def test_refined_gq_to_gp_expansion(k=12): # noqa for mu in Partition.all(k, strict=True): print('mu =', mu) print() print(Partition.printable(mu, shifted=True)) print() n = len(mu) q = SymmetricPolynomial._slow_refined_dual_stable_grothendieck_q(n, mu) expected = {} for a in zero_one_tuples(len(mu)): if not all(mu[i - 1] - a[i - 1] > mu[i] - a[i] for i in range(1, len(a))): continue if not all(mu[i] - a[i] > 0 for i in range(len(a))): continue nu = Partition.trim(tuple(mu[i] - a[i] for i in range(len(a)))) coeff = 2**(len(nu) - sum(a)) * sgn(nu, mu) * BETA**sum(a) assert coeff != 0 expected[nu] = coeff print(' expected =', expected) expected = sum([ coeff * SymmetricPolynomial._slow_refined_dual_stable_grothendieck_p( n, nu) for (nu, coeff) in expected.items() ]) print(' =', expected) assert q == expected print() print()
def test_gq_to_gp_expansion(): # noqa for mu in Partition.all(15, strict=True): print('mu =', mu) print() print(Partition.printable(mu, shifted=True)) print() n = len(mu) q = gq(n, mu) expansion = SymmetricPolynomial.gp_expansion(q) print(' mu =', mu, 'n =', n) print(' expansion =', expansion) assert all(len(nu) == len(mu) for nu in expansion) assert all(Partition.contains(mu, nu) for nu in expansion) # assert all(c % 2**(len(mu) - sum(nu) + sum(mu)) == 0 for nu, c in expansion.items()) expected = {} for a in zero_one_tuples(len(mu)): if not all(mu[i - 1] - a[i - 1] > mu[i] - a[i] for i in range(1, len(a))): continue if not all(mu[i] - a[i] > 0 for i in range(len(a))): continue nu = Partition.trim(tuple(mu[i] - a[i] for i in range(len(a)))) coeff = 2**(len(nu) - sum(a)) * sgn(nu, mu) * BETA**sum(a) assert coeff != 0 expected[nu] = coeff print(' expected =', expected) assert expansion == Vector(expected) print() print()