def test_GP_pieri_slow(): # noqa
for mu in Partition.all(10, strict=True):
for p in [1, 2, 3]:
ans = Vector()
for nu, tabs in Tableau.KOG_by_shape(p, mu).items():
ans += Vector(
{nu: utils.beta**(sum(nu) - sum(mu) - p) * len(tabs)})
f = utils.GP(len(mu) + 1, mu) * utils.GP(len(mu) + 1, (p, ))
assert ans == utils.GP_expansion(f)
def test_fast_KOG(): # noqa
for mu in Partition.all(7, strict=True):
for p in range(7):
counts = Tableau.KOG_counts_by_shape(p, mu)
tabs = Tableau.KOG_by_shape(p, mu)
print(mu, p)
print(counts)
print(tabs)
print()
assert set(counts) == set(tabs)
for nu in counts:
assert counts[nu] == len(tabs[nu])
def test_KOG(): # noqa
mu = (6, 4, 1)
assert set(Tableau.KOG(0, mu)) == {Tableau()}
assert set(Tableau.KOG(1, ())) == {Tableau({(1, 1): 1})}
nu = (7, 6, 3, 1)
assert set(Tableau.KOG_by_shape(5, mu)[nu]) == {
Tableau({
(1, 7): 1,
(2, 6): 1,
(2, 7): 5,
(3, 4): 2,
(3, 5): 4,
(4, 4): 3,
}),
Tableau({
(1, 7): 1,
(2, 6): 2,
(2, 7): 5,
(3, 4): 2,
(3, 5): 4,
(4, 4): 3,
}),
Tableau({
(1, 7): 1,
(2, 6): 2,
(2, 7): 5,
(3, 4): 3,
(3, 5): 5,
(4, 4): 4,
}),
Tableau({
(1, 7): 1,
(2, 6): 2,
(2, 7): 5,
(3, 4): 3,
(3, 5): 4,
(4, 4): 4,
}),
Tableau({
(1, 7): 1,
(2, 6): 4,
(2, 7): 5,
(3, 4): 1,
(3, 5): 3,
(4, 4): 2,
}),
Tableau({
(1, 7): 1,
(2, 6): 4,
(2, 7): 5,
(3, 4): 2,
(3, 5): 4,
(4, 4): 3,
}),
Tableau({
(1, 7): 1,
(2, 6): 4,
(2, 7): 5,
(3, 4): 2,
(3, 5): 3,
(4, 4): 3,
})
}
