Multiindex Equals Not Commutative

[hliatrussellinvestments]

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• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd

df1 = pd.DataFrame({
    'a': [0, 0, 1, 1],
    'b': [0, 1, 0, 1],
    'c': [0, 0, 0, 0],
    'v': [1, 2, 3, 4],
})
df1['a'] = df1['a'].astype('Int32')


df2 = pd.DataFrame({
    'a': [0, 0, 1, 1],
    'b': [0, 1, 0, 1],
    'v': [1, 2, 3, 4],
})
df2.set_index(['a', 'b'], inplace=True)

df1_agg = df1.groupby(['a', 'b']).agg({'v': 'max'})

print(df1_agg.index.equals(df2.index) == df2.index.equals(df1_agg.index))

Issue Description

For any 2 indexes, idx_1, idx_2, we should get the same result for idx_1.equals(idx_2) and idx_2.equals(idx_1). Currently they are not the same.

Expected Behavior

print(df1_agg.index.equals(df2.index) == df2.index.equals(df1_agg.index)) should print out True.

Installed Versions

INSTALLED VERSIONS

commit : bb1f651
python : 3.8.6.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19041
machine : AMD64
processor : Intel64 Family 6 Model 158 Stepping 13, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252
pandas : 1.4.0
numpy : 1.19.0
pytz : 2021.3
dateutil : 2.8.1
pip : 21.3.1
setuptools : 49.2.1
Cython : None
pytest : 5.4.1
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fastparquet : None
fsspec : 2021.10.0
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.5.4
sqlalchemy : 1.4.31
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None

[lukemanley]

Looks like this block is causing the behavior:

pandas/pandas/core/indexes/multi.py

Lines 3607 to 3613 in 9cc98a0

	if not isinstance(self_values, np.ndarray):
	# i.e. ExtensionArray
	if not self_values.equals(other_values):
	return False
	else:
	if not array_equivalent(self_values, other_values):
	return False

Here is an example:

import numpy as np
import pandas as pd
from pandas.core.dtypes.missing import array_equivalent

a = pd.array([1, 2, 3], dtype="Int32")
b = np.array([1, 2, 3])

a.equals(b)               # False
array_equivalent(a, b)    # True