def test_partition():
pytest.raises(ValueError, lambda: Partition(*range(3)))
pytest.raises(ValueError, lambda: Partition([1, 1, 2]))
a = Partition([1, 2, 3], [4])
b = Partition([1, 2], [3, 4])
c = Partition([x])
l = [a, b, c]
l.sort(key=default_sort_key)
assert l == [c, a, b]
l.sort(key=lambda w: default_sort_key(w, order='rev-lex'))
assert l == [c, a, b]
assert (a == b) is False
assert a <= b
assert (a > b) is False
assert a != b
assert (a + 2).partition == [[1, 2], [3, 4]]
assert (b - 1).partition == [[1, 2, 4], [3]]
assert (a - 1).partition == [[1, 2, 3, 4]]
assert (a + 1).partition == [[1, 2, 4], [3]]
assert (b + 1).partition == [[1, 2], [3], [4]]
assert a.rank == 1
assert b.rank == 3
assert a.RGS == (0, 0, 0, 1)
assert b.RGS == (0, 0, 1, 1)
def test_rgs():
pytest.raises(ValueError, lambda: RGS_unrank(-1, 3))
pytest.raises(ValueError, lambda: RGS_unrank(3, 0))
pytest.raises(ValueError, lambda: RGS_unrank(10, 1))
pytest.raises(ValueError, lambda: Partition.from_rgs(list(range(3)), list(range(2))))
pytest.raises(ValueError, lambda: Partition.from_rgs(list(range(1, 3)), list(range(2))))
assert RGS_enum(-1) == 0
assert RGS_enum(1) == 1
assert RGS_unrank(7, 5) == [0, 0, 1, 0, 2]
assert RGS_unrank(23, 14) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2]
assert RGS_rank(RGS_unrank(40, 100)) == 40
def test_sympyissue_9608():
a = Partition([1, 2, 3], [4])
b = Partition([1, 2], [3, 4])
assert list(ordered([a, b], Set._infimum_key)) # does not raise an error