def test_covers():
mu = ()
assert set(Partition.remove_inner_corners(mu)) == {()}
assert set(Partition.remove_shifted_inner_corners(mu)) == {()}
mu = (1, )
assert set(Partition.remove_inner_corners(mu)) == {(1, ), ()}
assert set(Partition.remove_shifted_inner_corners(mu)) == {(1, ), ()}
mu = (3, 2, 1)
assert set(Partition.remove_inner_corners(mu)) == {(3, 2, 1), (2, 2, 1),
(3, 1, 1), (3, 2),
(2, 1, 1), (2, 2),
(3, 1), (2, 1)}
assert set(Partition.remove_shifted_inner_corners(mu)) == {(3, 2),
(3, 2, 1)}
def stable_grothendieck_doublebar(cls,
num_variables,
mu,
nu=(),
degree_bound=None): # noqa
ans = SymmetricPolynomial()
if Partition.contains(mu, nu):
for x in Partition.remove_inner_corners(nu):
ans += BETA**(sum(nu) - sum(x)) * cls._stable_grothendieck(
num_variables, mu, x, degree_bound)
return ans
