def test_tableaux():
# generate tableaux and reverse plane partitions
from tableaux import Tableau
mu = (4, 2, 1)
a = Tableau.semistandard(3, mu)
b = Tableau.semistandard_setvalued(3, mu)
c = Tableau.semistandard_shifted(3, mu, diagonal_primes=True)
d = Tableau.semistandard_shifted_setvalued(4, mu, diagonal_primes=False)
e = Tableau.semistandard_rpp(3, mu)
f = Tableau.semistandard_shifted_rpp(3, mu, diagonal_nonprimes=False)
# serialize to change a Tableau into a dictionary
s = [t.serialize() for t in c]
def test_slow_dual_stable_grothendieck():
n = 3
mu = (1, )
g = SymmetricPolynomial._slow_dual_stable_grothendieck(n, mu)
print(g)
assert g == SymmetricMonomial(n, (1, ))
n = 3
mu = (2, )
g = SymmetricPolynomial._slow_dual_stable_grothendieck(n, mu)
print(g)
assert g == SymmetricMonomial(n, (1, 1)) + SymmetricMonomial(n, (2, ))
n = 3
mu = (2, 1)
for t in Tableau.semistandard_rpp(n, mu):
print(t)
g = SymmetricPolynomial._slow_dual_stable_grothendieck(n, mu)
print(g)
assert g == -BETA * SymmetricMonomial(
n,
(1, 1)) - BETA * SymmetricMonomial(n, (2, )) + 2 * SymmetricMonomial(
n, (1, 1, 1)) + SymmetricMonomial(n, (2, 1))
def _slow_dual_stable_grothendieck(cls, num_variables, mu, nu=()):
return (-BETA)**(sum(mu) - sum(nu)) * cls._slow_vectorize(
num_variables, Tableau.semistandard_rpp(num_variables, mu, nu),
-BETA**-1)