def test_orbit(self):
for conv in ['McClure-Smith', 'Berger-Fresse']:
x = Surjection_element({(1, 3, 1, 2, 1): 1}, convention=conv)
a = x.orbit(representation='trivial')
self.assertEqual(a, Surjection_element({(1, 2, 1, 3, 1): 1},
convention=conv))
b = x.orbit(representation='sign')
self.assertEqual(b, Surjection_element({(1, 2, 1, 3, 1): -1},
convention=conv))
def test_compose_bf(self):
i = 3
x = Surjection_element({(3, 2, 1, 2, 1, 3): 1},
convention='Berger-Fresse')
y = Surjection_element({(3, 1, 2, 1, 4, 3): 1},
convention='Berger-Fresse')
dx, dy = x.boundary(), y.boundary()
dx_y, x_dy = dx.compose(y, i), x.compose(dy, i)
xy = x.compose(y, i)
d_xy = xy.boundary()
self.assertEqual(d_xy - dx_y - (-1)**(x.degree) * x_dy, x.zero())
def test_suspension(self):
x = Surjection_element({(1, 3, 2, 1, 2, 3, 4): 1},
convention='Berger-Fresse')
y = Surjection_element({(1, 2, 3, 1, 2, 3): 1},
convention='Berger-Fresse')
sx = x.suspension()
sy = y.suspension()
xy = x.compose(y, 1)
self.assertEqual(xy.suspension(), sx.compose(sy, 1))
z = Surjection_element({(1, 2, 1, 3, 1, 2, 3): 1},
convention='Berger-Fresse')
sz = z.suspension()
xz = x.compose(z, 2)
self.assertEqual(xz.suspension(), sx.compose(sz, 1))
def test_rmul(self):
rho = SymmetricRing.rotation_element(3)
a, b = (rho * self.x).boundary(), rho * self.x.boundary()
self.assertEqual(a, b)
self.x.convention = 'Berger-Fresse'
a, b = (rho * self.x).boundary(), rho * self.x.boundary()
self.assertEqual(a, b)
self.assertEqual(3 * self.x, Surjection_element({(1, 3, 1, 2, 1): 3}))
def setUp(self):
self.x = Surjection_element({(1, 3, 1, 2, 1): 1})
def test_orbit(self):
a = self.x.orbit(representation='trivial')
self.assertEqual(a, Surjection_element({(1, 2, 1, 3, 1): 1}))
b = self.x.orbit(representation='sign')
self.assertEqual(b, Surjection_element({(1, 2, 1, 3, 1): -1}))