def test_gp_pieri(n=4, m=10, l=5):
for mu in Partition.all(m, strict=True):
if sum(mu) <= 1:
continue
f = gp(n, mu)
for p in range(1, l + 1):
g = gp(n, (p,))
actual = f * g
expected = 0
pieri = gp_pieri(mu, p)
for (lam, c) in pieri.items():
expected += gp(n, lam) * c
# print('gp_%s(x_%s)' % (mu, n), '*', 'gp_%s(x_%s)' % (p, n))
# print(' ', actual - expected)
# print()
assert actual == expected
pieri = {k: 2 * v for k, v in pieri.items()}
if p >= 2:
for (lam, c) in gp_pieri(mu, p - 1).items():
pieri[lam] = pieri.get(lam, 0) + c * beta
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:]
print(pieri)
print()
for lam in pieri:
co = pieri[lam].substitute(0, 1)
co = co - 1 if lam in [rho1, rho2] else co
klg = Tableau.KLG_counts(nu, lam, q)
print(lam, co, klg)
assert co == klg
print()
def rvector(nu, mu, p_max):
ans = RCACHE.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 rshapes(nu, mu):
c = sum(nu) - sum(lam)
v += 2**(len(lam) - c) * (-1)**(
columns(nu, lam) + c) * Tableau.KLG_counts(lam, mu, p)
if p == 0 and columns(nu, mu) == 1:
v *= -1
ans.append(v)
RCACHE[(nu, mu)] = ans
return ans
