BUG: IntervalIndex intersections are not intersections in many cases

[ivirshup]

• I have checked that this issue has not already been reported.

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

• (optional) I have confirmed this bug exists on the master branch of pandas.

---

Code Sample, a copy-pastable example

# Your code here
import pandas._testing as tm

idx_unique = tm.makeIntervalIndex(k=5)
idx_non_unique = idx_unique[[0, 0, 1, 2, 3, 4]]

assert idx_unique.intersection(idx_non_unique).equals(idx_non_unique)
assert idx_non_unique.intersection(idx_unique).equals(idx_non_unique)
# As an implementation note:
assert idx_non_unique._intersection_non_unique(idx_unique).equals(idx_non_unique)

All of these should probably fail

Problem description

Intersections on IntervalIndexes should not repeat duplicated elements, similar to all other Index types.

I came across this while writing tests for #38654

For example, if we defined a test:

def check_intersection_commutative(left, right):
    assert left.intersection(right).equals(right.intersection(left))

@pytest.mark.parametrize("index_maker", tm.index_subclass_makers_generator())
def test_intersection_uniqueness(index_maker):
    if index_make is tm.makeMultiIndex:
        pytest.pass()  # This index maker is bugged
    ind_unique = index_maker(k=5)
    ind_non_unique = idx_unique[[0, 0, 1, 2, 3, 4]]

    check_intersection_commutative(ind_unique, ind_non_unique)
    assert idx_unique.intersection(idx_non_unique).is_unique

Only IntervalIndex would fail (not including the bugged makeMultiIndex).

Expected Output

All of the assertions in the original example should fail.

Output of pd.show_versions()

dev environment

INSTALLED VERSIONS
------------------
commit           : 9f1a41dee0e9167361d9f435b4c3d499d01e415a
python           : 3.8.5.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.6.0
Version          : Darwin Kernel Version 19.6.0: Tue Nov 10 00:10:30 PST 2020; root:xnu-6153.141.10~1/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.3.0.dev0+210.g9f1a41dee0.dirty
numpy            : 1.18.5
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.1.1
setuptools       : 49.2.0.post20200712
Cython           : 0.29.21
pytest           : 5.4.3
hypothesis       : 5.20.3
sphinx           : 3.1.1
blosc            : None
feather          : None
xlsxwriter       : 1.2.9
lxml.etree       : 4.5.2
html5lib         : 1.1
pymysql          : None
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.16.1
pandas_datareader: None
bs4              : 4.9.1
bottleneck       : 1.3.2
fsspec           : 0.7.4
fastparquet      : 0.4.1
gcsfs            : 0.6.2
matplotlib       : 3.2.2
numexpr          : 2.7.1
odfpy            : None
openpyxl         : 3.0.4
pandas_gbq       : None
pyarrow          : 0.17.1
pyxlsb           : None
s3fs             : 0.4.2
scipy            : 1.5.1
sqlalchemy       : 1.3.18
tables           : 3.6.1
tabulate         : 0.8.7
xarray           : 0.16.0
xlrd             : 1.2.0
xlwt             : 1.3.0
numba            : 0.50.1

1.1.5

INSTALLED VERSIONS
------------------
commit           : b5958ee1999e9aead1938c0bba2b674378807b3d
python           : 3.8.6.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.6.0
Version          : Darwin Kernel Version 19.6.0: Tue Nov 10 00:10:30 PST 2020; root:xnu-6153.141.10~1/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.1.5
numpy            : 1.19.4
pytz             : 2020.1
dateutil         : 2.8.1
pip              : 20.3.3
setuptools       : 51.0.0
Cython           : 0.29.21
pytest           : 6.2.1
hypothesis       : None
sphinx           : 3.3.1
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.2
IPython          : 7.19.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fsspec           : 0.8.5
fastparquet      : 0.4.1
gcsfs            : None
matplotlib       : 3.3.3
numexpr          : 2.7.1
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : 2.0.0
pytables         : None
pyxlsb           : None
s3fs             : 0.4.2
scipy            : 1.5.4
sqlalchemy       : 1.3.18
tables           : 3.6.1
tabulate         : 0.8.7
xarray           : 0.16.2
xlrd             : 1.2.0
xlwt             : None
numba            : 0.52.0