def test_table_reduction(self):
b = BarrattEccles_element({
((1, 2, 3, 4), (1, 4, 3, 2)): 1,
((1, 2, 4, 3), (3, 4, 2, 1)): 2
})
dtr_b = b.table_reduction().boundary()
trd_b = b.boundary().table_reduction()
self.assertEqual(dtr_b, trd_b)
def test_compose(self):
i = 2
x = BarrattEccles_element({((1, 2, 3), (3, 2, 1), (1, 3, 2)): 1})
y = BarrattEccles_element({((1, 2, 3, 4), (4, 3, 2, 1), (4, 1, 3, 2)): 1})
d_xy = x.compose(y, i).boundary()
dx_y = x.boundary().compose(y, i)
x_dy = x.compose(y.boundary(), i)
self.assertEqual(d_xy, dx_y + (-1)**(x.degree) * x_dy)
class TestBarrattEccles_element(unittest.TestCase):
def setUp(self):
self.x = BarrattEccles_element({((1, 3, 2), (2, 3, 1)): 1})
def test_arity(self):
self.assertEqual(self.x.arity, 3)
def test_degree(self):
self.assertEqual(self.x.degree, 1)
def test_boundary(self):
self.assertEqual(self.x.boundary().boundary(), self.x.zero())
def test_rmul(self):
rho = SymmetricRing.rotation_element(3)
a, b = (rho * self.x).boundary(), rho * self.x.boundary()
self.assertEqual(a, b)
def test_orbit(self):
y = self.x.boundary().orbit(representation='trivial')
z = self.x.orbit(representation='trivial').boundary()
self.assertEqual(y, z.orbit('trivial'))
y = self.x.boundary().orbit(representation='sign')
z = self.x.orbit(representation='sign').boundary()
self.assertEqual(y, z.orbit('sign'))
def test_compose(self):
i = 2
x = BarrattEccles_element({((1, 2, 3), (3, 2, 1), (1, 3, 2)): 1})
y = BarrattEccles_element({
((1, 2, 3, 4), (4, 3, 2, 1), (4, 1, 3, 2)): 1
})
d_xy = x.compose(y, i).boundary()
dx_y = x.boundary().compose(y, i)
x_dy = x.compose(y.boundary(), i)
self.assertEqual(d_xy, dx_y + (-1)**(x.degree) * x_dy)
def test_table_reduction(self):
b = BarrattEccles_element({
((1, 2, 3, 4), (1, 4, 3, 2)): 1,
((1, 2, 4, 3), (3, 4, 2, 1)): 2
})
dtr_b = b.table_reduction().boundary()
trd_b = b.boundary().table_reduction()
self.assertEqual(dtr_b, trd_b)
def test_alexander_whitney(self):
pass
def setUp(self):
self.x = BarrattEccles_element({((1, 3, 2), (2, 3, 1)): 1})