def test_GQ_pieri_slow(): # noqa for mu in Partition.all(10, strict=True): for p in [1, 2, 3]: ans = Vector() for nu, tabs in Tableau.KLG_by_shape(p, mu).items(): ans += Vector( {nu: utils.beta**(sum(nu) - sum(mu) - p) * len(tabs)}) f = utils.GQ(len(mu) + 1, mu) * utils.GQ(len(mu) + 1, (p, )) assert ans == utils.GQ_expansion(f)
def test_fast_KLG(): # noqa for mu in Partition.all(7, strict=True): for p in range(7): counts = Tableau.KLG_counts_by_shape(p, mu) tabs = Tableau.KLG_by_shape(p, mu) print(mu, p) print(counts) print(tabs) print() assert set(counts) == set(tabs) for nu in counts: print('*', nu) assert counts[nu] == len(tabs[nu])
def test_KLG(): # noqa mu = (6, 4, 1) assert set(Tableau.KLG(0, mu)) == {Tableau()} assert set(Tableau.KLG(1, ())) == {Tableau({(1, 1): 1})} nu = (7, 6, 3, 1) assert set(Tableau.KLG_by_shape(5, mu)[nu]) == { Tableau({ (1, 7): -1, (2, 6): -1, (2, 7): 5, (3, 4): -2, (3, 5): 4, (4, 4): 3, }), Tableau({ (1, 7): -1, (2, 6): -2, (2, 7): 5, (3, 4): -2, (3, 5): 4, (4, 4): 3, }), Tableau({ (1, 7): -1, (2, 6): -2, (2, 7): 5, (3, 4): -3, (3, 5): 5, (4, 4): 4, }), Tableau({ (1, 7): -1, (2, 6): -2, (2, 7): 5, (3, 4): -3, (3, 5): 4, (4, 4): 4, }), Tableau({ (1, 7): -1, (2, 6): 4, (2, 7): 5, (3, 4): -1, (3, 5): 3, (4, 4): 2, }), Tableau({ (1, 7): -1, (2, 6): 4, (2, 7): 5, (3, 4): -2, (3, 5): 4, (4, 4): 3, }), Tableau({ (1, 7): -1, (2, 6): 4, (2, 7): 5, (3, 4): -2, (3, 5): 3, (4, 4): 3, }), Tableau({ (1, 7): -1, (2, 6): 4, (2, 7): 5, (3, 4): -2, (3, 5): 3, (4, 4): 2, }), Tableau({ (1, 7): -1, (2, 6): -2, (2, 7): 5, (3, 4): -3, (3, 5): 4, (4, 4): 3, }) }