def test_compose_bf(self):
i = 3
x = SurjectionElement({(3, 2, 1, 2, 1, 3): 1},
convention='Berger-Fresse')
y = SurjectionElement({(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_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, SurjectionElement({(1, 3, 1, 2, 1): 3}))
def test_orbit(self):
for conv in ['McClure-Smith', 'Berger-Fresse']:
x = SurjectionElement({(1, 3, 1, 2, 1): 1}, convention=conv)
a = x.orbit(representation='trivial')
self.assertEqual(
a, SurjectionElement({(1, 2, 1, 3, 1): 1}, convention=conv))
b = x.orbit(representation='sign')
self.assertEqual(
b, SurjectionElement({(1, 2, 1, 3, 1): -1}, convention=conv))
def test_suspension(self):
x = SurjectionElement({(1, 3, 2, 1, 2, 3, 4): 1},
convention='Berger-Fresse')
y = SurjectionElement({(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 = SurjectionElement({(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 setUp(self):
self.x = SurjectionElement({(1, 3, 1, 2, 1): 1})
class TestSurjectionElement(unittest.TestCase):
def setUp(self):
self.x = SurjectionElement({(1, 3, 1, 2, 1): 1})
def test_arity(self):
self.assertEqual(self.x.arity, 3)
def test_degree(self):
self.assertEqual(self.x.degree, 2)
def test_complexity(self):
self.assertEqual(self.x.complexity, 1)
def test_boundary(self):
self.assertEqual(self.x.boundary().boundary(), self.x.zero())
self.x.convention = 'Berger-Fresse'
self.assertEqual(self.x.boundary().boundary(), self.x.zero())
self.x.set_torsion(2)
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)
self.x.convention = 'Berger-Fresse'
a, b = (rho * self.x).boundary(), rho * self.x.boundary()
self.assertEqual(a, b)
self.assertEqual(3 * self.x, SurjectionElement({(1, 3, 1, 2, 1): 3}))
def test_orbit(self):
for conv in ['McClure-Smith', 'Berger-Fresse']:
x = SurjectionElement({(1, 3, 1, 2, 1): 1}, convention=conv)
a = x.orbit(representation='trivial')
self.assertEqual(
a, SurjectionElement({(1, 2, 1, 3, 1): 1}, convention=conv))
b = x.orbit(representation='sign')
self.assertEqual(
b, SurjectionElement({(1, 2, 1, 3, 1): -1}, convention=conv))
def test_call_simplicial(self):
s = self.x
s.convention = 'McClure-Smith'
x = Simplicial.standard_element(3)
ds_x = s.boundary()(x)
d_sx = s(x).boundary()
s_dx = s(x.boundary())
self.assertEqual(d_sx - ((-1)**(s.degree)) * s_dx, ds_x)
x = SimplicialElement({((0, 1, 2), (3, 4), (5, 6)): 1})
ds_x = s.boundary()(x, 2)
d_sx = s(x, 2).boundary()
s_dx = s(x.boundary(), 2)
self.assertEqual(d_sx - ((-1)**(s.degree)) * s_dx, ds_x)
def test_call_cubical(self):
s = self.x
y = Cubical.standard_element(3)
ds_y = s.boundary()(y)
d_sy = s(y).boundary()
sdy = s(y.boundary())
self.assertEqual(d_sy - ((-1)**(s.degree)) * sdy, ds_y)
def test_compose_bf(self):
i = 3
x = SurjectionElement({(3, 2, 1, 2, 1, 3): 1},
convention='Berger-Fresse')
y = SurjectionElement({(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 = SurjectionElement({(1, 3, 2, 1, 2, 3, 4): 1},
convention='Berger-Fresse')
y = SurjectionElement({(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 = SurjectionElement({(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))