def _slow_schur_p(cls, num_variables, mu, nu=()):
return cls._slow_vectorize(
num_variables,
Tableau.semistandard_shifted_marked(num_variables,
mu,
nu,
diagonal_primes=False))
def _slow_transposed_dual_stable_grothendieck_q(cls,
num_variables,
mu,
nu=()):
p = 0
for tab in Tableau.semistandard_shifted_marked(num_variables, mu, nu):
m = 1
for i in range(1, num_variables + 1):
r = len({x for x, y, v in tab if v[0] == i})
c = len({y for x, y, v in tab if v[0] == -i})
a = len({(x, y) for x, y, v in tab if abs(v[0]) == i})
x = Polynomial.x(i)
m *= x**(r + c) * (x + 1)**(a - r - c)
p += m
dictionary = {}
for e in p:
tup = num_variables * [0]
for i in e:
tup[i - 1] = e[i]
dictionary[tuple(tup)] = p[e]
return SymmetricPolynomial({
SymmetricMonomial(num_variables, alpha): coeff *
(-BETA**-1)**(sum(alpha))
for alpha, coeff in dictionary.items()
if Partition.is_partition(alpha)
}) * (-BETA)**(sum(mu) - sum(nu))
def test_from_string(m=4):
for n in range(m):
for mu in Partition.generate(n, strict=True):
for t in Tableau.semistandard_shifted_marked(n, mu):
u = Tableau(str(t))
if u != t:
print(t)
print(u)
print(t.boxes, u.boxes)
print()
assert Tableau(str(t)) == t
def test_semistandard_shifted_marked():
mu = ()
assert Tableau.semistandard_shifted_marked(0, mu) == {Tableau()}
assert Tableau.semistandard_shifted_marked(1, mu) == {Tableau()}
assert Tableau.semistandard_shifted_marked(2, mu) == {Tableau()}
mu = (1, )
assert Tableau.semistandard_shifted_marked(1, mu) == {
Tableau({(1, 1): 1}),
Tableau({(1, 1): -1}),
}
assert Tableau.semistandard_shifted_marked(1, mu,
diagonal_primes=False) == {
Tableau({(1, 1): 1}),
}
assert Tableau.semistandard_shifted_marked(2, mu) == {
Tableau({(1, 1): 1}),
Tableau({(1, 1): -1}),
Tableau({(1, 1): 2}),
Tableau({(1, 1): -2}),
}
assert Tableau.semistandard_shifted_marked(2, mu,
diagonal_primes=False) == {
Tableau({(1, 1): 1}),
Tableau({(1, 1): 2}),
}
mu = (3, 1)
assert Tableau.semistandard_shifted_marked(1, mu) == set()
assert Tableau.semistandard_shifted_marked(1, mu,
diagonal_primes=False) == set()
assert Tableau.semistandard_shifted_marked(2, mu) == {
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): 1,
(1, 3): 1
}),
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): 1,
(1, 3): 2
}),
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): 1,
(1, 3): -2
}),
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): -2,
(1, 3): 2
}),
Tableau({
(1, 1): 1,
(2, 2): -2,
(1, 2): 1,
(1, 3): 1
}),
Tableau({
(1, 1): 1,
(2, 2): -2,
(1, 2): 1,
(1, 3): 2
}),
Tableau({
(1, 1): 1,
(2, 2): -2,
(1, 2): 1,
(1, 3): -2
}),
Tableau({
(1, 1): 1,
(2, 2): -2,
(1, 2): -2,
(1, 3): 2
}),
Tableau({
(1, 1): -1,
(2, 2): 2,
(1, 2): 1,
(1, 3): 1
}),
Tableau({
(1, 1): -1,
(2, 2): 2,
(1, 2): 1,
(1, 3): 2
}),
Tableau({
(1, 1): -1,
(2, 2): 2,
(1, 2): 1,
(1, 3): -2
}),
Tableau({
(1, 1): -1,
(2, 2): 2,
(1, 2): -2,
(1, 3): 2
}),
Tableau({
(1, 1): -1,
(2, 2): -2,
(1, 2): 1,
(1, 3): 1
}),
Tableau({
(1, 1): -1,
(2, 2): -2,
(1, 2): 1,
(1, 3): 2
}),
Tableau({
(1, 1): -1,
(2, 2): -2,
(1, 2): 1,
(1, 3): -2
}),
Tableau({
(1, 1): -1,
(2, 2): -2,
(1, 2): -2,
(1, 3): 2
}),
}
assert Tableau.semistandard_shifted_marked(2, mu,
diagonal_primes=False) == {
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): 1,
(1, 3): 1
}),
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): 1,
(1, 3): 2
}),
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): 1,
(1, 3): -2
}),
Tableau({
(1, 1): 1,
(2, 2): 2,
(1, 2): -2,
(1, 3): 2
}),
}
mu = (3, 2)
assert Tableau.semistandard_shifted_marked(1, mu) == set()
assert Tableau.semistandard_shifted_marked(1, mu,
diagonal_primes=False) == set()
def _slow_schur_q(cls, num_variables, mu, nu=()):
return cls._slow_vectorize(
num_variables,
Tableau.semistandard_shifted_marked(num_variables, mu, nu))
