    xr.DataArray(np.arange(10), dims="x").set_xindex("x", MyIndex)
+
 Alignment
 ---------
 
@@ -198,6 +236,10 @@ regularly spaced 2-dimensional data) that internally relies on two
 
             return merge_sel_results(results)
 
+        def _repr_inline_(self, max_width: int) -> str:
+            dims = [idx.dim for idx in self._xy_indexes.values()]
+            return f"{type(self).__name__} (dims={dims})"
+
 
 This basic index only supports label-based selection. Providing a full-featured
 index by implementing the other ``Index`` methods should be pretty