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 forward(self):
if not self.is_symplectic:
return lambda x, y: InsertionAlgorithm.orthogonal_hecke(
x, y, self.multisetvalued)
else:
return lambda x, y: InsertionAlgorithm.symplectic_hecke(
x, y, self.multisetvalued)
def test_shifted_growth_words(n=4):
c = True
reasons = set()
for a in Permutation.involutions(n):
for w in a.get_involution_words():
print(w)
p, q = InsertionAlgorithm.orthogonal_hecke(w)
g, e, c, r = Partition.shifted_growth_diagram(w)
reasons |= set([x for row in r for x in row])
# Partition.print_growth_diagram(g)
# Partition.print_growth_diagram(e)
# Partition.print_growth_diagram(c)
# print(p)
# print(q)
pp, qq = Tableau.from_shifted_growth_diagram(g, e, c)
# print(pp)
# print(qq)
assert p == pp and q == qq
print(sorted(reasons))
def test_shifted_growth_diagram():
w = (4, 2, 1, 1, 2, 3, 2)
g, e, c, r = Partition.shifted_growth_diagram(w)
Partition.print_growth_diagram(g)
Partition.print_growth_diagram(e)
Partition.print_growth_diagram(c)
gtest = [[[], [], [], [], [], [], [], []],
[[], [], [], [1], [1], [1], [1], [1]],
[[], [], [1], [2], [2], [2], [2], [2]],
[[], [], [1], [2], [2], [2], [3], [3, 1]],
[[], [1], [2], [3], [3], [3, 1], [3, 1], [3, 2]]]
gtest = [[tuple(x) for x in row] for row in gtest]
assert g == gtest
etest = [[False, False, False, False, False, False, False, False],
[False, False, False, False, False, False, False, False],
[False, False, False, True, True, False, False, False],
[False, False, False, True, True, False, False, False],
[False, False, True, True, True, False, False, True]]
assert e == etest
ctest = [[None, None, None, None, None, None, None, None],
[None, None, None, None, 1, None, None, None],
[None, None, None, None, 2, 1, None, 1],
[None, None, None, None, 2, 1, None, None],
[None, None, None, None, 3, None, 2, None]]
assert c == ctest
p, q = Tableau.from_shifted_growth_diagram(g, e, c)
pp, qq = InsertionAlgorithm.orthogonal_hecke(w)
print(p)
print(q)
assert p == pp and q == qq
w = (4, 5, 1, 2, 3, 4, 6, 5, 6, 4)
g, e, c, r = Partition.shifted_growth_diagram(w)
Partition.print_growth_diagram(g)
Partition.print_growth_diagram(e)
Partition.print_growth_diagram(c)
Partition.print_growth_diagram(r)
p, q = Tableau.from_shifted_growth_diagram(g, e, c)
pp, qq = InsertionAlgorithm.orthogonal_hecke(w)
print(p)
print(q)
assert p == pp and q == qq
w = (1, 3, 2, 5, 6, 4, 3, 5, 2, 4, 5, 6)
g, e, c, r = Partition.shifted_growth_diagram(w)
Partition.print_growth_diagram(g)
Partition.print_growth_diagram(e)
Partition.print_growth_diagram(c)
Partition.print_growth_diagram(r)
p, q = Tableau.from_shifted_growth_diagram(g, e, c)
pp, qq = InsertionAlgorithm.orthogonal_hecke(w)
print(p)
print(q)
assert p == pp and q == qq
w = (3, 2, 1)
g, e, c, r = Partition.shifted_growth_diagram(w)
Partition.print_growth_diagram(g)
Partition.print_growth_diagram(e)
Partition.print_growth_diagram(c)
Partition.print_growth_diagram(r)
p, q = Tableau.from_shifted_growth_diagram(g, e, c)
pp, qq = InsertionAlgorithm.orthogonal_hecke(w)
print(p)
print(q)
assert p == pp and q == qq