def lvector(nu, mu, p_max):
ans = LCACHE.get((nu, mu), RowVector())
if len(ans) >= p_max:
return ans.subvector(p_max)
for p in range(len(ans), p_max):
v = 0
for lam in lshapes(nu, mu):
c = sum(lam) - sum(mu)
if p == 0:
d = Tableau.KOG_counts(nu, lam, p)
else:
d = 2 * Tableau.KOG_counts(nu, lam, p) + Tableau.KOG_counts(
nu, lam, p + 1)
v += d * 2**(len(mu) - c) * (-1)**(columns(lam, mu) + c)
if p == 0 and columns(nu, mu) == 1:
v *= -1
ans.append(v)
LCACHE[(nu, mu)] = ans
return ans
def test_gq_pieri(n=4, m=10, l=5):
for mu in Partition.all(m, strict=True):
if not mu:
continue
f = gq(n, mu)
for p in range(1, l + 1):
g = gq(n, (p,))
actual = f * g
expected = 0
pieri = gq_pieri(mu, p)
for (lam, c) in pieri.items():
expected += gq(n, lam) * c
# print('gq_%s(x_%s)' % (mu, n), '*', 'gq_%s(x_%s)' % (p, n))
# print(' ', actual - expected)
# print()
assert actual == expected
q = mu[0] if mu else 0
nu = (q + p,) + mu
print()
print(Partition.printable(nu, mu, shifted=True))
print()
print('mu =', mu, 'p =', p, 'q =', q)
print()
rho1 = (q + p,) + mu[1:]
rho2 = (q + p - 1,) + mu[1:]
for lam in pieri:
co = pieri[lam].substitute(0, 1)
co = co - 1 if lam in [rho1, rho2] else co
kog = Tableau.KOG_counts(nu, lam, q)
print(lam, co, kog)
assert co == kog
print()
