def test_orthogonal_hecke_insertion():
w = (4, 5, 1, 1, 3, 2)
i = (1, 1, 3, 4, 4, 6)
insertion, recording = InsertionAlgorithm.orthogonal_hecke(w)
p = Tableau({(1, 1): 1, (1, 2): 2, (1, 3): 4, (1, 4): 5, (2, 2): 3})
q = Tableau({
(1, 1): 1,
(1, 2): 2,
(1, 3): (-3, -4),
(1, 4): -6,
(2, 2): 5
})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_orthogonal_hecke(p, q) == (w, (1, 2, 3,
4, 5, 6))
insertion, recording = InsertionAlgorithm.orthogonal_hecke(w, i)
q = Tableau({
(1, 1): 1,
(1, 2): 1,
(1, 3): (-3, -4),
(1, 4): -6,
(2, 2): 4
})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_orthogonal_hecke(p, q) == (w, i)
def backward(self):
if not self.is_symplectic:
return lambda x, y: InsertionAlgorithm.inverse_orthogonal_hecke(
x, y, self.multisetvalued)
else:
return lambda x, y: InsertionAlgorithm.inverse_symplectic_hecke(
x, y, self.multisetvalued)