def test_slow_dual_stable_grothendieck_pq():
n = 3
mu = (1, )
g = SymmetricPolynomial._slow_dual_stable_grothendieck_p(n, mu)
h = SymmetricPolynomial._slow_dual_stable_grothendieck_q(n, mu)
print(g)
print(h)
print()
assert g == SymmetricMonomial(n, (1, ))
assert h == 2 * SymmetricMonomial(n, (1, ))
n = 3
mu = (2, )
for t in Tableau.semistandard_marked_rpp(3, mu, diagonal_nonprimes=False):
print(t)
g = SymmetricPolynomial._slow_dual_stable_grothendieck_p(n, mu)
print(g)
assert g == \
SymmetricPolynomial._slow_dual_stable_grothendieck(n, (1, 1)) + \
SymmetricPolynomial._slow_dual_stable_grothendieck(n, (2,))
n = 3
mu = (2, 1)
for t in Tableau.semistandard_marked_rpp(n, mu):
print(t)
g = SymmetricPolynomial._slow_dual_stable_grothendieck_p(n, mu)
h = SymmetricPolynomial._slow_dual_stable_grothendieck_q(n, mu)
print(g)
print(h)
print()
assert g == -BETA * SymmetricMonomial(
n,
(1, 1)) + -BETA * SymmetricMonomial(n, (2, )) + 2 * SymmetricMonomial(
n, (1, 1, 1)) + SymmetricMonomial(n, (2, 1))
n = 5
mu = (3, 2)
g = SymmetricPolynomial._slow_dual_stable_grothendieck_p(n, mu)
h = SymmetricPolynomial._slow_dual_stable_grothendieck_q(n, mu)
n = 6
mu = (3, 2, 1)
assert SymmetricPolynomial._slow_dual_stable_grothendieck_p(n, mu) == \
SymmetricPolynomial._slow_dual_stable_grothendieck(n, mu)
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 test_symmetric_functions():
nn = 6
for mu in Partition.all(nn):
for nu in Partition.all(nn, strict=True):
for n in range(nn):
print(n, mu, nu)
print()
f = SymmetricPolynomial.schur(n, mu, nu)
g = SymmetricPolynomial.stable_grothendieck(n, mu, nu)
h = SymmetricPolynomial.dual_stable_grothendieck(n, mu, nu)
fs = SymmetricPolynomial._slow_schur(n, mu, nu)
gs = SymmetricPolynomial._slow_stable_grothendieck(n, mu, nu)
hs = SymmetricPolynomial._slow_dual_stable_grothendieck(
n, mu, nu)
if f != fs:
print(f)
print(fs)
print()
if g != gs:
print(g)
print(gs)
print()
if h != hs:
print(h)
print(hs)
print()
print()
assert f == fs
assert g == gs
assert h == hs
hh = SymmetricPolynomial.schur_s(n, mu, nu)
kk = SymmetricPolynomial.stable_grothendieck_s(n, mu, nu)
if mu == nu:
assert f == 1
assert g == 1
assert h == 1
assert fs == 1
assert gs == 1
assert hs == 1
assert hh == 1
assert kk == 1
if not Partition.contains(mu, nu):
assert f == 0
assert g == 0
assert h == 0
assert fs == 0
assert gs == 0
assert hs == 0
assert hh == 0
assert kk == 0
print(f)
print(g)
print()
print(hh)
print(kk)
print()
assert g.lowest_degree_terms() == f
assert kk.lowest_degree_terms() == hh