def test_may_steenrod_structure(self):
t = SymmetricRing.transposition_element(6)
x = BarrattEccles.may_steenrod_structure(6, 3).boundary()
y = t * BarrattEccles.may_steenrod_structure(6, 2)
self.assertEqual(x, y)
n = SymmetricRing.norm_element(5, torsion=7)
x = BarrattEccles.may_steenrod_structure(5, 6, torsion=7).boundary()
y = n * BarrattEccles.may_steenrod_structure(5, 5, torsion=7)
self.assertEqual(x, y)
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_steenrod_adem_structure(self):
arity = 6
t = SymmetricRing.transposition_element(arity)
x = Surjection.steenrod_adem_structure(arity, 3).boundary()
y = t * Surjection.steenrod_adem_structure(arity, 2)
self.assertEqual(x, y)
arity = 5
n = SymmetricRing.norm_element(arity, torsion=7)
x = Surjection.steenrod_adem_structure(arity, 4, torsion=7).boundary()
y = n * Surjection.steenrod_adem_structure(arity, 3, torsion=7)
self.assertEqual(x, y)
t = SymmetricRing.transposition_element(arity)
x = Surjection.steenrod_adem_structure(
arity, 3, convention='McClure-Smith').boundary()
y = t * Surjection.steenrod_adem_structure(
arity, 2, convention='McClure-Smith')
self.assertEqual(x, y)
def test_rmul(self):
rho = SymmetricRing.rotation_element(2)
a, b = (rho * self.x).boundary(), rho * self.x.boundary()
self.assertEqual(a, b)