def test_involutions():
assert set(Permutation.involutions(1)) == {Permutation()}
assert set(Permutation.involutions(1, True)) == {Permutation(), Permutation(-1)}
assert set(Permutation.involutions(2)) == {Permutation(), Permutation(2, 1)}
assert set(Permutation.involutions(2, True)) == {
Permutation(),
Permutation(-1),
Permutation(2, 1),
Permutation(-2, -1),
Permutation(-1, -2),
Permutation(1, -2)
}
n = 6
assert set(Permutation.involutions(n)) == {
w for w in Permutation.all(n) if w.inverse() == w
}
assert set(Permutation.involutions(n, True)) == {
w for w in Permutation.all(n, True) if w.inverse() == w
}
assert len(set(Permutation.involutions(n))) == len(list(Permutation.involutions(n)))
assert set(Permutation.fpf_involutions(4)) == {
Permutation(2, 1, 4, 3),
Permutation(3, 4, 1, 2),
Permutation(4, 3, 2, 1),
}
def all(cls, n, k, l, decreasing=False):
for w in Permutation.all(n):
if w(n) == n:
continue
cg = cls(w.oneline, k, l, decreasing)
if cg.edges:
cg.generate()
def test_transitions_finite():
n = 4
for w in Permutation.all(n):
for r in range(1, n + 1):
phi_plus = {w * Permutation.transposition(r, j) for j in w.upper_transitions(r)}
phi_minus = {w * Permutation.transposition(i, r) for i in w.lower_transitions(r)}
assert all(w in v.bruhat_covers() for v in phi_plus)
assert all(w in v.bruhat_covers() for v in phi_minus)
def test_transitions_all():
n = 4
for w in Permutation.all(n):
for r in range(1, n + 1):
phi_plus = {w * Permutation.transposition(r, j, n) for j in w.upper_transitions(r)}
phi_minus = {w * Permutation.transposition(i, r, n) for i in w.lower_transitions(r)}
assert all(w in v.bruhat_covers() for v in phi_plus)
assert all(w in v.bruhat_covers() for v in phi_minus)
print (w.get_reduced_word())
print(r)
print([x.get_reduced_word() for x in phi_plus])
print([x.get_reduced_word() for x in phi_minus])
def test_all():
ans = 1
for n in range(2, 6):
ans *= n
assert len({w for w in Permutation.all(n, signed=False)}) == ans