def test_sl2_init_error_index_0():
with pytest.raises(Exception):
my_layers.SL2Element(False, (3, 1, 1))
with pytest.raises(Exception):
my_layers.SL2Element(False, (-1, 1, 1))
with pytest.raises(Exception):
my_layers.SL2Element(False, (1.5, ))
def test_sl2_init_error_index_s():
with pytest.raises(Exception):
my_layers.SL2Element(False, (1, 0))
with pytest.raises(Exception):
my_layers.SL2Element(False, (1, 2, 1))
with pytest.raises(Exception):
my_layers.SL2Element(False, (2, 1, 2, 5))
def test_cayley_class():
cayley = my_layers.CayleyGraph(5)
assert cayley.graph.vertex_list.keys() == my_layers.SL2Element.cayley_ball(
5).vertex_list.keys()
a = my_layers.SL2Element(False, (0, 1))
assert cayley.dist[a] == a.distortion([1, 1])
b = my_layers.SL2Element(False, (1, ))
assert cayley.dist[b] == b.distortion([1, 1])
def test_mult_r():
identity = my_layers.SL2Element(False, ())
r = my_layers.SL2Element(False, (1, ))
a = my_layers.SL2Element(False, (2, 1))
b = my_layers.SL2Element(False, (2, 1, 1))
c = my_layers.SL2Element(False, (2, 1, 2))
assert identity.times_r() == r
assert a.times_r() == b
assert b.times_r() == c
def test_distortion():
a = my_layers.SL2Element(False, (0, 1))
assert a.distortion([2, 2]) == (1, 1)
b = my_layers.SL2Element(False, (1, ))
assert b.distortion([2, 2]) == (2, 1)
c = a
for i in range(10):
c = a * c
assert c.distortion([2, 2]) == (1, 1)
def test_count_only_s():
a = my_layers.SL2Element(True, (1, 1, 1))
b = my_layers.SL2Element(True, (1, 1, 1, 1))
c = my_layers.SL2Element(False, (2, 1, 2))
d = my_layers.SL2Element(True, (2, ))
assert a.word_length(len_fun='r') == 2
assert b.word_length(len_fun='r') == 2
assert c.word_length(len_fun='r') == 4
assert d.word_length(len_fun='r') == 2
def test_inv():
a = my_layers.SL2Element(False, (0, 1))
assert a.inv() == a
b = my_layers.SL2Element(True, (1, ))
assert b.inv() == my_layers.SL2Element(True, (2, ))
c = my_layers.SL2Element(True, (1, 1, 2, 1))
assert c.inv() == my_layers.SL2Element(True, (0, 1, 1, 1, 2))
d = my_layers.SL2Element(False, (1, 1, 2, 1, 1))
assert d.inv() == my_layers.SL2Element(False, (2, 1, 1, 1, 2))
def test_mult_s():
identity = my_layers.SL2Element(False, ())
neg_identity = my_layers.SL2Element(True, ())
s = my_layers.SL2Element(False, (0, 1))
a = my_layers.SL2Element(False, (2, ))
b = my_layers.SL2Element(False, (2, 1))
c = my_layers.SL2Element(True, (2, ))
assert identity.times_s() == s
assert a.times_s() == b
assert b.times_s() == c
assert s.times_s() == neg_identity
def test_mult4():
a = my_layers.SL2Element(False, (2, 1, 2))
b = my_layers.SL2Element(False, (1, ))
c = my_layers.SL2Element(False, (0, 1))
assert a * b == a.times_r()
assert a * c == a.times_s()
def test_mult2():
a = my_layers.SL2Element(False, (2, 1, 1, 1))
b = my_layers.SL2Element(False, (2, 1, 1))
assert a * b == my_layers.SL2Element(False, (2, 1, 1, 1, 2, 1, 1))
def test_shift():
a = my_layers.SL2Element(False, (0, 1))
assert a.shift((2, 2)) == (1, 0)
def test_matrix_inv():
a = my_layers.SL2Element(False, (0, 1))
for i, j in product(range(2), range(2)):
assert a.inv_matrix()[i, j] == torch.tensor([[0, -1], [1, 0]],
dtype=torch.int)[i, j]
def test_sl2_cayley_ball():
for i in range(10):
assert my_layers.SL2Element.cayley_ball(i)
assert my_layers.SL2Element.cayley_ball(1).num_vertices == 6
assert my_layers.SL2Element.cayley_ball(2).num_vertices == 12
assert my_layers.SL2Element.cayley_ball(3).num_vertices == 20
set_o_elements = {
my_layers.SL2Element(False, ()),
my_layers.SL2Element(False, (1, )),
my_layers.SL2Element(False, (0, 1)),
my_layers.SL2Element(False, (2, )),
my_layers.SL2Element(False, (1, 1)),
my_layers.SL2Element(False, (0, 1, 1)),
my_layers.SL2Element(True, ()),
my_layers.SL2Element(True, (1, )),
my_layers.SL2Element(True, (0, 1)),
my_layers.SL2Element(True, (2, )),
my_layers.SL2Element(True, (1, 1)),
my_layers.SL2Element(True, (0, 1, 1))
}
assert set(my_layers.SL2Element.cayley_ball(
2).vertex_list.keys()) == set_o_elements
def test_sl2_element_equality():
x = my_layers.SL2Element(False, (2, 1))
y = my_layers.SL2Element(False, (2, ))
z = y.times_s()
assert x != y
assert x == z
