def test_symplectic_hecke_insertion():
w = (4, 2, 6, 1, 7, 5, 3, 4, 2, 1, 3, 2)
i = (1, 2, 2, 3, 3, 4, 5, 5, 6, 8, 8, 9)
insertion, recording = InsertionAlgorithm.symplectic_hecke(w)
p = Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 4,
(1, 4): 5,
(1, 5): 6,
(1, 6): 7,
(2, 2): 4,
(2, 3): 5,
(2, 4): 6,
(2, 5): 7,
(3, 3): 6,
(3, 4): 7,
})
q = Tableau({
(1, 1): 1,
(1, 2): -2,
(1, 3): 3,
(1, 4): -4,
(1, 5): 5,
(1, 6): -10,
(2, 2): 6,
(2, 3): -7,
(2, 4): -9,
(2, 5): -12,
(3, 3): 8,
(3, 4): -11,
})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_hecke(
p, q) == (w, tuple(range(1, 13)))
insertion, recording = InsertionAlgorithm.symplectic_hecke(w, i)
q = Tableau({
(1, 1): 1,
(1, 2): -2,
(1, 3): 2,
(1, 4): -3,
(1, 5): 3,
(1, 6): -8,
(2, 2): 4,
(2, 3): -5,
(2, 4): -6,
(2, 5): -9,
(3, 3): 5,
(3, 4): -8,
})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_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)
def test_symplectic_hecke_insertion_setvalued():
w = (2, 2, 4, 3)
i = (1, 1, 1, 4)
insertion, recording = InsertionAlgorithm.symplectic_hecke(w)
p = Tableau({(1, 1): 2, (1, 2): 3, (2, 2): 4})
q = Tableau({(1, 1): (1, 2), (1, 2): 3, (2, 2): 4})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_hecke(p,
q) == (w, (1, 2, 3, 4))
insertion, recording = InsertionAlgorithm.symplectic_hecke(w, i)
q = Tableau({(1, 1): (1, 1), (1, 2): 1, (2, 2): 4})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_hecke(p, q) == (w, i)
i = (1, 2, 3, 3)
insertion, recording = InsertionAlgorithm.symplectic_hecke(w, i, False)
q = Tableau({(1, 1): (1, 2), (1, 2): -3, (2, 2): 3})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_hecke(p, q, False) == (w, i)
w = (4, 2, 2, 3)
i = (2, 4, 4, 4)
insertion, recording = InsertionAlgorithm.symplectic_hecke(w)
p = Tableau({(1, 1): 2, (1, 2): 3, (2, 2): 4})
q = Tableau({(1, 1): 1, (1, 2): (-3, -2), (2, 2): 4})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_hecke(p,
q) == (w, (1, 2, 3, 4))
insertion, recording = InsertionAlgorithm.symplectic_hecke(w, i)
q = Tableau({(1, 1): 2, (1, 2): (-4, -4), (2, 2): 4})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_hecke(p, q) == (w, i)
i = (1, 1, 2, 3)
insertion, recording = InsertionAlgorithm.symplectic_hecke(w, i, False)
q = Tableau({(1, 1): 1, (1, 2): (1, 2), (2, 2): 3})
assert insertion == p
assert recording == q
assert InsertionAlgorithm.inverse_symplectic_hecke(p, q, False) == (w, i)