def test_next_f_d1():
# transition (D1)
t = Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 4,
(1, 4): 5,
(2, 2): 6,
(2, 3): 7,
(2, 4): 8,
(2, 6): 4
})
state = FState(t, (2, 6))
state, box = state.next()
i, j = box
t = Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 4,
(1, 4): 5,
(2, 2): 4,
(2, 3): 7,
(2, 4): 8,
(4, 3): 6
})
assert state == FState(t, (4, 3))
assert i == 2
assert j == 2
def test_next_f_c3():
# transition (C3)
t = Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 5,
(1, 4): 6,
(2, 2): 4,
(2, 3): 6,
(2, 4): 7,
(3, 3): 8,
(5, 3): 5
})
state = FState(t, (5, 3))
state, box = state.next()
i, j = box
t = Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 5,
(1, 4): 6,
(2, 2): 4,
(2, 3): 6,
(2, 4): 7,
(3, 3): 8,
(5, 4): 6
})
assert state == FState(t, (5, 4))
assert i == 2
assert j == 3
def test_next_f_c1():
# transition (C1)
t = Tableau({
(1, 1): 5,
(1, 2): 5,
(1, 3): 5,
(1, 4): 4,
(2, 2): 4,
(4, 3): 6
})
state = FState(t, (4, 3))
state, box = state.next()
i, j = box
t = Tableau({
(1, 1): 5,
(1, 2): 5,
(1, 3): 5,
(1, 4): 4,
(2, 2): 4,
(2, 3): 6
})
assert state == FState(t)
assert i == 2
assert j == 3
def test_next_f_r1():
# transition (R1)
state = FState().add(1)
t = Tableau().add(1, 2, 1)
assert state == FState(t, (1, 2))
state, box = state.next()
i, j = box
t = Tableau().add(1, 1, 1)
assert state == FState(t)
assert i == 1
assert j == 1
def test_reverse_insertion_complete():
n = 8
count = 200
for w in Permutation.symplectic_hecke_words(n):
count -= 1
if count == 0:
break
print(w)
p, q = FState.insertion_tableaux(*w)
print()
print(p)
print()
print(q)
v = FState.inverse_insertion(p, q)
print()
print(v)
print()
assert v == w
def test_next_f_r3():
# transition (R3)
#
# 1 2 3 1
# 5 5 3 4
#
t = Tableau({
(1, 1): 5,
(1, 2): 5,
(1, 3): 5,
(1, 4): 4,
(2, 2): 1,
(2, 3): 2,
(2, 4): 3,
(2, 6): 1
})
state = FState(t, (2, 6))
state, box = state.next()
i, j = box
# 2
#
# 1 2 3
# 5 5 5 4
#
t = Tableau({
(1, 1): 5,
(1, 2): 5,
(1, 3): 5,
(1, 4): 4,
(2, 2): 1,
(2, 3): 2,
(2, 4): 3,
(4, 3): 2
})
assert state == FState(t, (4, 3))
assert i == 2
assert j == 3
def test_reverse_insertion():
w = (2, 1, 4, 1, 4, 3, 4, 1, 2)
p, q = FState.insertion_tableaux(*w)
r = (2, 3, {-9})
assert q.values() == {1, -2, 3, -4, 5, 6, 7, -8, -9}
assert p == Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 4,
(2, 2): 4,
(2, 3): 5
})
s, box = FState(p).previous(r)
assert box == (2, 3)
assert s.tableau == Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 4,
(2, 2): 4,
(4, 3): 5
})
assert s.outer == (4, 3)
s, box = s.previous()
assert box == (2, 2)
assert s.tableau == Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 4,
(2, 2): 4,
(2, 5): 3
})
assert s.outer == (2, 5)
s, box = s.previous()
assert box == (1, 2)
assert s.tableau == Tableau({
(1, 1): 2,
(1, 2): 3,
(1, 3): 4,
(2, 2): 4,
(1, 5): 2
})
assert s.outer == (1, 5)
assert s.is_initial()
assert FState.inverse_insertion(p, q) == w
#
# 22
# 6 8 22
# 2 4 6 20
#
w = (2, 6, 8, 22, 4, 6, 20, 6)
p, q = FState.insertion_tableaux(*w)
assert p == Tableau({
(3, 3): 22,
(2, 2): 6,
(2, 3): 8,
(2, 4): 22,
(1, 1): 2,
(1, 2): 4,
(1, 3): 6,
(1, 4): 20
})
assert FState.inverse_insertion(p, q) == w
def test_fstate_insertion():
a = Tableau()
b = Tableau({(1, 1): 4})
c = Tableau({(1, 1): 2, (1, 2): 4})
d = Tableau({(1, 1): 2, (1, 2): 3, (2, 2): 4})
e = Tableau({(1, 1): 2, (1, 2): 3, (2, 2): 4, (1, 3): 4})
f = Tableau({(1, 1): 2, (1, 2): 3, (2, 2): 4, (1, 3): 4, (2, 3): 5})
state = FState()
assert state.is_terminal() and state.tableau == a
state, path = state.insert(4)
assert state.is_terminal() and state.tableau == b
assert path == [(1, 1)]
state, path = state.insert(2)
assert state.is_terminal() and state.tableau == c
assert path == [(1, 1), (1, 2)]
state, path = state.insert(3)
assert state.is_terminal() and state.tableau == d
assert path == [(1, 2), (2, 2)]
state, path = state.insert(1)
assert state.is_terminal() and state.tableau == e
assert path == [(1, 1), (2, 2), (1, 3)]
state, path = state.insert(2)
assert state.is_terminal() and state.tableau == f
assert path == [(1, 2), (2, 2), (2, 3)]
p, q = FState.insertion_tableaux(4, 2, 3, 1, 2)
assert p == f