def test_subpartitions():
assert set(Partition.subpartitions(())) == {()}
assert set(Partition.subpartitions([1])) == {(), (1, )}
assert set(Partition.subpartitions([1, 1])) == {(), (1, ), (1, 1)}
assert set(Partition.subpartitions([2, 1])) == {(), (1, ), (1, 1), (2, ),
(2, 1)}
assert len(list(Partition.subpartitions([2, 1]))) == 5
assert set(Partition.subpartitions((), True)) == {()}
assert set(Partition.subpartitions([1], True)) == {(), (1, )}
assert set(Partition.subpartitions([1, 1], True)) == {(), (1, )}
assert set(Partition.subpartitions([2, 1], True)) == {(), (1, ), (2, ),
(2, 1)}
assert len(list(Partition.subpartitions([2, 1], True))) == 4
def _test(n_max, v_max):
for n in range(n_max + 1):
for v in range(1, v_max + 1):
for lam1 in Partition.all(n):
for lam2 in Partition.all(n):
print()
print()
print('* v =', v, ', n =', n, ', mu =', lam1, ', nu =',
lam2)
print()
print('Computing LHS . . .')
print()
s = Polynomial()
for mu in Partition.all(n + max(sum(lam1), sum(lam2))):
a = SymmetricPolynomial.stable_grothendieck_doublebar(
v, mu, lam1).truncate(n).polynomial('x')
b = SymmetricPolynomial.dual_stable_grothendieck(
v, mu, lam2).truncate(n).polynomial('y')
s += (a * b).truncate(n)
print(' ', mu, ':', s, '|', a, '|', b)
print()
print('LHS =', s)
print()
print()
print('Computing RHS . . .')
print()
f = Polynomial.one()
x = Polynomial.x
y = Polynomial.y
for i in range(1, v + 1):
for j in range(1, v + 1):
a = x(i) * y(j)
term = Polynomial.one()
for e in range(1, n + 1):
term += a**e
f = (f * term).truncate(n)
print(' ', ' :', f)
print()
t = Polynomial()
for kappa in Partition.subpartitions(lam2):
a = SymmetricPolynomial.stable_grothendieck_doublebar(
v, lam2, kappa).truncate(n)
b = SymmetricPolynomial.dual_stable_grothendieck(
v, lam1, kappa).truncate(n)
t += (f * a.polynomial('x') *
b.polynomial('y')).truncate(n)
print(' ', kappa, ':', t)
print()
print('RHS =', t)
print()
print()
print('diff =', s - t)
print()
assert s == t
def _test_shifted_p(n_max, v_max):
for n in range(n_max + 1):
for v in range(1, v_max + 1):
for lam1 in Partition.all(n, strict=True):
for lam2 in Partition.all(n, strict=True):
print()
print()
print('* v =', v, ', n =', n, ', mu =', lam1, ', nu =',
lam2)
print()
print('Computing LHS . . .')
print()
s = Polynomial()
for mu in Partition.all(n + max(sum(lam1), sum(lam2)),
strict=True):
a = SymmetricPolynomial.stable_grothendieck_p_doublebar(
v, mu, lam1).truncate(n).polynomial('x')
b = SymmetricPolynomial.dual_stable_grothendieck_q(
v, mu, lam2).truncate(n).polynomial('y')
s += (a * b).truncate(n)
print(' ', mu, ':', s, '|', a, '|', b)
print()
print('LHS =', s)
print()
print()
print('Computing RHS . . .')
print()
f = kernel(n, v)
print(' ', ' :', f)
print()
t = Polynomial()
for kappa in Partition.subpartitions(lam2, strict=True):
a = SymmetricPolynomial.stable_grothendieck_p_doublebar(
v, lam2, kappa).truncate(n)
b = SymmetricPolynomial.dual_stable_grothendieck_q(
v, lam1, kappa).truncate(n)
t += (f * a.polynomial('x') *
b.polynomial('y')).truncate(n)
print(' ', kappa, ':', t)
print()
print('RHS =', t)
print()
print()
print('diff =', s - t)
print()
assert s == t
def fpf_grassmannians(cls, rank):
assert rank % 2 == 0
delta = tuple(range(rank - 2, 0, -2))
for mu in Partition.subpartitions(delta, strict=True):
yield cls.get_fpf_grassmannian(*mu)
def inv_grassmannians(cls, rank):
delta = tuple(range(rank - 1, 0, -2))
for mu in Partition.subpartitions(delta, strict=True):
yield cls.get_inv_grassmannian(*mu)
def grassmannians(cls, rank):
delta = tuple(range(rank - 1, 0, -1))
for mu in Partition.subpartitions(delta):
yield cls.get_grassmannian(*mu)
